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WarpPLS 5.0 User Manual - Collaborative for International

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1. Figure B 10 2 shows the grouped statistics data saved through the window shown in Figure B 10 1 The tab delimited txt file was opened with a spreadsheet program and contained the data on the left part of the figure The data on the left part of Figure B 10 2 was organized as shown above the bar chart next the bar chart was created using the spreadsheet program s charting feature If a simple comparison of 32 WarpPLS 5 0 User Manual means analysis using this software had been conducted in which the grouping variable in this case an indicator called ECU1 was the predictor and the criterion was the indicator called Effel those two variables would have been connected through a path in a simple path model with only one path Assuming that the path coefficient was statistically significant the bar chart displayed in Figure B 10 2 or a similar bar chart could be added to a report describing the analysis Some may think that it is overkill to conduct a comparison of means analysis using a SEM software package such as this but there are advantages in doing so One of those advantages is that this software calculates P values using a nonparametric class of estimation techniques namely resampling and stable estimation techniques Resampling techniques are sometimes referred to as bootstrapping techniques which may lead to confusion since bootstrapping is also the name of a type of resampling technique No
2. 40 WarpPLS 5 0 User Manual F 1 Create or edit the SEM model The window used to create or edit a model is shown in Figure F 1 A model can be edited if it has been created and saved before as part of a project While editing or creating a model you can choose from a number of menu options related to overall model functions latent variable functions direct link functions and moderating link functions As with other windows in this software there is a help menu option that provides access to this manual in a generic and context specific manner both displayed as PDF files The help menu option also provides links to Web resources Figure F 1 Create or edit the SEM model window ONN ER Create latent variable j Edit latent variable e j Create direct link Clear model deletes all latent variables Delete latent variable i i Delete direct link Cancel model creation editing all editing is lost Move latent variable k Delete moderating link Save model into jpg file a Create moderating link Model options Latent variable options Direct link options Moderating link options Help Choose one of the menu options above to perform a task You should start by creating latent variables using the latent variable menu options You can then drag and d links among them A guiding text box is shown at the top of the model editing and creation window The content of this guiding text box changes depending on the menu optio
3. Warp2 Warp2 Basic Warp3 and Warp3 Basic The View or change individual latent variable weight and loading starting value settings option allows you to set the initial values of the weights and loadings for each latent 18 WarpPLS 5 0 User Manual variable The default is 1 for all weights and loadings With this option latent variables measured in a reversed way as well as formative latent variables with most of their weights and loadings ending up being negative can be more easily operationalized Several of the options above and their component elements are discussed in more detail in the subsections below still in this section describing the main window options These subsections include further discussions about data labels general settings data modification settings individual inner model analysis algorithm settings as well as individual latent variable weight and loading starting value settings A further discussion of grouped descriptive statistics which can be saved through a sub option under the Data options is also provided 19 WarpPLS 5 0 User Manual B 5 Data labels Data labels can be added through the menu options Add data labels from clipboard and Add data labels from file see Figure B 5 Data labels are text identifiers that are entered by you through these options one column at a time Like the original numeric dataset the data labels are stored in a t
4. Adherence to and beliefs in lipid lowering medical treatments A structural equation modeling approach including the necessity concern framework Patient Education and Counseling 91 1 105 112 Biong H amp Ulvnes A M 2011 If the supplier s human capital walks away where would the customer go Journal of Business to Business Marketing 18 3 223 252 Bollen K A 1987 Total direct and indirect effects in structural equation models Sociological Methodology 17 1 37 69 Brewer T D Cinner J E Fisher R Green A amp Wilson S K 2012 Market access population density and socioeconomic development explain diversity and functional group biomass of coral reef fish assemblages Global Environmental Change 22 2 399 406 Cenfetelli R amp Bassellier G 2009 Interpretation of formative measurement in information systems research MIS Quarterly 33 4 689 708 Chatelin Y M Vinzi V E amp Tenenhaus M 2002 State of art on PLS path modeling through the available software Storrs CT Department of Economics University of Connecticut Chew L P 1989 Constrained Delaunay triangulations Algorithmica 4 1 4 97 108 Chin W W Marcolin B L amp Newsted P R 2003 A partial least squares latent variable modeling approach for measuring interaction effects Results from a Monte Carlo simulation study and an electronic mail emotion adoption study Information Systems Research 14 2 189 218
5. Because an S curve is a combination of two distorted U curves we can interpret each U curve section separately A straight U curve like the one shown on the left side of the graph before the inflection point can be interpreted as follows The first half of the U curve goes from approximately minus 3 4 to minus 2 5 standard deviations from the mean at which point the lowest team effectiveness value is reached for the U curve In that first half of the U curve an increase in team procedural structuring leads to a decrease in team effectiveness After that first half an increase in team procedural structuring leads to an increase in team effectiveness One interpretation is that the first half of the U curve refers to novice users of procedural structuring techniques That is the process of novice users struggling to use procedural 89 WarpPLS 5 0 User Manual structuring techniques more and more intensely which they may not be familiar with ends up leading to effectiveness losses for their teams At a certain point around minus 2 5 standard deviations that situation changes and the teams start to really benefit from procedural structuring possibly because the second half of the U curve refers to users with more experience using procedural structuring techniques The interpretation of the second U curve on the right this one an inverted U curve should be done in a similar fashion Usually there are multiple interpretations that can
6. Chiquoine B amp Hjalmarsson E 2009 Jackknifing stock return predictions Journal of Empirical Finance 16 5 793 803 Cohen J 1988 Statistical power analysis for the behavioral sciences Hillsdale NJ Lawrence Erlbaum Cronbach L J 1951 Coefficient alpha and the internal structure of tests Psychometrika 16 3 297 334 Dempster A P Laird N M amp Rubin D B 1977 Maximum likelihood from incomplete data via the EM algorithm Journal of the Royal Statistical Society Series B Methodological 39 1 1 38 Diamantopoulos A 1999 Export performance measurement Reflective versus formative indicators International Marketing Review 16 6 444 457 Diamantopoulos A amp Siguaw J A 2006 Formative versus reflective indicators in organizational measure development A comparison and empirical illustration British Journal of Management 17 4 263 282 104 WarpPLS 5 0 User Manual Diamantopoulos A amp Winklhofer H 2001 Index construction with formative indicators An alternative scale development Journal of Marketing Research 37 1 269 177 Dillon W R amp Goldstein M 1984 Multivariate analysis Methods and applications New York NY Wiley Edwards J R 2011 The fallacy of formative measurement Organizational Research Methods 14 2 370 388 Efron B Rogosa D amp Tibshirani R 2004 Resampling methods of estimation In N J Smelser amp P B Baltes Eds
7. WarpPLS 5 0 User Manual 5 COCO aD O OO aba cap D gt OQEAN CK CDO gt gt CORED TAT ane CEES G gt T ae C fore cixex no xe amp gt QOQ WarpPLS 5 0 User Manual WarpPLS 5 0 User Manual Ned Kock A ScriptWarp Systems Laredo Texas USA WarpPLS 5 0 User Manual WarpPLS 5 0 User Manual January 2015 Copyright by Ned Kock All rights reserved worldwide No part of this publication may be reproduced or utilized in any form or by any means electronic mechanical magnetic or otherwise without permission in writing from ScriptWarp Systems Software use agreement The use of the software that is the subject of this manual Sofware requires a valid license which has a limited duration usually no more than one year Individual and organizational licenses may be purchased from ScriptWarp Systems or any authorized ScriptWarp Systems reseller The Software is provided as is and without any warranty of any kind Free trial versions of the Software are made available by ScriptWarp Systems with the goal of allowing users to assess for a limited time usually one to three months the usefulness of the Software for their data modeling and analysis purposes Users are strongly advised to take advantage of those free trial versions and ensure that the Software meets their needs before purchasing a license Free trial versions of the Software are full implementations of the sof
8. s 1988 thresholds for small medium and large effect sizes A value lower than 0 1 for the GoF suggests that the explanatory power of a model may be too low to be considered acceptable 51 WarpPLS 5 0 User Manual SPR The SPR index is a measure of the extent to which a model is free from Simpson s paradox instances Pearl 2009 Wagner 1982 An instance of Simpson s paradox occurs when a path coefficient and a correlation associated with a pair of linked variables have different signs A Simpson s paradox instance is a possible indication of a causality problem suggesting that a hypothesized path is either implausible or reversed The SPR index is calculated by dividing the number of paths in a model that are not associated with Simpson s paradox instances by the total number of paths in the model At the time of this writing the SPR was an experimental index and thus the following recommendations should also be treated as experimental Ideally the SPR should equal 1 meaning that there are no instances of Simpson s paradox in a model acceptable values of SPR are equal to or greater than 0 7 meaning that at least 70 percent of the paths in a model are free from Simpson s paradox RSCR The RSCR index is a measure of the extent to which a model is free from negative R squared contributions which occur together with Simpson s paradox instances Pearl 2009 Wagner 1982 When a predictor latent variable makes a negative c
9. s original PLS algorithms Factor Based PLS Type CFM1 generates estimates of both true composites and factors in two stages explicitly accounting for measurement error Kock 2014 Like covariance based SEM algorithms this algorithm is fully compatible with common factor model assumptions including the assumption that all indicator errors are uncorrelated In its first stage this algorithm employs a new true composite estimation sub algorithm which estimates composites based on mathematical equations that follow directly from the common factor model The second stage employs a new variation sharing sub algorithm which can be seen as a soft version of the classic expectation maximization algorithm Dempster et al 1977 used in maximum likelihood estimation with apparently faster convergence and nonparametric properties Factor Based PLS Type REG1 and Factor Based PLS Type PTH1 are also factor based PLS algorithms that generate estimates of both composites and factors in two stages fully accounting for measurement error The Factor Based PLS Type REG1 algorithm first estimates composites via PLS Regression discussed below and then estimates factors employing variation sharing Kock 2014 Among the factor based algorithms available in this software this Factor Based PLS Type REG1 algorithm can be seen as the closest to Wold s original PLS design The Factor Based PLS Type PTH1 algorithm first estimates composites via
10. this software calculates model fit and quality indices as well as P values for most of its parameter estimates Publicly available PLS based SEM software usually do not provide those measures Some model elements may reduce the speed of the SEM analysis more than others These are formative latent variables with many indicators and more generally latent variables with 46 WarpPLS 5 0 User Manual many indicators even if they are reflective moderating effects particularly if they associate latent variables with many indicators setting the number of resamples for Bootstrapping or Blindfolding as 200 or higher and using Jackknifing as the resampling method if the sample size is larger than 200 In Jackknifing the number of resamples equals the sample size which is why using Jackknifing as the resample method may reduce the speed of the SEM analysis with relatively large samples Generating resamples and running calculations on them is one of the most computing intensive sub steps of the SEM analysis However Jackknifing often produces more stable parameter estimates with warped analysis So there is a tradeoff between speed and reliability when warping algorithms are being used This tradeoff may tip the balance in favor of using Jackknifing alone or in addition to Bootstrapping or Blindfolding even if the user has to wait longer for the results An alternative is the use of the stable quasi parametric methods Stablel Stabl
11. 0 125 0 125 0 125 0 076 0 076 0 076 CO gt GT EstSEPath 0 120 0 115 0 122 0 047 0 053 0 054 CO gt EU TruePath 0 400 0 400 0 400 0 400 0 400 0 400 CO gt EU AvgPath 0 347 0 347 0 347 0 347 0 347 0 347 CO gt EU Power 0 781 0 900 0 867 1 1 1 CO gt EU SEPath 0 131 0 131 0 131 0 072 0 072 0 072 CO gt EU EstSEPath 0 133 0 116 0 124 0 049 0 053 0 055 CO gt AC TruePath 0 250 0 250 0 250 0 250 0 250 0 250 CO gt AC AvgPath 0 224 0 224 0 224 0 218 0 218 0 218 CO gt AC Power 0 419 0 611 0 559 0 985 0 995 0 994 CO gt AC SEPath 0 141 0 141 0 141 0 061 0 061 0 061 CO gt AC EstSEPath 0 166 0 118 0 129 0 054 0 054 0 056 GT gt SU TruePath 0 500 0 500 0 500 0 500 0 500 0 500 GT gt SU AvgPath 0 333 0 333 0 333 0 347 0 347 0 347 GT gt SU Power 0 711 0 863 0 823 1 1 1 GT gt SU SEPath 0 206 0 206 0 206 0 160 0 160 0 160 GT gt SU EstSEPath 0 146 0 116 0 125 0 052 0 053 0 055 EU gt SU TruePath 0 230 0 230 0 230 0 230 0 230 0 230 EU gt SU AvgPath 0 175 0 175 0 175 0 163 0 163 0 163 EU gt SU Power 0 254 0 410 0 356 0 917 0 921 0 906 EU gt SU SEPath 0 131 0 131 0 131 0 085 0 085 0 085 EU gt SU EstSEPath 0 157 0 119 0 132 0 054 0 054 0 056 AC gt SU TruePath 0 200 0 200 0 200 0 200 0 200 0 200 AC gt SU AvgPath 0 159 0 159 0 159 0 147 0 147 0 147 AC gt SU Power 0 240 0 405 0 335 0 866 0 868 0 849 AC gt SU SEPath 0 137 0 137 0 137 0 073 0 073 0 073 AC gt SU EstSEPath 0 165 0 119 0 132 0 053 0 054 0 056 The column labels BOOT STBL2 and STBL3 respe
12. 4 or 4 Outliers can significantly change the shape of a nonlinear relationship but this may also be the case with linear relationships For example one single outlier may change the sign of a linear association from positive to negative 1 e changing the relationship from direct to inverse Because of this there is invariably the temptation of removing outliers from analyses This is often a mistake Giaquinta 2009 Hair et al 2009 as outliers can be invaluable in elucidating the true nature of an association Kaiser 2010 Rosenthal amp Rosnow 1991 Wold et al 2001 Generally speaking outliers should only be removed if there are good reasons to believe that they are due to measurement error After the software displays the pre processed and standardized data typically you will accept the data and move on to the next step If the data looks corrupted do not accept it click on the No button when asked if the data looks correct If there are problems in this step they will usually be related to problems with the raw data file Check that file and see if you can correct those problems As mentioned before in this manual one simple test can be used to try to find out if there are problems with a raw data file Try to open it with a spreadsheet program if it is originally a text file or to try to create a tab delimited text file with it if it is originally a spreadsheet file If you 38 WarpPLS 5 0 User Manual try
13. GT usefulness in the development of IT solutions EU ease of understanding AC accuracy and SU impact on redesign success for more details see Kock 2014c The meanings of the acronyms within parentheses are the following TruePath true path coefficient AvgPath mean path coefficient estimate SEPath standard error of path coefficient estimate TrueLoad true loading AvgLoad mean loading estimate and SELoad standard error of loading estimate When creating data for our Monte Carlo simulation we varied the following conditions percentage of missing data 0 30 40 and 50 and sample size 100 300 and 500 This led to a 4 x 3 factorial design with 12 conditions We created an analyzed 1 000 samples for each of these 12 conditions a total of 12 000 samples In this summarized set of results we restrict ourselves to 30 missing data and the sample size of 300 Full results for all percentages of missing data and sample sizes included in the simulation are available from Kock 2014c Since all loadings are the same in the true population model loading related estimates for only 95 WarpPLS 5 0 User Manual one indicator of the composites are shown This avoids crowding and repetition as the same pattern of results repeats itself in connection with all loadings The mean path coefficient estimates that are shown underlined were obtained through the application of the PLS Mode A algorithm to datasets where no dat
14. In this sense the path coefficients are inner model parameter estimates Latent variable A latent variable is a variable that is measured through multiple variables called indicators or manifest variables For example satisfaction with a meal may be a latent variable measured through two manifest variables that store the answers on a to 7 scale 1 strongly disagree 7 strongly agree to the following question statements I am satisfied with this meal and After this meal I feel full Latent variable block A latent variable block is a group of latent variables in which one or more predictor latent variables point at one criterion latent variable In a PLS based SEM analysis once latent variable scores are calculated a series of multiple least squares regressions are conducted to calculate path coefficients Each multiple least squares regression is performed on a latent variable block until all blocks are covered The term latent variable block is also used in the PLS based SEM literature to refer to a group of manifest variables linked to their assigned latent variable i e a latent variable and its indicators Latent variable score Latent variable scores are values calculated based on the indicators defined by the user as associated with the latent variable They are calculated using one of the outer model analysis algorithms available These scores may be understood as new columns in the data with the same number o
15. International Encyclopedia of the Social amp Behavioral Sciences pp 13216 13220 New York NY Elsevier Ehremberg A S C amp Goodhart G J 1976 Factor analysis Limitations and alternatives Cambridge MA Marketing Science Institute Enders C K 2010 Applied missing data analysis New York NY Guilford Press Ferguson G A 1981 Statistical analysis in psychology and education New York NY McGraw Hill Fornell C amp Larcker D F 1981 Evaluating structural equation models with unobservable variables and measurement error Journal of Marketing Research 18 1 39 50 Geisser S 1974 A predictive approach to the random effects model Biometrika 61 1 101 107 Gel Y R amp Gastwirth J L 2008 A robust modification of the Jarque Bera test of normality Economics Letters 99 1 30 32 Giaquinta M 2009 Mathematical analysis An introduction to functions of several variables New York NY Springer Goodhue D L Lewis W amp Thompson R 2012 Does PLS have advantages for small sample size or non normal data MIS Quarterly 36 3 981 1001 Guo K H Yuan Y Archer N P amp Connelly C E 2011 Understanding nonmalicious security violations in the workplace A composite behavior model Journal of Management Information Systems 28 2 203 236 Hahn C Johnson M D Herrmann A amp Huber F 2002 Capturing customer heterogeneity using a finite mixture PLS approach Schm
16. Rencher A C 1998 Multivariate statistical inference and applications New York NY John Wiley amp Sons Rigdon E E 2012 Rethinking partial least squares path modeling In praise of simple methods Long Range Planning 45 5 341 358 Robert C P amp Casella G 2010 Monte Carlo statistical methods New York NY Springer Rohatgi V K amp Sz kely G J 1989 Sharp inequalities between skewness and kurtosis Statistics amp Probability Letters 8 4 297 299 R nkk M amp Evermann J 2013 A critical examination of common beliefs about partial least squares path modeling Organizational Research Methods 16 3 425 448 Rosenthal R amp Rosnow R L 1991 Essentials of behavioral research Methods and data analysis Boston MA McGraw Hill Sarstedt M amp Ringle C M 2010 Treating unobserved heterogeneity in PLS path modeling A comparison of FIMIX PLS with different data analysis strategies Journal of Applied Statistics 37 8 1299 1318 Schumacker R E amp Lomax R G 2004 A beginner s guide to structural equation modeling Mahwah NJ Lawrence Erlbaum Sijtsma K 2009 On the use the misuse and the very limited usefulness of Cronbach s alpha Psychometrika 74 1 107 120 Spirtes P Glymour C amp Scheines R 1993 Causality prediction and search Berlin Germany Springer Verlag Stone M 1974 Cross validatory choice and assessment of statistical prediction
17. it seems that the Stable3 method yields fairly reliable results for path coefficients associated with direct effects Kock 2014b It is less clear if the Stable3 method or any of the other stable methods is advisable for the calculation of P values for path coefficients associated with indirect and total effects and research in this area is ongoing 27 WarpPLS 5 0 User Manual B 7 Data modification settings The View or change data modification settings option allows users to run their analyses with subsamples defined by a range restriction variable which is chosen from among the indicators available After Step 5 is completed latent variable scores can also be added to the model as standardized indicators This option also allows users to conduct their analyses with only ranked data see Figure B 7 Figure B 7 View or change data modification settings None Range restriction variable type 4 Unstandardized indicator None Standardized indicator Range restriction variable None Range min max for restriction variable Minimum value Maximum value 0 000 0 000 Use only ranked data in analysis Two range restriction variable types are available standardized and unstandardized indicators This means that the range restriction variable can be either a standardized or unstandardized indicator Once a range restriction variable is selected minimum and maximum values must be set i e a range wh
18. they are part of the same meal but their satisfaction indicators are not expected to be highly correlated with each other The reason is that some people may like the main course very much and not like the dessert Conversely other people may be vegetarians and hate the main course but may like the dessert very much If the indicators are not expected to be highly correlated with one another they cannot be expected to be highly correlated with their latent variable s score Here is a general rule of thumb that can be used to decide if a latent variable is reflectively or formatively measured If the indicators are expected to be highly correlated and are redundant in their meaning then the measurement model should be set as reflective If the indicators are not expected to be highly correlated and are clearly not redundant in meaning they measure different facets of the same construct even though they clearly refer to the same latent variable then the measurement model should be set as formative Setting a latent variable as formative or reflective affects the calculation of model parameters only with the PLS Mode B algorithm or with algorithms that employ the PLS Mode B algorithm or variations of it e g PLS Mode B Basic PLS Mode M With other algorithms setting a latent variable as formative or reflective is still recommended as it helps the user interpret outputs and conduct certain assessments e g validity assessments discussed
19. used or the degree to which specific features of the technology are used as well as team performance and or related variables expected to be influenced by technology use In the second scenario the researcher does not have data on the extent to which the technology is used but has data related to team performance and or other variables expected to be influenced by technology use before and after the technology is introduced This is a longitudinal data collection scenario for which a comparison of means test could be used Data analyses for all three scenarios are discussed by Kock 2013b based on this software showing the versatility of the software The main reason for this versatility is that most of the data analysis methods used in behavioral research can be conceptually seen as special cases of SEM 33 WarpPLS 5 0 User Manual C Step 1 Open or create a project file to save your work In Step 1 you will open or create a project file to save your work see Figure C 1 Project files are saved with the prj extension and contain all of the elements needed to perform a SEM analysis That is they contain the original data used in the analysis the graphical model the inner and outer model structures and the results Figure C 1 Step 1 window Enter the name of a file to Lave your work c coogaggegggEggg You are now in Step 1 Open or create a project file tc work When you press the Open project file button y
20. 000 0 152 0 000 Reflective 0 012 lt 0 001 9 430 0 143 Effe3 0 000 0 000 0 160 0 000 Reflective 0 013 lt 0 001 2 628 0 134 Effe4 0 000 0 000 0 158 0 000 Reflective 0 012 lt 0 001 8 708 0 150 Effe5 10 000 0 000 0 149 0 000 Reflective 0 011 lt 0 001 6 612 0 136 Effe6 o 000 0 000 0 139 0 000 Reflective 0 010 lt 0 001 5 548 0 125 Effe7 0 000 0 000 0 183 0 000 Reflective 0 013 lt 0 001 4 209 0 165 ECUEmail 0 000 0 000 0 000 0 321 Formative 0 266 0 114 4 434 1 0 068 L FFI Fmaillist 9 000 0 000 0 000 0 405 Formative 0 297 0 087 4 693 1 0156 Notes P values lt 0 05 and VIFs lt 2 5 are desirable for formative indicators VIF indicator variance inflation factor WLS indicator weight loading sign 1 Simpson s paradox in I v ES indicator effect size As with indicator loadings standard errors are also provided here for the weights in the column indicated as SE for indicators associated with all latent variables These standard errors can be used in specialized tests Among other purposes they can be used in multi group analyses with the same model but different subsamples Here users may want to compare the measurement models to ascertain equivalence using a multi group comparison technique such as the one documented by Kock 2013 and thus ensure that any observed between group differences in structural model coefficients particularly in path coefficients are not
21. 66 WarpPLS 5 0 User Manual variables in PLS based SEM Kock amp Lynn 2012 and also in slightly different contexts Cenfetelli amp Bassellier 2009 Petter et al 2007 On the other hand two criteria one more conservative and one more relaxed are recommended by the multivariate analysis literature in connection with VIFs They may apply in this type of context as well although they may be more adequate in path analyses where all latent variables are measured through single indicators More conservatively it is recommended that VIFs be lower than 5 a more relaxed criterion is that they be lower than 10 Hair et al 1987 2009 Kline 1998 Q squared coefficients are also known as Stone Geisser Q squared coefficients so named after their principal original proponents Geisser 1974 Stone 1974 The Q squared coefficient is a nonparametric measure traditionally calculated via blindfolding It is used for the assessment of the predictive validity or relevance associated with each latent variable block in the model through the endogenous latent variable that is the criterion variable in the block The Q squared coefficient is sometimes referred to as a resampling analog of the R squared coefficient It is often similar in value to that measure even though the Q squared coefficient can more easily assume negative values Acceptable predictive validity in connection with an endogenous latent variable is suggested by a Q squared coeffi
22. An extended set of stable P value calculation methods is now available to users Stablel Stable2 and Stable3 The Stable1 method was the software s default up until version 4 0 when it was called simply the stable method The Stable2 and Stable3 methods have been developed as alternatives to the Stablel method that rely on the direct application of exponential smoothing formulas for the formulas see Kock 2014b and that can thus be more easily implemented and tested by methodological researchers A Monte Carlo experiment shows that the Stable2 and Stable3 methods yield estimates of the actual standard errors that are consistent with those obtained via bootstrapping in many cases yielding more precise estimates of the actual standard errors Kock 2014b The more accurate of the two methods appears to be the Stable3 method which is now the software s default New missing data imputation methods Several missing data imputation methods are now available to users Arithmetic Mean Imputation the software s default Multiple Regression Imputation Hierarchical Regression Imputation Stochastic Multiple Regression Imputation and Stochastic Hierarchical Regression Imputation The missing data imputation method chosen by the user will be employed in the execution of Step 3 and also after that when the option Redo missing data imputation via data pre processing is selected The option is available under the WarpPLS 5 0 User
23. AvgPath 0 390 0 348 0 367 0 354 0 333 0 300 CO gt GT SEPath 0 075 0 113 0 110 0 113 0 138 0 162 CO gt EU TruePath 0 400 0 400 0 400 0 400 0 400 0 400 CO gt EU AvgPath 0 349 0 312 0 321 0 313 0 289 0 262 CO gt EU SEPath 0 069 0 101 0 108 0 106 0 133 0 151 CO gt AC TruePath 0 250 0 250 0 250 0 250 0 250 0 250 CO gt AC AvgPath 0 219 0 198 0 206 0 195 0 188 0 161 CO gt AC SEPath 0 062 0 078 0 090 0 083 0 100 0 108 GT gt SU TruePath 0 500 0 500 0 500 0 500 0 500 0 500 GT gt SU AvgPath 0 381 0 357 0 359 0 352 0 334 0 312 GT gt SU SEPath 0 127 0 152 0 156 0 158 0 179 0 195 EU gt SU TruePath 0 230 0 230 0 230 0 230 0 230 0 230 EU gt SU AvgPath 0 192 0 183 0 199 0 178 0 188 0 163 EU gt SU SEPath 0 062 0 072 0 077 0 078 0 082 0 089 AC gt SU TruePath 0 200 0 200 0 200 0 200 0 200 0 200 AC gt SU AvgPath 0 165 0 157 0 176 0 154 0 166 0 141 AC gt SU SEPath 0 058 0 067 0 073 0 072 0 077 0 081 GT3 lt GT TrueLoad 0 700 0 700 0 700 0 700 0 700 0 700 GT3 lt GT AvgLoad 0 811 0 691 0 606 0 649 0 623 0 652 GT3 lt GT SELoad 0 113 0 042 0 120 0 076 0 115 0 090 The column labels NUD MEAN MREGR HREGR MSREG and HSREG respectively refer to no missing data Arithmetic Mean Imputation Multiple Regression Imputation Hierarchical Regression Imputation Stochastic Multiple Regression Imputation and Stochastic Hierarchical Regression Imputation The latent variables in the model used as a basis for the simulation are CO communication flow orientation
24. LN LN Fluency Warp2 basic Warp3 Warp3 basic Fluency Natu Notes do not forget to save your settings LN Linear W2 Warp2 W2b Warp2 basic W3 Warp3 W3b Warp3 basic Individual inner model algorithms can be set for both regular and interaction effect latent variables the latter are associated with moderating effects If no choice is made for an individual inner model algorithm the default inner model analysis algorithm is used If a model is changed after an analysis is conducted the individual inner model algorithms are set to the default inner model analysis algorithm This option allows users to customize their analyses based on theory and past empirical research If theory or results from past empirical research suggest that a specific link between two latent variables is linear then the corresponding path can be set to be analyzed using the Linear algorithm Conversely if theory or results from past empirical research suggest that a specific link between two latent variables should have the shape of a U curve or J curve the corresponding path can be set to be analyzed using the Warp2 algorithm or the Warp2 Basic algorithm 30 WarpPLS 5 0 User Manual B 9 Individual latent variable weight and loading starting value settings The View or change individual latent variable weight and loading starting value settings option allows users to set the initial values of the weights and loadings for each latent variable
25. Lee K J 2012 Quality of nursing doctoral education in Korea Towards policy development Journal of Advanced Nursing 68 7 1494 1503 Klaassen C A Mokveld P J amp Es B V 2000 Squared skewness minus kurtosis bounded by 186 125 for unimodal distributions Statistics amp probability letters 50 2 131 135 Kline R B 1998 Principles and practice of structural equation modeling New York NY The Guilford Press Kock N 2011 A mathematical analysis of the evolution of human mate choice traits Implications for evolutionary psychologists Journal of Evolutionary Psychology 9 3 219 247 Kock N 2011b Using WarpPLS in e collaboration studies Mediating effects control and second order variables and algorithm choices International Journal of e Collaboration 7 3 1 13 Kock N 2013 Advanced mediating effects tests multi group analyses and measurement model assessments in PLS based SEM Laredo TX ScriptWarp Systems Kock N 2013b Using WarpPLS in e collaboration studies What if I have only one group and one condition International Journal of e Collaboration 9 3 1 12 Kock N 2014 A note on how to conduct a factor based PLS SEM analysis Laredo TX ScriptWarp Systems Kock N 2014b Stable P value calculation methods in PLS SEM Laredo TX ScriptWarp Systems Kock N 2014c Single missing data imputation in PLS SEM Laredo TX ScriptWarp Systems Kock N 2014d One tailed
26. Robust Path Analysis discussed below and then estimates factors employing variation sharing Kock 2014 By doing so this algorithm addresses several of the concerns about Wold s original PLS algorithms raised in an important critical article by R nkk amp Evermann 2013 This algorithm can also be seen as addressing the call for simplicity in a thought provoking article on PLS by Rigdon 2012 Unlike the Factor Based PLS Type CFM lLalgorithm the Factor Based PLS Type REG1 and Factor Based PLS Type PTH1 algorithms do not impose certain common factor model assumptions that rarely hold in practice such as the assumption that all indicator errors are uncorrelated PLS Regression has been the default outer model algorithm since the software s inception and is maintained as such as a matter of tradition This algorithm iterates until the outer model 22 WarpPLS 5 0 User Manual weights become stable with the following calculations being performed in successive iterations for each latent variable in the model a the outer model weights are calculated through a least squares regression where the latent variable is the predictor and the indicators are the criteria and b the latent variable is calculated as an exact linear combination of the indicator scores In the PLS Regression algorithm the inner model does not influence the outer model That is the weights are not influenced by the links connecting latent variables which are cr
27. add one or more latent variable scores to the model as new standardized indicators and also to add all latent variable scores as new indicators Adding one or more latent variable scores at a time may be advisable in certain cases such as in hierarchical analyses using selected latent variable scores as indicators at each level In these cases adding all latent variable scores at once may soon clutter the set of indicators available to be used in the SEM model The option of adding latent variable scores to the model as new standardized indicators is useful in the removal of outliers through the use of restricted ranges for latent variable scores particularly for outliers that are clearly visible on the plots depicting associations among latent variables As briefly mentioned earlier this option is also useful in hierarchical analyses where users define second order and higher order latent variables and then conduct analyses with different models including latent variables of different orders This software uses algorithms that are fairly computing intensive in some cases employing multiple checks and optimization sub algorithms in each sub step Therefore the speed with which the analysis is conducted may be a little slower than that of some other publicly available SEM software The differences in speed are not significant though and normally the results generated by this software are more complete and in many cases more reliable For example
28. algorithms SEM method PLSA PLSF PLSA PLSF PLSA PLSF Sample size 50 50 100 100 300 300 EU gt TE TruePath 0 400 0 400 0 400 0 400 0 400 0 400 EU gt TE AvgPath 0 339 0 380 0 309 0 385 0 303 0 394 EU gt TE SEPath 0 125 0 161 0 128 0 127 0 110 0 070 EU gt TP TruePath 0 300 0 300 0 300 0 300 0 300 0 300 EU gt TP AvgPath 0 260 0 301 0 248 0 294 0 234 0 297 EU gt TP SEPath 0 135 0 157 0 108 0 133 0 085 0 079 TE gt TP TruePath 0 200 0 200 0 200 0 200 0 200 0 200 TE gt TP AvgPath 0 201 0 234 0 189 0 225 0 174 0 203 TE gt TP SEPath 0 144 0 163 0 098 0 132 0 061 0 079 EU3 lt EU TrueLoad 0 700 0 700 0 700 0 700 0 700 0 700 EU3 lt EU AvgLoad 0 793 0 692 0 802 0 695 0 808 0 699 EU3 lt EU SELoad 0 129 0 108 0 113 0 077 0 112 0 049 The column labels PLSA and PLSF respectively refer to the PLS Mode A and Factor Based PLS Type CFM1 algorithms The latent variables in the model used as a basis for the simulation are EU e collaboration technology use TE team efficiency and TP team performance for more details see Kock 2014 The meanings of the acronyms within parentheses are the following TruePath true path coefficient AvgPath mean path coefficient estimate SEPath standard error of path coefficient estimate TrueLoad true loading AvgLoad mean loading estimate and SELoad standard error of loading estimate In the Monte Carlo simulation 300 samples were created for each of the following sample size
29. and cross loadings structure loadings and cross loadings and normalized structure loadings and cross loadings Figure H 4 1 Indicator loadings and cross loadings options View indicator loadings and cross loadings View combined loadings and cross loadings View indicator weights View normalized combined loadings and cross loadings View latent variable coefficients View pattern loadings and cross loadings View correlations among latent variables and errors View normalized pattern loadings and cross loadings View block variance inflation factors View structure loadings and cross loadings View correlations among indicators View normalized structure loadings and cross loadings Combined loadings and cross loadings are shown in a window as illustrated in Figure H 4 2 The same is true for other combinations of loadings and cross loadings which are shown in similar windows Combined loadings and cross loadings are provided in a table with each cell referring to an indicator latent variable link Latent variable names are listed at the top of each column and indicator names at the beginning of each row In this table the loadings are from a structure matrix i e unrotated and the cross loadings from a pattern matrix i e rotated Indicator types as defined are also provided reflective or formative Figure H 4 2 Combined loadings and cross loadings window ECUVar Proc Effi Effe Type as defined SE ECUVari 1 000 0 000 0 000 0
30. and errors menu options see Figure H 7 1 allow users to view tables containing correlations among latent variables the P values associated with those correlations square roots of AVEs correlations among latent variable error terms or residuals and the VIFs associated with latent variable error terms see figures H 7 2 and H 7 3 Figure H 7 1 Correlations among latent variables and errors options View correlations among latent variables and errors View correlations among latent variables with sq rts of AVEs View block variance inflation factors View correlations among latent variable error terms with VIFs Figure H 7 2 Correlations among latent variables with square roots of AVEs Correlations among I vs with sq rts of AVEs Proc Effi Effe ECU Proc 0 848 0 460 0 348 0 371 Effi 0 460 0 842 0 540 0 101 Effe 0 348 0 540 0 912 0 157 Ecu 0 371 0 101 0 157 0 335 Figure H 7 2 Correlations among latent variable error terms with VIFs Correlations among l v error terms with VIFs e Proc e Effi e Effe e Proc 1 001 0 025 0 028 e Effi 0 025 1 001 0 002 e Effe__ 0 028 0 002 1 001 In most research reports users will typically show the table of correlations among latent variables with the square roots of the average variances extracted on the diagonal to demonstrate that their measurement instruments pass widely accepted criteria for discriminant validity assessment A measurement instr
31. and outputs the ubiquity of measurement error in SEM analyses as well as data analyses in general would tend to make strong and sweeping claims regarding accuracy and statistical power likely to be proven exaggerated or even wrong Researchers analyzing empirical data typically do not know the underlying distributions of their data and of error terms Data analysis software tools help researchers uncover characteristics of those distributions with incomplete information Given this it seems reasonable to conclude that all SEM algorithms and software tools that implement these algorithms have limitations in their accuracy avoidance of false positives and statistical power i e avoidance of false negatives Accuracy and statistical power seem to suffer particularly when very small samples and deviations from normality are observed in the context of small effect sizes Goodhue et al s 2012 extensive analysis of various SEM algorithms illustrates these limitations although its negative results may have been exacerbated by the fairly low path coefficients that they used for small and medium effect sizes Those path coefficients were based on effect sizes that were calculated using the stepwise regression procedure proposed by Cohen 1988 for the calculation of f squared coefficients which is generally not compatible with PLS based SEM algorithms This theme is further explored later in this user manual This software attempts to ameliorate t
32. axis or the horizontal axis The Y axis label is the text shown next to the Y axis or the vertical axis Multivariate and bivariate relationship graphs usually differ only when two or more predictor latent variables point at one criterion latent variable in a latent variable block The addition of predictors will normally reduce the path coefficients in a latent variable block Because of this typically a multivariate relationship graph will have a lower overall inclination or steepness than its corresponding bivariate relationship graph However this is not always the case In statistical suppression instances MacKinnon et al 2000 a multivariate relationship graph will have a greater overall inclination than its corresponding bivariate relationship graph In Simpson s paradox instances Pearl 2009 Wagner 1982 multivariate and bivariate relationship graphs will have reversed overall inclinations e g one will be positive and the other negative This software is arguably the first and only at the time of this writing to provide both multivariate and bivariate representations of nonlinear relationships The mathematics underlying the rendering of these representations is complex and somewhat novel Therefore these representations should be treated as experimental by users of this software and any conclusions derived from visual inspection of these representations should be treated with caution The View focused relationship gra
33. been obtained through a strictly linear analysis What this software does is not unlike what a researcher would do if he or she modified predictor latent variable scores prior to the calculation of path coefficients using a function like the logarithmic function An example is provided in the equation below where a logarithmic transformation is applied to LVp1 LVc pl log LVp1 p2 LVp2 E This software however does that automatically and for a much wider range of functions with modification constants included For example in the term A log B LVp1 the constants A and B are modification constants using simply log LVp1 as a modifier function in an equation like the one above assumes that A 1 and B 1 which may be incorrect assumptions that will lead to distorted results and mistaken conclusions As mentioned above often the path coefficients p1 p2 will go up in value due to warped analysis but that may not always be the case Given the nature of multivariate analysis an increase in a path coefficient may lead to a decrease in a different path coefficient for predictor latent variables associated with the same criterion latent variable because each path coefficient in a block is calculated in a way that controls for the effects of the other predictor latent variables That is in any given block of latent variables the predictor latent variables compete for the explained variance in the criterion latent variable There is
34. business statistics Analysis of variance regression and time series New York NY Holt Rihehart and Winston Mueller R O 1996 Basic principles of structural equation modeling New York NY Springer Nevitt J amp Hancock G R 2001 Performance of bootstrapping approaches to model test statistics and parameter standard error estimation in structural equation modeling Structural Equation Modeling 8 3 353 377 Newman D A 2014 Missing data Five practical guidelines Organizational Research Methods 17 4 372 411 Nunnally J C 1978 Psychometric theory New York NY McGraw Hill Nunnally J C amp Bernstein I H 1994 Psychometric theory New York NY McGraw Hill Ogasawara H 1999 Standard errors for the direct oblimin solution with Kaiser s normalization Japanese Journal of Psychology 70 4 333 338 Pearl J 2009 Causality Models reasoning and inference Cambridge England Cambridge University Press Peterson R A amp Yeolib K 2013 On the relationship between coefficient alpha and composite reliability Journal of Applied Psychology 98 1 194 198 Petter S Straub D amp Rai A 2007 Specifying formative constructs in information systems research MIS Quarterly 31 4 623 656 Preacher K J amp Hayes A F 2004 SPSS and SAS procedures for estimating indirect effects in simple mediation models Behavior Research Methods Instruments amp Computers 36 4 717 731
35. by causality assessment coefficients Taking the example above one possible alternative explanation is that increased job performance causes employment to be maintained at more advanced ages supporting the direction of causality from Job performance to Age instead of the reverse path It can also mean that because of sampling problems those with greater job performance included in the sample tended to be older Yet another alternative explanation is that there is no link between Job performance and Age and that the inclusion of another control variable artificially induces that link which tends to happen when path coefficients are associated with negligible R squared contributions i e lower than 0 02 Whatever the case may be ideally models should be free from Simpson s paradox instances 82 WarpPLS 5 0 User Manual because as noted below these instances generally detract from the explanatory power of the model Because an instance of Simpson s paradox occurs when a path coefficient and a correlation associated with a pair of linked variables have different signs the corresponding contribution to the R squared of the criterion variable in the latent variable block where it occurs is negative see Mueller 1996 for a discussion of this effect in the context of evolutionary biology see Kock 2011 The View R squared contributions option allows users to view the values of the individual contributions
36. definition are the following two I am satisfied with this meal and After this meal I feel full Therefore the latent variable satisfaction with a meal can be said to be reflectively measured through two indicators Those indicators store answers to the two question statements This latent variable could be represented in a model graph as Satisf and the indicators as Satisf1 and Satisf2 Notwithstanding this simplified example users should strive to have more than two indicators be latent variable the more indicators the better since the number of indicators is inversely related to the amount of measurement error Kock 2014 Nunnally 1978 Nunnally amp Bernstein 1994 A formative latent variable is one in which the indicators are expected to measure certain attributes of the latent variable but the indicators are not expected to be highly correlated with 44 WarpPLS 5 0 User Manual the latent variable itself because they i e the indicators are not expected to be highly correlated with one another For example let us assume that the latent variable Satisf satisfaction with a meal is now measured using the two following question statements I am satisfied with the main course and I am satisfied with the dessert Here the meal comprises the main course say filet mignon and a dessert such as a fruit salad Both main course and dessert make up the meal i e
37. each row to the corresponding row of the original numeric dataset Data labels can later be shown on graphs either next to each data point that they refer to or as part of a graph s legend The Save grouped descriptive statistics option is a special option that allows you to save descriptive statistics means and standard deviations organized by groups defined based on certain parameters this option is discussed in more detail at the end of this section The View or save latent variable a k a factor scores option allows you to view or save the latent variable scores generated by the software There is another option that allows you to save latent variable scores available as a menu option on the window used to view and save model analysis results which becomes available later after Step 5 is completed These two options return the same latent variable scores in most cases The exception to the general rule above is a situation in which you specified a range restriction for your analysis In this case only the latter option will return the range restricted latent variable scores These latent variable scores will generally have a smaller number of rows than the original dataset because they are range restricted and thus will not be exactly matched to the original dataset 15 WarpPLS 5 0 User Manual B 3 Modify The Modify menu options allow you to add new data labels and raw data to your dataset redo missing
38. features when compared with the previous version It has undergone extensive testing in house prior to its release as a beta version and has been in the hands of users for several months prior to its upgrade to stable Nevertheless given the large number of new features and the inherent interconnectedness of features it is very likely that this stable version will still contain some software bugs which we expect to be minor WarpPLS 5 0 User Manual A 3 New features in version 5 0 Factor Based PLS algorithms There has been a long and in some instances fairly antagonistic debate among proponents and detractors of the use of Wold s original PLS algorithms in the context of SEM This debate has been fueled by one key issue Wold s original PLS algorithms do not deal with actual factors as covariance based SEM algorithms do but with composites which are exact linear combinations of indicators Kock 2014d The new factor based algorithms provided in this version have been developed specifically to address this perceived limitation of Wold s original PLS algorithms These new algorithms are called Factor Based PLS Type CFM1 Factor Based PLS Type REG1 and Factor Based PLS Type PTH1 New descriptive statistics for indicators and latent variables An extended set of descriptive statistics is now provided for both indicators and latent variables The descriptive statistics provided include minimum and maximum values medians mod
39. if the data has rank problems which usually happens when the sample size is very small relative to the number of existing indicators A related cause of rank problems is a sample with many repeated or linearly dependent values on different rows or columns which sometimes is an indication of data fabrication Please note that the term rank here comes from matrix algebra and is unrelated to the same term used in the context of ranked data as discussed earlier in connection with the software settings If there are rank problems this does not mean that you cannot proceed with the SEM analysis However the results may be unstable and in some cases completely unreliable On the other hand it is not uncommon for rank problems to be reported and still the results of the ensuing SEM analysis turn out to be reliable This is due to the general robustness of PLS based methods for SEM analysis At the end of this step a window will be displayed with the pre processed data which will be standardized Standardized data columns have means that equal zero and standard deviations that equal one If you use the Arithmetic Mean Imputation method for dealing with missing data the software s default previously missing values will be shown as zero since they were replaced with the averages or means of the columns Standardized data usually ranges from 4 to 4 with outliers assuming values toward the left or right end of those extremes sometimes beyond
40. later in this manual Formative measurement has been facing increasing criticism particularly since the late 1990s see Edwards 2011 for a particularly critical and cogent discussion Given this growing criticism it is recommended that the Cronbach s alpha coefficients associated with formative latent variables be equal to or greater than 0 6 for reasons related to measurement error theory Kock 2014 Nunnally 1978 Nunnally amp Bernstein 1994 Since loadings tend to be relatively low with formative latent variables and weights relatively high reliability measures such as the Cronbach s alpha coefficient tend to also be relatively low Nevertheless Cronbach s alpha coefficients equal to or greater than 0 6 can be achieved by increasing the number of indicators used in formative measurement 45 WarpPLS 5 0 User Manual G Step 5 Perform the SEM analysis and view the results Step 5 performs the SEM analysis based on the model created in Step 4 After you click on the button to perform the SEM analysis the software will show a wait bar This wait bar will update you on the progress of the SEM analysis which usually will take only a few seconds or less for simple to moderately complex models As soon as the SEM analysis is completed the software will show the results in graphical format on a window That window also has menu options that allow you to view more details about the results including some that are not shown o
41. likelihood that one or more will be redundant increases This will be reflected in high VIFs Indicator weight loading signs WLS are provided for the indicators of all latent variables A negative WLS i e 1 for an indicator means that the indicator in question is making a negative contribution to the R squared of its latent variable That is a negative WLS suggests the existence of a Simpson s paradox instance Pearl 2009 Wagner 1982 in the outer model associated with a specific indicator assigned to a latent variable A Simpson s paradox instance in this context is a possible indication of a causality problem suggesting that a hypothesized link between an indicator and a latent variable is either implausible or reversed Therefore it is recommended that all indicator WLS values be positive for both formative and reflective latent variables Indicators associated with negative WLS values may be considered for removal 63 WarpPLS 5 0 User Manual Effect sizes are provided in the column indicated as ES for the indicators of all latent variables As with the effect sizes for paths the effect sizes for indicators are calculated as the absolute values of the individual contributions of the corresponding indicators to the R squared coefficients of the latent variable to which each indicator is associated Similarly to the effect sizes for paths with the indicator effect sizes users of this software can ascertain whether the in
42. options allow you to view or save data and various statistics mostly descriptive statistics into tab delimited txt files The tab delimited txt file is the general file format used by the software to save most of the files containing analysis and summarization results These files can be opened and edited using Excel Notepad and other similar spreadsheet or text editing software These menu options are discussed in more detail later The Modify menu options These menu options allow you to add new data labels and raw data to your dataset redo missing data imputation as well as add one or more latent variable scores a k a factor scores to the dataset as new standardized indicators Also available is the option of adding all latent variable scores at once to the dataset as new standardized indicators Data labels can be shown on graphs as text next to data points or as legends for data points using different markers These menu options are discussed in more detail later The Settings menu options You can view or change general SEM analysis settings through the Settings menu options Here you can select the analysis algorithms used in the SEM analysis the resampling method used to calculate standard errors and P values as well as other elements that will define how the SEM analysis will be conducted These menu options are discussed in more detail later The Help menu options There are several help menu options a
43. possible problems in future versions of the software In very slow computers with limited computing power only the command prompt window may be displayed for as long as a few minutes The reason for this is that the computer needs to load a large runtime module prior to actually running this software Users should not try to do anything during this time as that will only delay the launch of the software s main window 11 WarpPLS 5 0 User Manual B 1 The SEM analysis steps The software s main window see Figure B 1 2 is where the SEM analysis starts The top left part of the main window contains a brief description of the five steps through which the SEM analysis takes place The steps are executed by pressing each of the push buttons on the top right part of the window Not all menu options and push buttons become available right away Menu options and push buttons become available as the analysis progresses Figure B 1 2 The main window showing the steps after a complete analysis was conducted Project Data Modify Settings Help Welcome to WarpPLS 5 0 a software developed by Ned Kock using MATLAB C and Java B Proceed to Step 4 This software will help you conduct a structural equation modeling SEM analysis using the method of warped partial least squares analysis The analysis will be conducted through the following steps Proceed to Step 2 Step 1 Open or create a project file to save your work
44. predictor predictor collinearity in a latent variable block containing one or more latent variable predictors and one latent variable criterion Kock amp Lynn 2012 For example let us assume that there is a block of latent variables in a model with three latent variables A B and C predictors pointing at latent variable D In this case VIFs are calculated for A B and C and are estimates of the multicollinearity among these predictor latent variables A rule of thumb rooted in the use of this software for many SEM analyses in the past as well as past methodological research suggests that block VIFs of 3 3 or lower suggest the existence of no vertical multicollinearity in a latent variable block Kock amp Lynn 2012 This is also the recommended threshold for VIFs in slightly different contexts Cenfetelli amp Bassellier 2009 Petter et al 2007 On the other hand two criteria one more conservative and one more relaxed are also recommended by the multivariate analysis literature and can also be seen as applicable in connection with VIFs in this context More conservatively it is recommended that block VIFs be lower than 5 a more relaxed criterion is that they be lower than 10 Hair et al 1987 2009 Kline 1998 These criteria may be particularly relevant in the context of path analyses where all latent variables are measured through single indicators technically these are not true latent variables The reason why th
45. roots of AVEs For convergent validity assessment the AVE threshold frequently recommended for acceptable validity is 0 5 Fornell amp Larcker 1981 and applies only to reflective latent variables Full collinearity VIFs are shown for all latent variables separately from the VIFs calculated for predictor latent variables in individual latent variable blocks These VIFs are calculated based on a full collinearity test Kock amp Lynn 2012 which enables the identification of not only vertical but also lateral collinearity and allows for a test of collinearity involving all latent variables in a model Vertical or classic collinearity is predictor predictor latent variable collinearity in individual latent variable blocks Lateral collinearity is a term coined by Kock amp Lynn 2012 that refers to predictor criterion latent variable collinearity a type of collinearity that can lead to particularly misleading results Full collinearity VIFs can also be used for common method bias tests Kock amp Lynn 2012 Lindell amp Whitney 2001 that are more conservative than and arguably superior to the traditionally used tests relying on exploratory factor analyses A rule of thumb rooted in the use of this software for many SEM analyses in the past suggests that full collinearity VIFs of 3 3 or lower suggest the existence of no multicollinearity in the model and no common method bias This is also the recommended threshold for VIFs for latent
46. see Figure B 9 This is a specialized option that will only rarely be used The default starting value for all latent variables is 1 While any real number can be used here normally only l and 1 are used Figure B 9 View or change individual latent variable weight and loading starting value settings Natu Perform Fluency Fluency Natu 1 00 1 00 1 00 1 00 Note do not forget to save your settings This option reflects a little known characteristic of classic PLS based SEM analyses which is that they do not always converge to the same solution The estimated coefficients depend on the starting values of weights and loadings thus leading to different solutions depending on the initial configurations of those starting values Even in simple models often at least two solutions exist as long as latent variables are used with multiple indicators By convention the solution most often accepted as valid is the one associated with the default starting value for all latent variables which is 1 With this option latent variables measured in a reversed way can be more easily operationalized An example would be a latent variable reflecting boredom being measured through a set of indicators that individually reflect excitement In this type of scenario generally the starting value of weights and loadings for the latent variable should be set to 1 This option can also be useful with formative latent variables for which most of the we
47. simply click No when asked if the data looks correct Raw data can be read directly from Excel files with extensions xls or xlsx or text files where the data is tab delimited or comma delimited When reading from an xls or xlsx file that contains a workbook with multiple worksheets make sure that the worksheet that contains the data is the first on the workbook If the workbook has multiple worksheets the file import wizard used in Step 2 will typically select the first worksheet as the source or raw 36 WarpPLS 5 0 User Manual data If the desired worksheet is not the first in the workbook in many cases the user will be able to select the proper worksheet through the wizard but this selection can lead to mistakes when made by novice users Raw data files whether Excel or text files must have indicator names in the first row and numeric data in the following rows They may contain empty cells or missing values these will be automatically replaced with values calculated by one of the missing data imputation algorithms available in a later step The View or change missing data imputation settings option under Settings allows you to set the missing data imputation method to be used by the software in the next step Users may want to employ non automated approaches to deal with missing data such as deleting the rows with missing cells or manually replacing them with the average of nearby values
48. to do either of these things and the data looks messed up e g corrupted or missing column names then it is likely that the original file has problems which may be hidden from view For example a spreadsheet file may be corrupted but that may not be evident based on a simple visual inspection of the contents of the file using spreadsheet software 39 WarpPLS 5 0 User Manual F Step 4 Define the variables and links in the SEM model In Step 4 you will define the latent variables and links in the SEM model The sub steps that make up this step are discussed in more detail in the subsections below This software employs a graphical interface that allows users to create and edit model elements visually and directly i e without the need of a scripting language You will define the latent variables by selecting the indicators that are associated with them and the measurement method used either formative or reflective The process of defining the latent variables in a SEM model in this fashion is often called defining the outer model in SEM lingo Model links can be of two types direct and moderating links Direct links connect pairs of latent variables Moderating links connect latent variables and direct links that is they refer to effects in which a latent variable moderates the relationship between a pair of latent variables The process of defining model links is often referred to as defining the inner model
49. 000 Reflective 0 050 0 000 0 844 0 039 0 030 Reflective 0 051 0 040 0 885 0 081 0 130 Reflective 0 051 0 044 0 814 0 047 0 111 Reflective 0 052 0 006 0 014 0 896 0 019 Reflective 0 051 0 065 0 035 0 884 0 126 Reflective 0 051 0 005 0 052 0 821 0 026 Reflective 0 052 0 079 0 117 0 813 0 011 Reflective 0 052 0 008 0 043 0 796 0 200 Reflective 0 052 0 041 0 060 0 050 0 931 Reflective 0 051 0 032 0 007 0 051 0 947 Reflective 0 050 0 006 0 024 0 080 0 831 Reflective 0 051 0 007 0 018 0 038 0 952 Reflective 0 050 0 036 0 075 0 006 0 917 Reflective 0 051 0 032 0 026 0 066 0 906 Reflective 0 051 0 074 0 007 0 132 0 894 Reflective 0 051 In the combined loadings and cross loadings window since loadings are from a structure matrix and unrotated they are always within the 1 to 1 range With some exceptions which are discussed below this obviates the need for a normalization procedure to avoid the presence of loadings whose absolute values are greater than 1 The expectation here is that for reflective latent variables loadings which are shown within parentheses will be high and cross 58 WarpPLS 5 0 User Manual loadings will be low The type of the latent variable as defined by the user namely reflective or formative is also provided in this window to facilitate the application of validity and reliability tests The criteria used in these tests are typically different for formative an
50. 1989 which are usually the ones implemented through other PLS based SEM software tools Moderating links are typically associated with moderating cause effect hypotheses or interaction effect hypotheses Testing a moderating link s strength through the calculation of a path coefficient and statistical significance through the calculation of a P value is equivalent to testing a moderating cause effect or interaction effect hypothesis Moderating links should be used with moderation no pun intended because they may introduce multicollinearity into the model and also because they tend to add nonlinearity to the model By introducing multicollinearity into the model they may make some model parameter estimates unstable and biased Delete moderating link This option allows you to delete an existing moderating link You will click on the moderating link that you want to delete after which the link will be deleted After you create a model and choose the option Save model and close a wait bar will be displayed on the screen telling you that the SEM model structure is being created This is an important sub step where a number of checks are made In this sub step if there are any moderating links in the model new latent variables are created to store information about those moderating effects using a product indicator procedure described and validated by Chin et al 2003 The more moderating links a model has the longer this sub step will t
51. EL ssccsssssscesssscccccsssscccssscescsssscccsesssssecees 40 F31C REATE OR EDIT THE SEM MODEL 795225 5c a Sees soba wea A a Nota ea a Se eA GAs GINS BDL ad aR 41 F2 CREATE OR EDIT LATENT VARIABLE ansero rere tit rea Er EEEE RE E A a A E aaa E A A ET E Eai 44 G STEP 5 PERFORM THE SEM ANALYSIS AND VIEW THE RESULTS essseesseccessseossseceesssseossocoeesseosssocesssseessecoceesse 46 H VIEW AND SAVE RESULTS osscciscsrissrecesecserseisoesirosesnsiessorosssiassdesoossrsst seess ko sapio oseon seeds seossduasesesteasesdesebeccsbudneledssdsecosess 48 H I VEW CEN RAT R SUO a a a AORA A E A R E s 50 H 2 VIEW PATH COEFFICIENTS AND P VALUES 3 17 c0ss2000ecuce coscsenssvvevectacssSeleeedsoveeckade cvedssanssluedeetads aa EEEE NE ST EEE RRS 54 H 3 VIEW STANDARD ERRORS AND EFFECT SIZES FOR PATH COEFFICIENTS cssssccccccccccesesssssececeeccceeessesssnseeceecceseeesssesssseeeeeceeeees 56 H 4 VIEW INDICATOR LOADINGS AND CROSS LOADINGS cccsssessssseececceeeeesessssaeeeecceeeesssssseeeeeecececeeseesssaeseeeceeeceseeesaaeeaaeeeeeeceess 58 He 5 VIEW INDIGATOR WEIGHTS amp so EE EEE EE E E E E E T 62 H 6 VIEW LATENT VARIABLE COEFFICIENTS ssssessssceececccssesesesssaneeeecceeeessssssaeeeeeeeceecesseessaeeesececeseseessaaaeeceeeeeeceeseesaaaeeeseceeseeses 65 H 7 VIEW CORRELATIONS AMONG LATENT VARIABLES AND ERRORS ccsssssessssceeeeeceeeesesessssaeeeeccceceessesseeeeececeeceseeesssaseeeceeeeees 68 H 8 VIEW BLOCK VARIANCE I
52. H 11 illustrates the latter option the classic view which is so named because it was the option used in previous versions of the software Figure H 11 Indirect and total effects window Close Help Total effects ECU Effi 0 173 0 180 0 526 Proc Ef Number of paths for total effects Effe P values for total effects ECU Effi 0 057 0 025 lt 0 001 For each set of indirect and total effects the following values are provided the path coefficients associated with the effects the number of paths that make up the effects the P values associated with effects calculated via resampling using the selected resampling method the standard errors associated with the effects and effect sizes associated with the effects Indirect effects are aggregated for paths with a certain number of segments As such the software provides separate reports within the same output window for paths with 2 3 etc segments The software also provides a separate report for sums of indirect effects as well as for total effects All of these reports include P values standard errors and effect sizes Having access to indirect and total effects can be critical in the evaluation of downstream effects of latent variables that are mediated by other latent variables especially in complex models with multiple mediating effects along concurrent paths Indirect effects also allow for direct estimations via resampling of the P values associated with medi
53. LS 5 0 User Manual A Introduction Structural equation modeling SEM employing the partial least squares PLS method or PLS based SEM for short has been and continue being extensively used in a wide variety of fields Examples of fields in which PLS based SEM is used are information systems Guo et al 2011 Kock amp Lynn 2012 marketing Biong amp Ulvnes 2011 international business Ketkar et al 2012 nursing Kim et al 2012 medicine Berglund et al 2012 and global environmental change Brewer et al 2012 This software provides users with a wide range of features several of which are not available from other SEM software For example this software is the first and only at the time of this writing to explicitly identify nonlinear functions connecting pairs of latent variables in SEM models and calculate multivariate coefficients of association accordingly Additionally this software is the first and only at the time of this writing to provide classic PLS algorithms together with factor based PLS algorithms for SEM Kock 2014 Factor based PLS algorithms generate estimates of both true composites and factors fully accounting for measurement error They are equivalent to covariance based SEM algorithms but bring together the best of both worlds so to speak Factor based PLS algorithms combine the precision of covariance based SEM algorithms under common factor model assumptions Kock 2014 with the nonpa
54. Manual Modify menu options Kock 2014c provides a detailed discussion of these methods as well as of a Monte Carlo simulation whereby the methods relative performances are investigated Incremental code optimization This is conducted in each new version of this software At several points the code was optimized for speed stability and coefficient estimation precision This led to incremental gains in speed even as a number of new features were added Several of these new features required new and complex calculations mostly to generate coefficients that were not available before WarpPLS 5 0 User Manual A 4 Experimental features Some of the features provided by the software are still at an experimental stage and may change in the future as more tests are conducted Normally this is indicated in this user manual whenever it is the case Other novel features of this software may prove useful for applications different from the ones they were originally intended for For example an extensive set of causality assessment coefficients is provided by the software Yet the topic of causality assessment in the context of SEM is controversial Pearl 2009 A causality assessment coefficient that is provided to inform the user of the possibility of a reverse link may prove in the future to be useful to identify a specific type of bias due to measurement error Finally while this software aims at providing a wide range of features
55. NFLATION FACTORS H 9 VIEW CORRELATIONS AMONG INDICATORS sssssssccccccesesessssssneeeececeeesesesssseeeeeeceseeseeeessaaeeeeecceceseeessseeeeeeeseeeeeseessasseeeeeeeeeees H 10 VIEW PLOT LINEAR AND NONLINEAR RELATIONSHIPS AMONG LATENT VARIABLES sssccccccccceessssssseeeeeecceeccesessssseeeeeceeeeeees 73 H 11 VIEW INDIRECT AND TOTAL EFFECTS H 12 VIEW CAUSALITY ASSESSMENT COEFFICIENTS cccccccccsssssssscceccceccecessesssaaeeeeecceseesssssaaeaeeeececeecsesessaaeeceeeeeeeesseeesaaeeeeceeeeeens 82 I CONCLUDING REMARKS AND ADDITIONAL ISSUES sssssccsssssecesssscccsessssccsssscccssssssccensssccscsseessssssscesessssscceses 86 T 1 WARPING FROM A CONCEPTUAL PERSPECTIVE cssssccccccccsesssssssnecececccesesssessneeeeeecesessssssasaeeeecececesesesaaeeeeeceeeseeseeeaaeeeeeeceeeens 87 I 2 INTERPRETING WARPED RELATIONSHIPS 1 3 CORRELATION VERSUS COLLINEARITY crn o aa E ois A dates A R cues aceugeguaavsdees cee deegovs Sovinsssdseieds ious a a T 1 4 STABLE P VALUE CALCULATION METHODS 523 a SR A AOA EAA EEEE EE Wade ETET EE E SA EE aes 93 I 5 MISSING DATA IMPUTATION METHODS 1 6 FACTOR BASED PICS ALGORITHMS frentea e dues a r AE E E E R E EE dt JE GLOSSARY AEE EEEE ANE ET AANA ETEA A AERES ESE ETTA APAE AE E AT T K ACKNOWLEDGEMENTS Te IRE FERRE NGES ii2cfavssscuccsonsccscicsssceteuacossedoaccecascacvsdesnecsteshouccdcueccessdcscseestunaceacnsteondtensceassgoascesshcoce deseecesssdanechecnscchesccdcocdsceossesses WarpP
56. Step 2 Read the raw data used in the SEM analysis Step 3 Pre process the data for the SEM analysis Step 4 Define the variables and links in the SEM model Step 5 Perform the SEM analysis and view the results Proceed to Step 5 Proceed to Step 3 View save analysis results Press a Proceed to Step button when you are ready to continue Unavailable steps are grayed out they will be made available as you progress through the steps For more help click on the Help menu option at the top of this window The steps must be carried out in the proper sequence For example Step 5 which is to perform the SEM analysis and view the results cannot be carried out before Step 1 takes place which is to open or create a project file to save your work This is the main reason why steps have their push buttons grayed out and deactivated until it is time for the corresponding steps to be carried out The bottom left part of the main window shows the status of the SEM analysis after each step in the SEM analysis is completed this status window is updated A miniature version of the SEM model graph is shown at the bottom right part of the main window This miniature version is displayed without results after Step 4 is completed After Step 5 is completed this miniature version is displayed with results The Project menu options There are three project menu options available Save project Save
57. Tenenhaus et al 2005 Average variances extracted AVEs and full collinearity variance inflation factors VIFs are also provided for all latent variables and are used in the assessment of discriminant validity and overall collinearity respectively 65 WarpPLS 5 0 User Manual Adjusted R squared coefficients Theil 1958 Wooldridge 1991 are equivalent to R squared coefficients with the key difference that they correct for spurious increases in R squared coefficients due to predictors that add no explanatory value in each latent variable block Consistently with general recommendations made by Cohen 1988 values of R squared coefficients and adjusted R squared coefficients below 0 02 suggest combined effects of predictors in latent variable blocks that are too weak to be considered relevant from a practical point of view Therefore models where R squared coefficients or adjusted R squared coefficients are below 0 02 should be considered for revision as the explanatory power in sub models i e latent variable blocks is below reasonable expectations Revisions in these models could involve inner and outer model changes such as removal or change in location of mediating latent variables as well as removal or reassignment of indicators The following criteria one more conservative and the other two more relaxed are suggested in the assessment of the reliability of a measurement instrument These criteria apply only to reflective lat
58. VIF values may result from the inclusion of new latent variables that overlap in meaning with existing latent variables It is generally undesirable to have different latent variables in the same model that measure the same underlying construct those should be combined into one single latent variable Thus the AVIF and AFVIF indices bring in new dimensions that add to a comprehensive assessment of a model s overall predictive and explanatory quality Because of the way in which these indices are calculated for more details see Kock amp Lynn 2012 the AFVIF is not sensitive to variations in collinearity due to the use of nonlinear algorithms The AVIF on the other hand is sensitive to the use of nonlinear algorithms Therefore it is recommended that both indices A VIF and AF VIF be reported in studies as they are not redundant indices It is recommended ideally that both the A VIF and AF VIF be equal to or lower than 3 3 particularly in models where most of the variables are measured through two or more indicators A more relaxed acceptable criterion is that both indices be equal to or lower than 5 particularly in models where most variables are single indicator variables and thus not true latent variables The reason for these differences in criteria in different contexts is that PLS based SEM algorithms in general tend to be particularly effective at reducing collinearity Kock amp Lynn 2012 but only if multiple indicators a
59. When data is ranked typically the value distances that typify outliers in data on ratio scales whether standardized or unstandardized are significantly reduced This effectively eliminates outliers from the data without any decrease in sample size Often some information is lost due to ranking e g the distances among data points based on answers on ratio scales Two related menu options allow you to view or save standardized pre processed indicator data View or save standardized pre processed indicator data and View or save standardized ranked pre processed indicator data The latter option ranks the data prior to standardizing it Ranking often has little effect on ordinal data e g data on Likert type scales and a major impact on ratio data e g yearly income The options that refer to unstandardized data allow you to view or save pre processed data prior to standardization The options that refer to standardized data allow you to view or save pre processed data after standardization that is after all indicators have been transformed in such a way that they have a mean of zero and a standard deviation of one The View or save data labels option allows you to view or save data labels These are text identifiers that are entered by you separately through one of the Modify menu options Like the original numeric dataset the data labels are stored in a table Each column of this table refers to one data label and
60. a table with the absolute path correlation differences and their respective P values The absolute path correlation differences can be used together with the absolute path correlation ratios to identify paths that need special attention because path correlation ratios alone can sometimes provide an inflated perception of problems especially when paths and correlations are both very small Generally speaking a path that meets the following criteria should be seen as referring to a link that needs special attention in terms of possible elimination or careful interpretation absolute path correlation ratio greater than 1 3 and P value for absolute path correlation difference equal to a lower than 0 05 However a path that meets these criteria will not necessarily be associated with causality problems it may in fact suggest a particularly interesting and unique finding see e g MacKinnon et al 2000 One useful and interesting property of nonlinear algorithms such as the Warp2 and Warp3 algorithms is that often bivariate nonlinear coefficients of association calculated using those algorithms vary depending on the hypothesized direction of causality That is they tend to be stronger in one direction than the other which means that the residual or error is greater when the hypothesized direction of causality is in one way or the other As such they can be used together with other coefficients as partial evidence in support or against hypothesize
61. a third variable the confounder Particularly problematic are situations in which error terms are so highly correlated that they can be considered redundant which are indicated by high VIFs in the diagonal of this table To rule out these situations and consistently with recommendations by Kock amp Lynn 2012 it is recommended that the VIFs associated with the error terms be equal to or lower than 3 3 69 WarpPLS 5 0 User Manual H 8 View block variance inflation factors Block variance inflation factors VIFs are provided in table format see Figure H 8 for each latent variable that has two or more predictors in a latent variable block Block VIFs cannot be calculated for latent variables with only one predictor or no predictor Here each VIF is associated with one of the two or more predictors and relates to the link between that predictor and its latent variable criterion When one predictor latent variable points at two or more different latent variables in the model then that latent variable is said to have multiple criteria associated with it Figure H 8 Block variance inflation factors window Close Help ECUVar i Effi Proc ECUVar Proc Effi 1 007 Efe 1 231 eea In this context a VIF is a measure of the degree of vertical collinearity Kock amp Lynn 2012 or redundancy among the latent variables that are hypothesized to affect another latent variable This classic type of collinearity refers to
62. a was missing NMD Note that they generally underestimate the true path coefficients This underestimation stems from the use of composites discussed earlier which leads to an attenuation of composite correlations Nunnally amp Bernstein 1994 This correlation attenuation extends to the path coefficients Kock 2014 leading to the observed underestimation The opposite effect is observed in connection with loadings which tend to be overestimated in PLS based SEM analyses employing PLS Mode A As noted earlier these problems are addressed in this software through the availability of Factor Based PLS algorithms Multiple Regression Imputation MREGR yielded the least biased mean path coefficient estimates followed by Arithmetic Mean Imputation MEAN When we look at mean loading estimates Arithmetic Mean Imputation MEAN yielded the least biased results followed by Stochastic Hierarchical Regression Imputation HSREG and Hierarchical Regression Imputation HREGR Compared with the no missing data condition NMD none of the methods induced a reduction in standard errors for path coefficients This is noteworthy since prior results outside the context of PLS based SEM have tended to show a significant downward bias in standard errors particularly for non stochastic missing data imputation varieties Such downward bias in standard errors has led to concerns regarding an inflation in type I errors and warnings against the use of single mis
63. ab Projmgt Moderating relationships involve three latent variables the moderating variable and the pair of variables that are connected through a direct link The sign and strength of a path coefficient for a moderating relationship refer to the effect of the moderating variable on the sign and strength of the path for the direct relationship that it moderates For example if the path for 76 WarpPLS 5 0 User Manual the direct relationship has its sign going from negative to positive and becomes significantly stronger in that direction as one moves from the low to the high range of the moderating variable then the sign of the path coefficient for the corresponding moderating relationship will be positive and the path coefficient will be relatively high possibly high enough to yield a statistically significant effect No moderating relationship graph currently available from this software accurately represents the true nature of a moderating relationship This comment seems to apply to all other publicly available SEM software tools to the best of our knowledge and at the time of this writing Therefore various graphs are provided so that users can choose the one that in their view best illustrates the relationship An accurate representation of a moderating relationship would be that of a multivariate distortion in the surface representing the relationship The distortion refers to a twisting of the surface around the moderating var
64. able Each column of this table refers to one data label and each row to the corresponding row of the original numeric dataset Data labels can later be shown on graphs either next to each data point that they refer to or as part of the legend for a graph Once they have been added data labels can be viewed or saved using the View or save data labels option Figure B 5 Add data labels from file window You are about to read data labels Data labels can be read from the clipboard or from a file but only ONE column of labels can be read at a time Cells cannot be empty contain spaces or contain only numbers they must be combinations of letters or of letters and numbers Valid examples Age gt 17 Y2001 AFR HighSuccess Invalid examples 123 Age gt 17 Y 2001 If the source of the labels is a file its type can be any of the following xls or xlsx An Excel file txt A tab delimited or comma delimited text file The file must have the names of the labels in the first row and the label values associated with those names in the following rows The number of label values should be same as the original sample size Press the Ok button to continue Press the Go back button to go back to the main window For more help click on the Help menu option at the top of this window While data labels can be read from the clipboard or from a file only one column of labels can be read at a time Data lab
65. ach latent variable These can be useful in some specialized applications e g users may want to generate customized graphs based on those scores Figure H 1 1 View and save results window View Save es Help SEM analysis oie eee The main results are shown in the graph below You can now view and save other more detailed Choose one of the View or Save menu options above to do so f Save Close Help Save all model estimates into a tab delimited bt file s Close Help Save correlations among indicators into a tab delimited bt file View general results Save latent variable a k a factor scores into a tab delimited bt file Save model into jpg file View path coefficients and P values View standard errors and effect sizes for path coefficients View indicator loadings and cross loadings View indicator weights Ey R 0 22 View latent variable coefficients f View correlations among latent variables and errors View block variance inflation factors fap ped View correlations among indicators View plot linear and nonlinear relationships among latent variables View indirect and total effects View causality assessment coefficients Just to be clear the factor scores are the latent variable scores even though classic PLS algorithms approximate latent variables though composites not factors This is generally perceived as a limitation of classic PLS algorithms Kock 2014 2014d which is addressed through the Fa
66. ake In models where only reflective variables are involved in a moderating link typically this sub step will not take longer than a few seconds Moderating links with formative variables may lead to longer wait times because formative variables are usually more complex frequently with significantly more indicators than reflective variables Instead of the product indicator approach described by Chin et al 2003 one can use an alternative two stage approach In the first stage of this alternative approach the latent variables that are part of a moderating relationship will be added to the model as new indicators This can be done via the options Add one or more latent variable a k a factor scores as new standardized indicators or Add all latent variable a k a factor scores as new standardized indicators which are available under the Modify menu options In the second stage the new one indicator latent variables will be used in the definition of a moderating relationship 43 WarpPLS 5 0 User Manual F 2 Create or edit latent variable The latent variable creation window is show in Figure F 2 and it is virtually identical to the latent variable editing window The latent variable will appear in the model graph as soon as you click on the menu option under Save which saves the latent variable and closes the latent variable creation or editing window A latent variable is not saved as part of a project until t
67. al data is retained in unranked format When data measured on ratio scales is ranked typically the value distances that typify outliers are significantly reduced effectively eliminating outliers without any 28 WarpPLS 5 0 User Manual decrease in sample size Contrary to popular belief this cannot be achieved through standardization only Often some information is lost due to ranking e g the distances among data points based on answers on ratio scales Thus a concomitant increase in collinearity may be observed but typically not to the point of threatening the credibility of the results The option of using only ranked data in the analysis can be very useful in assessments of whether the presence of outliers significantly affects path coefficients and respective P values especially when outliers are not believed to be due to measurement error 29 WarpPLS 5 0 User Manual B 8 Individual inner model algorithm settings The View or change individual inner model algorithm settings option allows users to set inner model algorithms for individual paths see Figure B 8 The algorithms available are the same as those that can be selected as default inner model analysis algorithms Linear Warp2 Warp Basic Warp3 and Warp3 Basic Figure B 8 View or change individual inner model algorithm settings Click on a relationship cell to view change inner model algorithm Perform Fluency Fluency Natu Warp2 Natu Perform
68. alenbach Business Review 54 3 243 269 Hair J F Anderson R E amp Tatham R L 1987 Multivariate data analysis New York NY Macmillan Hair J F Black W C Babin B J amp Anderson R E 2009 Multivariate data analysis Upper Saddle River NJ Prentice Hall Hayes A F amp Preacher K J 2010 Quantifying and testing indirect effects in simple mediation models when the constituent paths are nonlinear Multivariate Behavioral Research 45 4 627 660 Jarque C M amp Bera A K 1980 Efficient tests for normality homoscedasticity and serial independence of regression residuals Economics Letters 6 3 255 259 Kaiser H F 1958 The varimax criterion for analytic rotation in factor analysis Psychometrika 23 3 187 200 Kaiser H M 2010 Mathematical programming for agricultural environmental and resource economics Hoboken NJ Wiley Keil M Tan B C Wei K K Saarinen T Tuunainen V amp Wassenaar A 2000 A cross cultural study on escalation of commitment behavior in software projects MIS Quarterly 24 2 299 325 105 WarpPLS 5 0 User Manual Ketkar S Kock N Parente R amp Verville J 2012 The impact of individualism on buyer supplier relationship norms trust and market performance An analysis of data from Brazil and the U S A International Business Review 21 5 782 793 Kim M J Park C G Kim M Lee H Ahn Y H Kim E Yun S N amp
69. an be easily dragged and dropped with the pointing device e g mouse anywhere within the 42 WarpPLS 5 0 User Manual window that contains the model This option is a carryover from a previous version maintained for consistency and for those users who still want to use it It allows a user to move a latent variable across the model by first clicking on the variable and then on the destination position Create direct link This option allows you to create a direct link between one latent variable and another The arrow representing the link points from the predictor latent variable to the criterion latent variable Direct links are usually associated with direct cause effect hypotheses testing a direct link s strength through the calculation of a path coefficient and statistical significance through the calculation of a P value is equivalent to testing a direct cause effect hypothesis Delete direct link This option allows you to delete an existing direct link You will click on the direct link that you want to delete after which the link will be deleted Create moderating link This option allows you to create a link between a latent variable and a direct link When the underlying algorithm used for outer model estimation is PLS Regression or one of the Factor Based PLS algorithms both formative and reflective latent variables can be part of moderating links Arguably this is not possible with the PLS modes M A and B see Lohmller
70. an also be removed from the dataset and thus from the analysis by a more time consuming procedure The user should first save the latent variable scores into a file using the appropriate Save menu option in the results window after Step 5 is completed Then the user should add those scores to the original dataset the rows will be in the same order Next the user should open the modified dataset with a spreadsheet software tool e g Excel The outlier should be easy to identify on the dataset e g a value greater than 4 and should be eliminated Then the user should re read this modified file as if it was the original data file and run all of the SEM analysis steps again 79 WarpPLS 5 0 User Manual H 11 View indirect and total effects Through the View indirect and total effects options the software allows users to view outputs for indirect and total effects Bollen 1987 Kock amp Gaskins 2014 associated with all latent variables that are linked via one or more paths with more than one segment The options available are View indirect and total effects table view and View indirect and total effects classic view The difference between these two options is that the former shows indirect and total effects outputs in extendable table format and the latter in wrapped text format The former option corresponding to the table view is recommended in complex models with many links among latent variables Figure
71. approaches mentioned above would be to rely on the estimation of indirect effects These indirect effects and related P values are automatically calculated by the software and allow for the test of multiple mediating effects at once including effects with more than one mediating variable Kock amp Gaskins 2014 provide an empirical illustration of the use of this approach Indirect and total effects are discussed in more detail later Another type of analysis that can employ standard errors for path coefficients is what is often referred to as a multi group analysis where path and measurement model coefficients usually weights can be compared One of the main goals of this type of analysis is to compare pairs of path coefficients for identical models but based on different samples An example would be the analysis of the same model but with data collected in two different countries See Kock 2013 for a more detailed discussion on the use of effect sizes and other coefficients generated by this software on advanced mediating effects tests comprehensive multi group analyses and measurement model assessments 57 WarpPLS 5 0 User Manual H 4 View indicator loadings and cross loadings The View indicator loadings and cross loadings menu options see Figure H 4 1 allow users to view combined loadings and cross loadings normalized combined loadings and cross loadings pattern loadings and cross loadings normalized pattern loadings
72. approaches would lead to false positives and false negatives in terms of support and lack of support for hypothesized directions of causality is an issue that will require future research particularly research employing Monte Carlo simulations Robert amp Casella 2010 where the true directions of causality are known 84 WarpPLS 5 0 User Manual A path meeting the above criteria for both Warp2 and Warp3 algorithms in terms of support for causal direction reversal may in some cases appear to lead to an absurd conclusion Upon further consideration however reversing the path may not sound as absurd For example let us say that a path from the variable Age time from birth measured in years pointing at the variable Job performance self assessed measured through multiple indicators on Likert type scales meets the above criteria suggesting that it should be reversed This may be interpreted as suggesting that Job performance causes Age in the sense that increased job performance causes someone to age or causes time to pass faster These could be seen as absurd conclusions even if we consider work as a possible cause of oxidative stress and thus accelerated decrepitude note that Age is defined as time from birth measured in years However a different interpretation is that increased job performance causes employment to be maintained at more advanced ages supporting the direction of causality f
73. atent variable 100 WarpPLS 5 0 User Manual measured through two manifest variables which assume as values the answers on a to 7 scale 1 strongly disagree 7 strongly agree to the following question statements I am satisfied with this meal and After this meal I feel full Outer model In a SEM analysis the outer model is the part of the model that describes the relationships among the latent variables that make up the model and their indicators In this sense the weights and loadings are outer model parameter estimates Portable document format PDF This is an open standard file format created by Adobe Systems and widely used for exchanging documents It is the format used for this software s documentation Q squared coefficient This measure is also known after its main proponents as the Stone Geisser Q squared coefficient Geisser 1974 Stone 1974 The Q squared coefficient is a nonparametric measure traditionally calculated via blindfolding It is used for the assessment of the predictive validity or relevance associated with each latent variable block in the model through the endogenous latent variable that is the criterion variable in the block The Q squared coefficient is sometimes referred to as a resampling analog of the R squared It is often similar in value to that measure The Q squared coefficient can assume negative values Reflective latent variable A reflective latent variable is one in which a
74. ating effects that have 80 WarpPLS 5 0 User Manual traditionally relied on non automated and thus time consuming calculations based on linear Preacher amp Hayes 2004 and nonlinear Hayes amp Preacher 2010 assumptions 81 WarpPLS 5 0 User Manual H 12 View causality assessment coefficients The View causality assessment coefficients options allow users to view a number of coefficients associated with individual paths that can be used in causality assessment The options available are View path correlation signs View R squared contributions View path correlation ratios View path correlation differences View Warp2 bivariate causal direction ratios View Warp2 bivariate causal direction differences View Warp3 bivariate causal direction ratios and View Warp3 bivariate causal direction differences The topic of causality assessment in the context of SEM is controversial Pearl 2009 Therefore these causality assessment coefficients should be treated as experimental by users of this software and any conclusions derived from them should be treated with caution Figure H 12 Causality assessment coefficients options View causality assessment coefficients View path correlation signs View R squared contributions View path correlation ratios View path correlation differences View Warp2 bivariate causal direction ratios View Warp2 bivariate causal direction differen
75. be plausible depending on context and other data Other data may include qualitative data which can be very useful when combined with quantitative data As can be inferred from this example it is not easy to interpret nonlinear relationships But the apparent simplicity of strictly linear modeling or linear estimations of possibly nonlinear relationships is nothing but a mirage 90 WarpPLS 5 0 User Manual 1 3 Correlation versus collinearity Let us consider a theoretical case in which two predictor variables point at a criterion variable and the predictor variables are uncorrelated In this case the value of the R for the criterion variable the positive square root of the R squared will be a function of two other correlation values R and Ro which are the correlations between each of the predictor variables and the criterion The value of the VIF which is itself a function of R will consequently be a function of R and R gt The values of the VIF for the scenario above are plotted in Figure I 3 generated based on a simulation with MATLAB Three dimensions are needed because three variables are involved As it can be seen the variable VIF can reach unacceptably high values clearly suggestive of collinearity and for much lower values of R and R than in the case when only two variables are present Let us assume that we were to set the threshold of VIF for collinearity at 3 3 In this case a correlation of 0 835 or higher woul
76. cause in this basic version the signs of path coefficients are initially assigned as the signs of the corresponding correlations obtained without any warping 24 WarpPLS 5 0 User Manual The Warp3 algorithm the default algorithm used by the software tries to identify relationships among latent variables defined by functions whose first derivatives are U curves These types of relationships follow a pattern that is more similar to an S curve or a somewhat distorted S curve An S curve can be seen as a combination of two connected U curves one of which is inverted Examples of S curve functions are the sigmoid hyperbolic sine and hyperbolic tangent The logistic function is a type of sigmoid function and thus is also an example of S curve function Similarly to the Warp2 Basic algorithm the Warp3 Basic algorithm is a variation of the Warp3 algorithm that tends to reduce the number of instances of Simpson s paradox Wagner 1982 in the final results Again here this happens because the signs of path coefficients are initially assigned as the signs of the corresponding correlations obtained without any warping In summary with the exception of the Linear algorithm all of the default inner model analysis algorithms perform nonlinear transformations on the predictor latent variable scores prior to the calculation of path coefficients In other words except for the Linear algorithm these algorithms warp the predictor latent variable s
77. ces View Warp3 bivariate causal direction ratios View Warp3 bivariate causal direction differences The View path correlation signs option allows users to identify path specific Simpson s paradox instances Pearl 2009 Wagner 1982 by inspecting a table with the path correlation signs shown in the table as the values 1 and 1 A negative path correlation sign or the value 1 is indicative of a Simpson s paradox instance A Simpson s paradox instance is a possible indication of a causality problem suggesting that a hypothesized path is either implausible or reversed The interpretation of individual Simpson s paradox instances can be difficult This may be especially the case with demographic variables when these are included in the model as control variables suggesting what may appear to be unlikely or impossible reverse directions of causality For example let us say that a negative path correlation sign occurs when we include the control variable Age time from birth measured in years into a model pointing at the variable Job performance self assessed measured through multiple indicators on Likert type scales This may be interpreted as suggesting that Job performance causes Age in the sense that increased job performance causes someone to age or causes time to pass faster Alternative explanations frequently exist for Simpson s paradox instances as well as for other red flags suggested
78. cidentally concentrated on the left part of the screen This option corrects that by automatically redrawing all symbols in the model graph so that the center of the model graph coincides with the center of the model screen Show hide indicators This option shows or hides the list of indicators for each latent variable The indicators are shown on a vertical list next to each latent variable and without the little boxes that are usually shown in other SEM software This display option is used to give the model graph a cleaner look It also has the advantage that it saves space in the model graph for latent variables Normally you will want to keep the indicators hidden except when you are checking whether the right indicators were selected for the right latent variables That is normally you will show the indicators to perform a check and then hide them during most of the model building process Clear model deletes all latent variables This option deletes all latent variables essentially clearing the model Given that choosing this option by mistake can potentially cause some serious loss of work not to mention some major user aggravation the software shows a dialog box asking you to confirm that you want to clear the model before it goes ahead and deletes all latent variables Even if you choose this option by mistake and confirm your choice also by mistake a double mistake you can still undo it by choosing the option Cancel model creat
79. cient greater than zero The unimodality tests for which results are provided are the Rohatgi Sz kely test Rohatgi amp Sz kely 1989 and the Klaassen Mokveld van Es test Klaassen et al 2000 The normality tests for which results are provided are the classic Jarque Bera test Jarque amp Bera 1980 Bera amp Jarque 1981 and Gel amp Gastwirth s 2008 robust modification of this test Since these tests are applied to latent variables which are combinations either of indicators or of indicators and measurement errors the outcomes of these tests can be seen as multivariate unimodality and normality test results Both unimodality and normality test results take the form of a Yes or No meaning that the latent variable distributions are or are not respectively unimodal or normal No unimodality or normality for at least one latent variable or indicator is usually seen as an sign that the nonparametric methods used in this software are particularly appropriate That is users of this software can justify employing it by noting that not all latent variables are unimodal and normal It is noteworthy that the non normality justification for the use of non parametric PLS based SEM methods has been widely employed in the past but typically without any accompanying test of normality 67 WarpPLS 5 0 User Manual H 7 View correlations among latent variables and errors The View correlations among latent variables
80. cients of association provide support for the hypothesized directions of the causal links in a model The NLBCDR index is calculated by dividing the number of path related instances in a model where the support for the reversed hypothesized direction of causality is more than weak by the total number of path related instances involved in this test this is discussed in more detail later All of the available nonlinear algorithms are used in this test Therefore the total number of path related instances involved in this test is greater than the total number of paths At the time of this writing the NLBCDR was an experimental index and thus the following recommendation should also be treated as experimental Acceptable values of NUBCDR are equal to or greater than 0 7 meaning that in at least 70 percent of path related instances in a model the support for the reversed hypothesized direction of causality is weak or less Here less may mean that the support for reversed hypothesized direction of causality is less than weak e g neutral or that the hypothesized direction of causality is supported 53 WarpPLS 5 0 User Manual H 2 View path coefficients and P values Path coefficients and respective P values are shown together as can be seen in Figure H 2 Each path coefficient is displayed in one cell where the column refers to the predictor latent variable and the row to the criterion For example let us consider the case in which the ce
81. cores by finding best fitting nonlinear functions that minimize sums of squared residuals on a bivariate basis This process can be seen as another least squares minimization stage that is in between those used in the calculation of latent variable scores and path coefficients One of several resampling methods may be selected for the calculation of P values and related coefficients e g standard errors In the calculation of P values a one tailed test is generally recommended if the coefficient is assumed to have a sign positive or negative which should be reflected in the hypothesis that refers to the corresponding association Kock 2014d Hence this software reports one tailed P values for coefficients used in hypothesis testing e g path coefficients from which two tailed P values can be easily obtained if needed Kock 2014d The available resampling methods are the following Stable1 Stable2 and Stable3 Bootstrapping Jackknifing Blindfolding and Parametric With the Stable1 method the software s default up until version 4 0 when it was called simply the stable method P values are calculated through nonlinear fitting of standard errors to empirical standard errors generated with the other resampling methods available In other words the Stablel method could be viewed as a quasi parametric method that yields P values that try to approximate the average P values generated by the software s other resampling m
82. cting a table with the absolute Warp3 bivariate causal direction differences and their respective P values The absolute Warp3 bivariate causal direction differences can be used together with the Warp3 bivariate causal direction ratios to identify paths that need special attention because Warp3 bivariate causal direction ratios alone can sometimes provide an inflated perception of problems especially when paths in one direction and the other are both very small Generally speaking a path that meets the following criteria should be seen as referring to a link that needs special attention in terms of possible direction reversal Warp3 bivariate causal direction ratio greater than 1 3 and P value for absolute Warp3 bivariate causal direction difference equal to a lower than 0 05 Since ratios and P values are generated for the Warp2 and Warp3 algorithms a more relaxed approach would be to consider for special attention in terms of possible direction reversal only links that meet both the criteria for Warp2 and Warp3 above Another approach also somewhat relaxed would be to consider for special attention only links that meet the criteria that refer to the nonlinear algorithm used for the calculation of the path coefficient associated with the link either Warp2 or Warp3 this includes the basic options Having said that the above criteria arguably apply to paths calculated using the Linear algorithm The extent to which using more or less relaxed
83. ctively refer to the Bootstrapping Stable2 and Stable3 methods The latent variables in the model used as a basis for the simulation are CO communication flow orientation GT usefulness in the development of IT solutions EU ease of understanding AC accuracy and SU impact on redesign success for more details see Kock 2014b The meanings of the acronyms within parentheses are the following TruePath true path coefficient AvgPath mean path coefficient estimate Power statistical power SEPath standard error of path coefficient estimate and EstSEPath method specific standard error of path coefficient estimate 93 WarpPLS 5 0 User Manual To conduct the simulation we created an analyzed 1 000 samples for each of the following sample sizes 50 100 200 300 and 500 The PLS Mode A algorithm was used in the analyses In this summarized set of results we restrict ourselves to sample sizes 50 and 300 Full results for all sample sizes included in the simulation are available from Kock 2014b As we can see the mean path coefficient estimates differ from the true path coefficients across different sample sizes and generally underestimate the true path coefficients This underestimation stems from the use of composites in PLS Mode A which in turn leads to the known composite correlation attenuation Nunnally amp Bernstein 1994 This attenuation propagates to the path coefficients Kock 2014 This problem is a
84. ctor Based PLS algorithms The latter Factor Based PLS algorithms estimate latent variables through the estimation of the true factors The term factor is often used when we refer to latent variables in the broader context of SEM analyses in general The reason is that factor analysis from which the term factor originates can be seen as a special case of SEM analysis The path coefficients are noted as beta coefficients Beta coefficient is another term often used to refer to path coefficients in PLS based SEM analyses this term is commonly used in multiple regression analyses The P values are displayed below the path coefficients within parentheses The R squared coefficients are shown below each endogenous latent variable i e a latent variable that is hypothesized to be affected by one or more other latent variables and reflect the percentage of the variance in the latent variable that is explained by the latent variables that are hypothesized to affect it To facilitate the visualization of the results the path 48 WarpPLS 5 0 User Manual coefficients and P values for moderating effects are shown in a way similar to the corresponding values for direct effects namely next to the arrows representing the effects 49 WarpPLS 5 0 User Manual H 1 View general results General SEM analysis results include the version of WarpPLS used in the SEM analysis project file details such as the project file name an
85. cur e g severe collinearity or model misspecification Average variance extracted AVE A measure associated with a latent variable which is used in the assessment of the discriminant validity of a measurement instrument Less commonly it can also be used for convergent validity assessment Composite reliability coefficient This is a measure of reliability associated with a latent variable Another name for it is Dillon Goldstein rho coefficient Unlike the Cronbach s alpha coefficient another measure of reliability the compositive reliability coefficient takes indicator loadings into consideration in its calculation It often is slightly higher than the Cronbach s alpha coefficient Construct A conceptual entity measured through a latent variable Sometimes it is referred to as latent construct The terms construct or latent construct are often used interchangeably with the term latent variable Convergent validity of a measurement instrument Convergent validity is a measure of the quality of a measurement instrument the instrument itself is typically a set of question statements A measurement instrument has good convergent validity if the question statements or other measures associated with each latent variable are understood by the respondents in the same way as they were intended by the designers of the question statements Cronbach s alpha coefficient This is a measure of reliability associated a la
86. d causal links The View Warp2 bivariate causal direction ratios option allows users to identify instances in which the Warp2 algorithm suggests that causality may be reversed by inspecting a table with the Warp2 bivariate causal direction ratios These ratios are calculated by dividing the path coefficient obtained for the reversed link by the path coefficient obtained for the link with the hypothesized direction The following interpretations are suggested for Warp2 bivariate 83 WarpPLS 5 0 User Manual causal direction ratios ratio gt 1 supports reversed link 1 lt ratio lt 1 3 weak support 1 3 lt ratio lt 1 7 medium 1 7 lt ratio strong In the same way that one can distinguish between a statistically significant and non significant direct association one can also distinguish between a statistically significant and non significant Warp bivariate causal direction reversal instance The View Warp2 bivariate causal direction differences option allows users to do just that by inspecting a table with the absolute Warp bivariate causal direction differences and their respective P values The absolute Warp2 bivariate causal direction differences can be used together with the Warp2 bivariate causal direction ratios to identify paths that need special attention because Warp bivariate causal direction ratios alone can sometimes provide an inflated perception of problems especially when paths in one direction and th
87. d reflective latent variables P values are provided for indicators associated with all latent variables These P values are often referred to as validation parameters of a confirmatory factor analysis Kline 1998 Schumacker amp Lomax 2004 since they result from a test of a model where the relationships between indicators and latent variables are defined beforehand Conversely in an exploratory factor analysis Ehremberg amp Goodhart 1976 relationships between indicators and latent variables are not defined beforehand but inferred based on the results of a factor extraction algorithm The principal components analysis algorithm is one of the most popular of these algorithms even though it is often classified as outside the scope of classic factor analysis Confirmatory factor analyses instead of exploratory factor analyses are usually conducted in conjunction with SEM analyses For research reports users will typically use the table of combined loadings and cross loadings provided by this software when describing the convergent validity of their measurement instrument A measurement instrument has good convergent validity if the question statements or other measures associated with each latent variable are understood by the respondents in the same way as they were intended by the designers of the question statements In this respect two criteria are recommended as the basis for concluding that a measurement model has acceptable converg
88. d suggest collinearity in a situation involving only two variables Kock amp Lynn 2012 Figure I 3 The relationship between the VIF and the Rs for three variables The points at which the VIF values increase steeply are indicated as peaks including small peaks on the three dimensional plot Here a combination of values of R and R3 in the range of 0 6 to 0 8 lead to VIF values that are suggestive of collinearity for a threshold level of 3 3 For example if R and R are both equal to 0 625 the corresponding VIF will be 4 57 As models become more complex from a structural perspective with more variables in them the absolute values of the correlations that can lead to significant multicollinearity goes progressively down Even if not in the same block latent variables may still be redundant and cause interpretation problems when correlations are relatively low This is why it is important that users of this software take the various VIFs that are reported into consideration when assessing their models 91 WarpPLS 5 0 User Manual The example above also illustrates the fact that the concepts of collinearity and correlation are distinct concepts even though they are often confused Collinearity is a multivariate notion whereas correlation refers to a pair of variables Kock amp Lynn 2012 Two or more variables are said to be collinear when they measure the same attribute of an object the latter is also called a construct In t
89. d when the file was last saved model fit and quality indices shown in Figure H 1 2 which are discussed in more detail below and general model elements such as the algorithm and resampling method used in the SEM analysis Figure H 1 2 General results window Model fit and quality indices Average path coefficient APC 0 196 P lt 0 001 Average R squared ARS 0 169 P lt 0 001 Average adjusted R squared AARS 0 164 P lt 0 001 Average block VIF AVIF 1 361 acceptable if lt 5 ideally lt 3 3 Average full collinearity VIF AFVIF 1 571 acceptable if lt 5 ideally lt 3 3 Tenenhaus GoF GoF 0 292 small gt 0 1 medium gt 0 25 large gt 0 36 Sympson s paradox ratio SPR 1 000 acceptable if gt 0 7 ideally 1 R squared contribution ratio RSCR 1 000 acceptable if gt 0 9 ideally 1 Statistical suppression ratio SSR 1 000 acceptable if gt 0 7 Nonlinear bivariate causality direction ratio NLBCDR 0 861 acceptable if gt 0 7 Under the project file details both the raw data path and file are provided Those are provided for completeness because once the raw data is imported into a project file it is no longer needed for the analysis Once a raw data file is read it can even be deleted without any effect on the project file or the SEM analysis Ten global model fit and quality indices are provided average path coefficient APC average R squared ARS average adjusted R squared AARS av
90. data imputation as well as add one or more latent variable scores a k a factor scores to the dataset as new standardized indicators see Figure B 3 Also available is the option of adding all latent variable scores at once to the dataset as new standardized indicators Data labels can be shown on graphs as text next to data points or as legends for data points using different markers These menu options are discussed individually below Some of them are discussed in more detail later in this document Figure B 3 Modify menu options Add data labels from clipboard Add data labels from file Add raw data from clipboard Add raw data from file Redo missing data imputation via data pre processing Add one or more latent variable a k a factor scores as new standardized indicators Add all latent variable a k a factor scores as new standardized indicators The menu options Add data labels from clipboard and Add data labels from file allow you to add data labels into the project file Data labels are text identifiers that are entered by you through these options one column at a time Like the original numeric dataset the data labels are stored in a table Each column of this table refers to one data label and each row to the corresponding row of the original numeric dataset Data labels can later be shown on graphs either next to each data point that they refer to or as part of the legend for a graph Data labels can be
91. ddressed in this software through the availability of Factor Based PLS algorithms Generally the method specific standard errors of path coefficient estimates obtained via Stable3 were the closest to the actual or true standard errors of path coefficient estimates This suggests that standard errors estimated via Stable3 are not only stable when compared with those estimated via Bootstrapping but also more accurate Moreover both Stable2 and Stable3 led to greater statistical power than Bootstrapping at small sample sizes This is noteworthy because power tends to be compromised the most with small sample sizes and to invariably increase as sample sizes go up regardless of the standard error and P value calculation method used 94 WarpPLS 5 0 User Manual 1 5 Missing data imputation methods A Monte Carlo simulation was conducted to assess the performance of five missing data imputation methods implemented through this software Arithmetic Mean Imputation Multiple Regression Imputation Hierarchical Regression Imputation Stochastic Multiple Regression Imputation and Stochastic Hierarchical Regression Imputation Table I 5 adapted from Kock 2014c summarizes the results of this simulation Table I 5 Summarized Monte Carlo experiment results for missing data imputation methods Missing data imputation NMD MEAN MREGR HREGR MSREG HSREG scheme CO gt GT TruePath 0 450 0 450 0 450 0 450 0 450 0 450 CO gt GT
92. dicator effects are small medium or large The values usually recommended are 0 02 0 15 and 0 35 respectively Cohen 1988 Values below 0 02 suggest effects that are too weak to be considered relevant from a practical point of view even when the corresponding P values are statistically significant It is recommended that all indicator effect sizes be equal to or greater than 0 02 for both formative and reflective latent variables Indicators with effect sizes that do not meet this criterion may be considered for removal 64 WarpPLS 5 0 User Manual H 6 View latent variable coefficients Several estimates are provided for each latent variable these can be used in research reports for discussions on the measurement instrument s reliability discriminant and predictive validity as well as overall collinearity see Figure H 6 R squared adjusted R squared and Q squared coefficients are provided only for endogenous latent variables and reflect the percentages of explained variance and predictive validity associated with each of those latent variables respectively Composite reliability and Cronbach s alpha coefficients are provided for all latent variables Also provided for all latent variables are minimum and maximum values medians modes skewness and excess kurtosis coefficients results of unimodality and normality tests and histograms Figure H 6 Latent variable coefficients window Commor Easgen Easund Complet R squar
93. discussed here combine variations in terms of two main aspects whether the scales are standardized or unstandardized and whether the graphs refer to multivariate or bivariate relationships By default latent variable scores are standardized aggregations of indicators The latter namely the indicators are originally in unstandardized format Therefore to obtain the unstandardized equivalents of the latent variable scores some decisions must be made and extra calculations performed The unstandardized equivalents of latent variable scores are always approximations Unstandardization of scales for latent variable scores whereby standardized scales are converted to their unstandardized equivalents is based on the unstandardization option chosen by the user using the Settings menu option Three unstandardization options are available Highest loading indicator the default option whereby the mean and standard deviation of the highest loading indicator is used in the unstandardization Average of indicators whereby the mean and standard deviation of the average of indicators is used and Weighted average of indicators whereby the mean and standard deviation of the weighted average of indicators is used Through the Settings menu option the user can also set the graph title the X axis label and the Y axis label The graph title is the text shown at the top of the graph The X axis label is the text shown next to the X
94. due to measurement model differences P values are provided for weights associated with all latent variables These values can also be seen together with the P values for loadings as the result of a confirmatory factor analysis In research reports users may want to report these P values as an indication that formative latent variable measurement items were properly constructed This also applies to moderating latent variables that pass criteria for formative measurement when those variables do not pass criteria for reflective measurement As in multiple regression analysis Miller amp Wichern 1977 Mueller 1996 it is recommended that weights with P values that are equal to or lower than 0 05 be considered valid items in a formative latent variable measurement item subset Formative latent variable indicators whose weights do not satisfy this criterion may be considered for removal With these P values users can also check whether moderating latent variables satisfy validity and reliability criteria for formative measurement if they do not satisfy criteria for reflective measurement This can help users demonstrate validity and reliability in hierarchical analyses involving moderating effects where double triple etc moderating effects are tested For 62 WarpPLS 5 0 User Manual instance moderating latent variables can be created added to the model as standardized indicators and then their effects modeled as being moderated by ot
95. e as those provided in the combined loadings and cross loadings table The cross loadings however are different Also these two criteria generally apply to the version of this table that is not normalized 61 WarpPLS 5 0 User Manual H 5 View indicator weights Indicator weights are provided in a table much in the same way as indicator loadings are see Figure H 5 All cross weights are zero because of the way they are calculated through PLS based alrgorithms Each latent variable score is calculated as an exactly linear combination of its indicators or of its indicators and measurement error where the weights are multiple regression coefficients linking the indicators to the latent variable Figure H 5 Indicator weights window Proc Effi Effe ECU Type as defined SE P value VIF ES Procl 0 393 0 000 0 000 0 000 Reflective 0 031 lt 0 001 1 781 0 333 Proc2 0 421 0 000 0 000 0 000 Reflective 0 030 lt 0 001 2 051 0 375 Proc3 0 362 0 000 0 000 0 000 Reflective 0 035 lt 0 001 1 593 0 292 Effil 0 000 0 245 0 000 0 000 Reflective 0 014 lt 0 001 3 800 0 218 Effi2 o 000 0 222 0 000 0 000 Reflective 0 016 lt 0 001 4 036 0 194 Effi3 0 000 0 238 0 000 0 000 Reflective 0 019 lt 0 001 2 414 0 194 Effi4 0 000 0 206 0 000 0 000 Reflective 0 019 lt 0 001 2 522 0 168 Effi5 0 000 0 278 0 000 0 000 Reflective 0 020 lt 0 001 2 494 0 227 Effel 0 000 0 000 0 157 0 000 Reflective 0 013 lt 0 001 7 843 0 147 Effe2 10 000 0
96. e in these cases showing legends instead of data labels next to points avoids graph crowding The options available are View multivariate relationship graph with data points and legends standardized scales View multivariate relationship graphs with data points and legends unstandardized scales View bivariate relationship graph with data points and legends standardized scales and View bivariate relationship graphs with data points and legends unstandardized scales The View relationship graphs with data points and labels options allow users to view graphs with the best fitting lines or curves the data points used to produce the best fitting lines or curves and data labels next to the data points to which they refer These options show all the data points and thus do not provide the effect of zooming in on the best fitting line or curve area They are useful in cases where few data points are available because in these cases showing data labels next to points provides a clear picture of what each data point refers to without graph crowding The options available are View multivariate relationship graph with data points and labels standardized scales View multivariate relationship graphs with data points and labels unstandardized scales View bivariate relationship graph with data points and labels standardized scales and View bivariate relationship graphs with data points and labels un
97. e of outliers due to errors in data collection This opinion is not shared by the original developer of the Bootstrapping method Bradley Efron see e g Efron et al 2004 Not considering the stable methods arguably Jackknifing is particularly good at addressing problems associated with the presence of outliers due to errors in data collection Generally speaking Jackknifing tends to generate more stable resample path coefficients and thus more reliable P values with small sample sizes lower than 100 and with samples containing outliers see e g Chiquoine amp Hjalmarsson 2009 Monte Carlo simulations suggest that the stable methods perform better than Jackknifing in this respect Again not considering the stable methods Bootstrapping tends to generate more stable resample path coefficients and thus more reliable P values with larger samples and with 26 WarpPLS 5 0 User Manual samples where the data points are evenly distributed on a scatter plot Monte Carlo simulations suggest that the stable methods perform better than Bootstrapping in this respect as well The use of Bootstrapping with small sample sizes lower than 100 has been discouraged Nevitt amp Hancock 2001 Generally speaking Bootstrapping and Jackknifing can be seen as complementary resampling methods in that one tends to perform well in situations where the other does not and vice versa Nevertheless the stable methods p
98. e other are both very small Generally speaking a path that meets the following criteria should be seen as referring to a link that needs special attention in terms of possible direction reversal Warp2 bivariate causal direction ratio greater than 1 3 and P value for absolute Warp2 bivariate causal direction difference equal to a lower than 0 05 Since the Warp3 and Warp2 algorithms are different a similar set of outputs exists in connection with Warp3 bivariate causal direction inferences to those available for Warp2 Often these different sets outputs will be fairly consistent but sometimes they will not The View Warp3 bivariate causal direction ratios option allows users to identify instances in which the Warp3 algorithm suggests that causality may be reversed by inspecting a table with the Warp3 bivariate causal direction ratios These ratios are calculated by dividing the path coefficient obtained for the reversed link by the path coefficient obtained for the link with the hypothesized direction The following interpretations are suggested for Warp3 bivariate causal direction ratios ratio gt 1 supports reversed link 1 lt ratio lt 1 3 weak support 1 3 lt ratio lt 1 7 medium 1 7 lt ratio strong The View Warp3 bivariate causal direction differences option allows users to distinguish between a statistically significant and non significant Warp3 bivariate causal direction reversal instance Users can do that by inspe
99. e the predictors and the latent variable the criterion PLS Mode B Basic is a variation of PLS Mode B in which the inner model influences the outer model through the signs of the correlations among latent variables The Robust Path Analysis algorithm is a simplified algorithm in which latent variable scores are calculated by averaging the scores of the indicators associated with the latent variables That is in this algorithm weights are not estimated through PLS Regression This algorithm is called robust path analysis because the P values can be calculated through the nonparametric resampling or stable methods implemented through the software If all latent variables are measured with single indicators the Robust Path Analysis algorithm will yield latent variable scores and outer model weights that are identical to those generated through the other algorithms Many relationships in nature including relationships involving behavioral variables are nonlinear and follow a pattern known as U curve or inverted U curve In this pattern a variable affects another in a way that leads to a maximum or minimum value where the effect is either maximized or minimized respectively This type of relationship is also referred to as a J curve pattern a term that is more commonly used in economics and the health sciences The term U curve is used here also to refer to nonlinear relationships that can be represented as sections of a U curve As such i
100. e2 and Stable3 This alternative is highly recommended particularly with the Stable3 method the software s default As their name implies these methods yield stable coefficients They also provide fairly accurate estimates of standard errors which are used in the calculation of P values These methods do not actually generates resamples so calling them resampling methods is done here for simplicity in the grouping of settings options Because no resamples are generated these are rather efficient methods from a computing load perspective These methods can be particularly useful in the analysis of large datasets as in these cases creating resamples can be computationally very taxing With the emergence of the concept of big data the need to analyze large datasets is becoming increasingly common 47 WarpPLS 5 0 User Manual H View and save results As soon as the SEM analysis is completed the software shows the results in graphical format on a window which also contains a number of menu options that allow you to view and save more detailed results see Figure H 1 1 The graph with the results shows path coefficients respective P values and R squared coefficients The Save menu options allow users to save all of the results that they can view with the majority of those results saved under the option to save all model estimates into a tab delimited text file Additionally users can save the factor scores calculated for e
101. eated by the user in Step 4 The following outer model algorithms are similar to PLS Regression but in them the inner model influences the outer model PLS Mode M PLS Mode M Basic PLS Mode A PLS Mode A Basic PLS Mode B and PLS Mode B Basic These are classic PLS algorithms that have been historically associated with PLS based SEM software Chatelin et al 2002 Temme et al 2006 In them the iterative process leading to the calculation of latent variable scores involves the intermediate calculation of path coefficients correlations and signs of correlations These are used as inputs in the calculation of weights in successive iterations typically leading to the addition of collinearity among latent variables that are linked The above collinearity inflation that occurs when the inner model influences the outer model often has the effect of strengthening associations among linked latent variables This is a real phenomenon that has been presented as a weakness of PLS based SEM and that has been referred to as the capitalization on error problem of PLS based algorithms see e g Goodhue et al 2012 This problem is generally overstated as PLS based algorithms in general tend to also reduce collinearity That is when the inner model influences the outer model collinearity is indeed increased but often not to the extent that the increase offsets the previous collinearity decrease that normally results from the use of PLS based algorit
102. ed 0 009 0 453 0 003 Adj R squared 0 002 0 446 0 003 Composite reliab 0 926 0 897 0 860 Cronbach s alpha 0 881 0 828 0 755 Avg var extrac 0 607 0 744 0 672 Full collin VIF 1 761 2 291 1 178 Q squared 0 010 0 454 0 006 Min 2 871 2 982 2 329 Max 1 850 1 931 2 815 Median 0 039 0 034 0 033 Mode 0 039 0 034 0 614 Skewness 0 765 0 537 0 111 Exc kurtosis 0 561 0 002 0 206 Unimodal RS Yes Unimodal KMV Yes Normal JB Normal RJB Histogram Composite reliability and Cronbach s alpha coefficients are measures of reliability Serious questions have been raised regarding Cronbach s alpha s Cronbach 1951 Kline 2010 psychometric properties However while the Cronbach s alpha coefficient is reported by this software and the Factor Based PLS algorithms employ it as a basis for the estimation of measurement error and composite weights no assumptions are made about the coefficient s main purported psychometric properties that have been the target of criticism Sijtsma 2009 This is an important caveat in light of measurement error theory Nunnally amp Bernstein 1994 Users should also keep in mind that an alternative and generally more acceptable reliability measure is available the composite reliability coefficient Dillon amp Goldstein 1984 Peterson amp Yeolib 2013 Composite reliability coefficients are also known as Dillon Goldstein rho coefficients
103. el analysis algorithm resampling method and number of resamples Through these sub options users can set outer and default inner model algorithms separately Users are also allowed to set inner model algorithms for individual paths through a different option If users choose not to set inner model algorithms for individual paths in an analysis of a new model i e a model that has just been created their choice of default inner model algorithm is automatically used for all paths The View or change data modification settings option allows you to select a range restriction variable type range restriction variable range min max values for the restriction variable and whether to use only ranked data in the analysis Through these sub options users can run their analyses with subsamples defined by a range restriction variable which is chosen from among the indicators available They can also conduct their analyses with only ranked data whereby all of the data is automatically ranked prior to the SEM analysis When data on a ratio scale is ranked typically the value distances that typify outliers are significantly reduced effectively eliminating outliers without any decrease in sample size The View or change individual inner model analysis algorithm settings option allows you to set inner model algorithms for individual paths That is for each path a user can select a different algorithm from among the following choices Linear
104. el cells cannot be empty contain spaces or contain only numbers they must be combinations of letters or of letters and numbers Valid examples are the following Age gt 17 Y2001 AFR and HighSuccess These would normally be entered without the quotation marks which are used here only for clarity Some invalid examples are 123 Age gt 17 and Y 2001 20 WarpPLS 5 0 User Manual B 6 General settings The View or change general settings option allows users to set the outer model analysis algorithm default inner model analysis algorithm resampling method and number of resamples see Figure B 6 Through these sub options users can set outer and default inner model algorithms separately Users are also allowed to set inner model algorithms for individual paths but through a different settings option If users choose not to set inner model algorithms for individual paths their choice of default inner model algorithm is automatically used for all paths Figure B 6 View or change general settings window Factor Based PLS Type CFM1 Factor Based PLS Type REG1 Factor Based PLS Type PTH1 PLS Regression PLS Mode M PLS Mode M Basic Outer model analysis algorithm 3 PLS Mode A PLS regression PLS Mode A Basic PLS Mode B Default inner model analysis algorithm PLS Mode B Basic Linear Robust Path Analysis Linear Warp2 gt Warp2 Basic Stable Warp3 No of resamples sample
105. elds completely unbiased results If one such perfect software tool existed the percentages of false positives and false negatives based on a number of trials with the software using simulated data would all be zero That is no false positives or false negatives of any kind e g association strength direction of causality would occur Achieving this level of perfection is the driving force behind the development of this software even though this level of perfection will never be achieved simply because it is not achievable Some additional issues regarding this quest for perfection are discussed in the following subsections 86 WarpPLS 5 0 User Manual 1 1 Warping from a conceptual perspective What this software does when it warps relationships is relatively simple at a conceptual level It identifies a set of functions FI LVp1 F2 LVp2 that relate blocks of latent variable predictors LVp1 LVp2 to a criterion latent variable LVc in this way LVc p1 F1 LVp1 p2 F2 LVp2 E In the equation above p1 p2 are path coefficients and E is the error term of the equation All variables are standardized Any model can be decomposed into a set of blocks relating latent variable predictors and criteria in this way Typically the more the functions Fl LVp1 F2 LVp2 look like curves and unlike lines the greater is the difference between the path coefficients p1 p2 and those that would have
106. ends View relationship graphs with data points gt View multivariate relationship graph with data points standardized scales p gt View multivariate relationship graph with data points unstandardized scales View relationship graphs with data points and labels View bivariate relationship graph with data points standardized scales View bivariate relationship graph with data points unstandardized scales Several graphs a k a plots for direct effects can be viewed by clicking on a cell containing a relationship type description These cells are the same as those that contain path coefficients in the path coefficients table that was shown earlier Among the options available are graphs showing the points as well as the curves that best approximate the relationships see Figure H 10 2 The View focused relationship graphs options allow users to view graphs that focus on the best fitting line or curve and that exclude data points to provide the effect of zooming in on the best fitting line or curve area The options available are View focused multivariate 73 WarpPLS 5 0 User Manual relationship graph standardized scales View focused multivariate relationship graph unstandardized scales View focused bivariate relationship graph standardized scales and View focused bivariate relationship graph unstandardized scales The options above like other direct effects graph options
107. ent validity that the P values associated with the loadings be equal to or lower than 0 05 and that the loadings be equal to or greater than 0 5 Hair et al 1987 2009 Indicators for which these criteria are not satisfied may be removed This does not apply to formative latent variable indicators which are assessed in part based on P values associated with indicator weights If the offending indicators are part of a moderating effect then you should consider removing the moderating effect if it does not meet the requirements for formative measurement Moderating effect latent variable names are displayed on the table as product latent variables e g Effi Proc Moderating effect indicator names are displayed on the table as product indicators e g Effi 1 Proc1 Long names are reduced to avoid a crowded look High P values for moderating effects to the point of being non significant at the 0 05 level may suggest multicollinearity problems which can be further checked based on the latent variable coefficients generated by the software more specifically the full collinearity VIFs Some degree of collinearity is to be expected with moderating effects since the corresponding product variables are likely to be correlated with at least their component latent variables Moreover moderating effects add nonlinearity to models which can in some cases compound multicollinearity problems Because of these and other related issues modera
108. ent variable indicators Reliability is a measure of the quality of a measurement instrument the instrument itself is typically a set of question statements A measurement instrument has good reliability if the question statements or other measures associated with each latent variable are understood in the same way by different respondents More conservatively both the composite reliability and the Cronbach s alpha coefficients should be equal to or greater than 0 7 Fornell amp Larcker 1981 Nunnaly 1978 Nunnally amp Bernstein 1994 The more relaxed version of this criterion which is widely used is that one of the two coefficients should be equal to or greater than 0 7 This typically applies to the composite reliability coefficient which is usually the higher of the two Fornell amp Larcker 1981 An even more relaxed version sets this threshold at 0 6 Nunnally amp Bernstein 1994 If a latent variable does not satisfy any of these criteria the reason will often be one or a few indicators that load weakly on the latent variable These indicators should be considered for removal AVEs are normally used for discriminant validity assessment and less commonly for convergent validity assessment For discriminant validity assessment AVEs are used in conjunction with latent variable correlations This is discussed in more detail later together with the discussion of the table of correlations among latent variables that includes square
109. erage block variance inflation factor A VIF average full collinearity VIF AF VIF Tenenhaus GoF GoF Simpson s paradox ratio SPR R squared contribution ratio RSCR statistical suppression ratio SSR and nonlinear bivariate causality direction ratio NLBCDR For the APC ARS and AARS P values are also provided These P values are calculated through a process that involves resampling estimations coupled with corrections to counter the standard error compression effect associated with adding random variables in a way analogous to Bonferroni corrections Rosenthal amp Rosnow 1991 This is necessary since the model fit and quality indices are calculated as averages of other parameters The interpretation of the model fit and quality indices depends on the goal of the SEM analysis If the goal is to only test hypotheses where each arrow represents a hypothesis then the model fit and quality indices are as a whole of less importance However if the goal is to find out whether one model has a better fit with the original data than another then the model fit and quality indices are a useful set of measures related to model quality When assessing the model fit with the data several criteria are recommended These criteria are discussed below together with the discussion of the model fit and quality indices APC ARS and AARS Typically the addition of new latent variables into a model will increase the ARS even if those latent variabl
110. es skewness and excess kurtosis coefficients as well as results of unimodality and normality tests These are now complemented by histograms which can be viewed on the screen and saved as files Unimodality and normality tests Often the use of PLS based SEM methods is justified based on them making no data normality assumptions but typically without any accompanying test of normality This is addressed in this version through various outputs of unimodality and normality tests which are now provided for all indicators and latent variables The unimodality tests performed are the Rohatgi Sz kely test and the Klaassen Mokveld van Es test The normality tests performed are the classic Jarque Bera test and Gel amp Gastwirth s robust modification of this test Where these tests are applied to individual indicators they can be seen as univariate or bivariate unimodality and normality tests Where these tests are applied to latent variables they can be seen as multivariate unimodality and normality tests New 3D graphs and graph rotation Rocky and smooth 3D graphs can now be viewed with data points excluded Corresponding graphs with data points included are also available The 3D graph displays with data points excluded are analogous to those used in the focused 2D graphs Additionally users can now incrementally rotate 3D graphs in the following directions up down left and right New stable P value calculation methods
111. es are weakly associated with the existing latent variables in the model However that will generally lead to a decrease in the APC since the path coefficients associated with the new latent variables will be low Thus the APC and ARS will counterbalance each other and will only increase together if the latent variables that are added to the model enhance the overall predictive and explanatory quality of the model The AARS is generally lower than the ARS for a given model The reason is that it averages adjusted R 50 WarpPLS 5 0 User Manual squared coefficients Theil 1958 Wooldridge 1991 which themselves correct for spurious increases in R squared coefficients due to predictors that add no explanatory value in each latent variable block It is recommended that the P values for the APC ARS and AARS all be equal to or lower than 0 05 that is significant at the 0 05 level A more relaxed rule would be that the P values for the APC and ARS only be equal to or lower than 0 05 AVIF and AFVIF The AVIF index will increase if new latent variables are added to the model in such a way as to add vertical collinearity in the model s latent variable blocks The AFVIF index will increase if new latent variables are added to the model in such a way as to add full collinearity into the model 1 e either vertical or lateral collinearity see Kock amp Lynn 2012 Full collinearity is often referred to as muticollinearity High AVIF and AF
112. ese criteria may be particularly relevant in the context of path analyses is that without multiple indicators per latent variable the PLS based SEM algorithms do not have the raw material that they need to reduce collinearity PLS based SEM algorithms are particularly effective at reducing collinearity but chiefly when true latent variables are present that is when latent variables are measured through multiple indicators High block VIFs usually occur for pairs of predictor latent variables and suggest that the latent variables measure the same construct If this is not due to indicator assignment problems it 70 WarpPLS 5 0 User Manual would arguably call for the removal of one of the latent variables from the block or from the model 71 WarpPLS 5 0 User Manual H 9 View correlations among indicators The software allows users to view the correlations among all indicators included in the model in table format Only the correlations for indicators included in the model are shown through the menu option View correlations among indicators available from the View and save results window This option is useful for users who want to run a quick check on the correlations among indicators while they are trying to identify possible sources of multicollinearity This option may also be useful in the identification of candidate indicators for latent variables through the anchor variable procedure developed by K
113. ethods The Stable2 and Stable3 methods have been developed as alternatives to the Stablel method Unlike the Stable1 method they rely on the direct application of exponential smoothing formulas for details see Kock 2014b and that can thus be more easily implemented and tested by methodological researchers A Monte Carlo experiment shows that the Stable2 and Stable3 methods yield estimates of the actual standard errors that are consistent with those obtained via bootstrapping in many cases yielding more precise estimates of the actual standard errors Kock 2014b The more accurate of the two methods appears to be the Stable3 method which also appears to be more accurate than the Stable method As such the Stable3 method is set as the software s default starting in version 5 0 With the Parametric method P values are calculated assuming multivariate normality and also that path coefficient estimates are distributed as expected based on the central limit theorem Neither the Parametric method nor the three stable methods Stable1 Stable2 and Stable3 actually generates resamples so calling them resampling methods is done here for simplicity in the grouping of settings options Because no resamples are generated these are the most efficient 25 WarpPLS 5 0 User Manual of the methods from a computing load perspective These methods can be particularly useful in the analysis of large datasets as in these cases creating resample
114. example would be the removal of only 2 indicators out of 16 by the use of this rule of thumb with the Cronbach s alpha coefficient remaining equal to or greater than 0 6 Otherwise the criteria below should be employed Two criteria one more conservative and one more relaxed are recommended by the multivariate analysis literature in connection with VIFs criteria that can arguably also be used in this type of context More conservatively it is recommended that VIFs be lower than 5 a more relaxed criterion is that they be lower than 10 Hair et al 1987 2009 Kline 1998 High VIFs usually occur for pairs of indicators in formative latent variables and suggest that the indicators measure the same facet of a formative construct This calls for the removal of one of the indicators from the set of indicators used for the formative latent variable measurement These criteria are generally consistent with formative latent variable theory see e g Diamantopoulos 1999 Diamantopoulos amp Winklhofer 2001 Diamantopoulos amp Siguaw 2006 Among other characteristics formative latent variables are expected often by design to have many indicators Yet given the nature of multiple regression indicator weights will normally go down as the number of indicators go up as long as those indicators are somewhat correlated and thus P values will normally go up as well Moreover as more indicators are used to measure a formative latent variable the
115. f rows as the original data unless a range restricted analysis is conducted and which generally tend to maximize the loadings and minimize the cross loadings of a pattern matrix of loadings after an oblique rotation Latent variable error An error variable that accounts for the variance in an endogenous latent variable that is not accounted for by the latent variable predictors that point at the endogenous latent variable The terms error and residual are used interchangeably in this document Nevertheless they refer to subtly different entities Technically speaking the term error typically refers to the error variable in the true population model which is assumed to be uncorrelated with latent variables other than the endogenous latent variable to which it is associated Conversely the term residual typically refers to the corresponding estimated error the difference between the expected value of the latent variable and its point estimate which in practice is often correlated with latent variables other than the endogenous latent variable to which it is associated This is an example of a broader occurrence in multivariate analyses more often than not sample specific estimates violate assumptions about the theoretical true values even if slightly Manifest variable A manifest variable is one of several variables that are used to indirectly measure a latent variable For example satisfaction with a meal may be a l
116. h a pair of linked variables Like a Simpson s paradox instance a statistical suppression instance is a possible indication of a causality problem Spirtes et al 1993 suggesting that a hypothesized path may be either implausible or reversed The SSR index is calculated by dividing the number of paths in a model that are not associated with medium or greater statistical suppression instances by the total number of paths in the model A medium or greater statistical suppression instance is characterized by an absolute path correlation ratio that is greater than 1 3 At the time of this writing the SSR was an experimental index and thus the following recommendation should also be treated as experimental Acceptable values of SSR are equal to or greater than 0 7 meaning that at least 70 percent of the paths in a model are free from statistical suppression NLBCDR One interesting property of nonlinear algorithms is that bivariate nonlinear coefficients of association vary depending on the hypothesized direction of causality That is they tend to be stronger in one direction than the other which means that the residual or error is greater when the hypothesized direction of causality is in one way or another As such they can be used together with other coefficients as partial evidence in support or against hypothesized causal links The NUBCDR index is a measure of the extent to which bivariate nonlinear 52 WarpPLS 5 0 User Manual coeffi
117. h the anchor variable procedure discussed by Kock amp Verville 2012 This can be done prior to defining the variables and links in a model This can also be done after the model is defined and an analysis is conducted particularly in cases where the results suggest outer model misspecification Examples of outer model misspecification are instances in which indicators are mistakenly included in the model by being assigned to certain latent variables and instances in which indicators are assigned to the wrong latent variables Kock amp Lynn 2012 Kock amp Verville 2012 The View of save raw indicator data option allows you to view or save the raw data used in the analysis This is a useful feature for geographically distributed researchers conducting collaborative analyses With it those researchers do not have to share the raw data as a separate file as that data is already part of the project file Two menu options allow you to view or save unstandardized pre processed indicator data This pre processed data is not the same as the raw data as it has already been through the automated missing value correction procedure in Step 3 The options that allow you to view or 14 WarpPLS 5 0 User Manual save unstandardized pre processed indicator data are View or save unstandardized pre processed indicator data and View or save unstandardized ranked pre processed indicator data The latter option refers to ranked data
118. he model is saved as part of the project and the project file is saved Figure F 2 Create latent variable window Save Close Help Latent variable name nolvname max 8 characters View remove Add indicators indicators a al sEmail Elst A sTele_Voice ECU Effe Effi Proc Rand10 Remove L Add _ Measurement model Reflective You create a latent variable by entering a name for it which must have no more than 8 characters but to which not many other restrictions apply The latent variable name may contain letters numbers and even special characters such as or It cannot contain the special character however because this character is used later by this software in selected outputs to indicate that a latent variable is associated with a moderating effect After entering a name for a latent variable you then select the indicators that make up the latent variable and define the measurement model as reflective or formative A reflective latent variable is one in which all the indicators are expected to be highly correlated with one another and with the latent variable itself For example the answers to certain question statements by a group of people measured on a to 7 scale 1 strongly disagree 7 strongly agree and answered after a meal are expected to be highly correlated with the latent variable satisfaction with a meal Among question statements that would arguably fit this
119. her latent variables an example of double moderation In addition to P values variance inflation factors VIFs are provided for the indicators of all latent variables including moderating latent variables These can be used for indicator redundancy assessment In reflective latent variables indicators are expected to be redundant This is not the case with formative latent variables In formative latent variables indicators are expected to measure different facets of the same construct which means that they should not be redundant The VIF threshold of 3 3 has been recommended in the context of PLS based SEM in discussions of formative latent variable measurement Cenfetelli amp Bassellier 2009 Petter et al 2007 A rule of thumb rooted in the use of this software for many SEM analyses in the past suggests an even more conservative approach that capping VIFs to 2 5 for indicators used in formative measurement leads to improved stability of estimates The multivariate analysis literature however tends to gravitate toward higher thresholds Also capping VIFs at 2 5 or 3 3 may in some cases severely limit the number of possible indicators available Given this it is recommended that VIFs be capped at 2 5 or 3 3 if this does not lead to a major reduction in the number of indicators available to measure formative latent variables and if the Cronbach s alpha coefficient associated with the formative latent variable does not fall below 0 6 One
120. his sense the variables satisfaction with a technology and excitement about the technology may be collinear if the question statements related to these two variables are seen as referring to the same object attribute affective response to the technology by the respondents of a questionnaire Two variables are said to be correlated if they vary in concert with each other even though the variables may measure totally different object attributes e g a person s weight from 1 to 20 years of age and the price of gasoline during those years 92 WarpPLS 5 0 User Manual 1 4 Stable P value calculation methods A Monte Carlo simulation was conducted to assess the performance of three P value calculation methods implemented through this software Bootstrapping Stable2 and Stable3 Performance was assessed in terms of statistical power and closeness to the actual standard errors obtained through the analyses of simulated samples Standard errors are used together with path coefficients to obtain P values Table I 4 adapted from Kock 2014b summarizes the results of this simulation Table I 4 Summarized Monte Carlo experiment results for P value calculation methods Method BOOT STBL2 STBL3 BOOT STBL2 STBL3 Sample size 50 50 50 300 300 300 CO gt GT TruePath 0 450 0 450 0 450 0 450 0 450 0 450 CO gt GT AvgPath 0 383 0 383 0 383 0 388 0 388 0 388 CO gt GT Power 0 905 0 954 0 946 1 1 1 CO gt GT SEPath
121. his situation in connection with accuracy and statistical power by providing an extensive set of features and outputs that can be used by researchers to reveal as many aspects of the underlying relationships as possible Some of the features provided are specifically aimed at increasing accuracy and statistical power For example Jackknifing one of the resampling methods provided tends to generate relatively low standard errors with small samples and medium to high effect sizes This could increase statistical power with small samples and medium to high effect sizes making the use of Jackknifing more appropriate than Bootstrapping in these cases The same may be true for the stable methods particularly Stable3 In fact Monte Carlo simulations suggest that the stable methods perform better than Jackknifing in this respect This software s extensive range of features may also help further research on SEM methods in general 10 WarpPLS 5 0 User Manual B The main window Prior to displaying the software s main window a command prompt window may be shown and kept open for the duration of the SEM analysis session Do not try to close this command prompt window if it is shown because it will list warnings and error messages that will likely be very useful in troubleshooting Moreover those warnings and error messages will indicate where in the source code they are happening which will help the software developer correct any
122. hms PLS Mode M is often referred as the MIMIC or mixed mode In it the inner model influences the outer model through path coefficients and correlations depending on whether the links go into or out from each latent variable respectively PLS Mode M in fact uses either PLS Mode A or PLS Mode B based on whether latent variables are defined as reflective or formative respectively The PLS modes A and B are discussed below PLS Mode M Basic is a variation of PLS Mode M in which the inner model influences the outer model through the signs of correlations among latent variables This corresponds to what Lohm ller 1989 refers to as a basic scheme also referred to as a centroid scheme Tenenhaus et al 2005 For the purposes of PLS based SEM the schemes known as centroid and factorial are largely redundant Tenenhaus et al 2005 but they share a common property They tend to reduce the number of instances of Simpson s paradox Wagner 1982 in the SEM analysis results Because of this property and the fact that these two schemes are redundant this software implements only one of them the centroid scheme This scheme is referred to as basic for simplicity and consistency with prior seminal publications that set the foundations of PLS based SEM see e g Lohmdller 1989 PLS Mode A is often referred to as the reflective mode which is arguably incorrect because both reflective and forma
123. i seevanteese se soi seus lv ash gees sdeess a 12 De DAT Aas ET EN EEE E E ai E ba NIB oak Saw E esa Sop OEE RB EL ESE SIE IEEE Bebe B3 MODIFY s kannaa n a a n biveresectced scutes telboed a a a ccugiaetsaeevtetencieet ee sieeade rented sabeate dante dea eheees B 4 SETTINGS BS DATASIA BEES EEE EE og sn 0is Selec b Eco es Sweets bas halic E EE E Sh aegs ibs das Sindh Seve Aaa aoa he B26 GENERAL SETTINGS sescisss52 cccvccnsecesssese sua daieacscacssveussucestincss usedevesasvncs oeeeee ces ess vavuanergcisscsv es sdb vgenncesaceuseusesy dase ceecencdcvssestnegieensesces B 7 DATA MODIFICATION SETTINGS B 8 INDIVIDUAL INNER MODEL ALGORITHM SETTINGS ccccccccccsssessceececeeccceeeesessseeeecceceeseeessesseeeeececeseesessaseeeeeeeceeeeeesseasaaeeeees 30 B 9 INDIVIDUAL LATENT VARIABLE WEIGHT AND LOADING STARTING VALUE SETTINGS csssssssceccccceeeeeessessseeeeecceeeeessssasseeeeees 31 BIO GROUPED DESCRIPTIVE STATISTICS 333 a oe sabee see aoe ee ee ae AA EO ASH A EEEE TEO 32 C STEP 1 OPEN OR CREATE A PROJECT FILE TO SAVE YOUR WORK 0 csscccsssssccsssssceccsscscccsssscccsenscceccsseeee 34 D STEP 2 READ THE RAW DATA USED IN THE SEM ANALYSIS ccsssscscsssscccsssscecesssscccscsssccccsssccccsssssccesesssseeeees 36 E STEP 3 PRE PROCESS THE DATA FOR THE SEM ANALYSIS 1 ccccsssssscssssscessssecescsscccccnsscccessecsesscnccecesssseseees 38 F STEP 4 DEFINE THE VARIABLES AND LINKS IN THE SEM MOD
124. iable axis with a multivariate adjustment and with corresponding changes in the overall inclinations of the sections of the surface representing the direct effect being moderated The mathematical underpinnings of such representation were still under development at the time of this writing and may be available for implementation in future versions of this software The View moderating relationship in one rocky 3D graph options allow users to view 3D graphs where the surfaces are generated through Delaunay triangulations Chew 1989 Lee amp Schachter 1980 without smoothing Surfaces can be viewed with data points excluded or included The displays with data points excluded are analogous to those used in the focused 2D graphs The options to view surfaces with data points excluded are View rocky 3D graph for moderating effect standardized scales and View rocky 3D graph for moderating effect unstandardized scales The options to view surfaces with data points included are View rocky 3D graph for moderating effect with data points standardized scales and View rocky 3D graph for moderating effect with data points unstandardized scales The Rotate menu option allows the user to rotate a 3D graph up down left and right Through the Settings menu option the user can set the following 3D graph options the graph title the moderating variable M axis label the X axis label and the Y axis label The g
125. ich in turn has the effect of restricting the analysis to the rows in the dataset within that particular range The option of selecting a range restriction variable and respective range is useful in multi group analyses whereby separate analyses are conducted for group specific subsamples saved as different project files and the results then compared against one another One example would be a multi country analysis with each country being treated as a subsample but without separate datasets for each country having to be provided as inputs Let us assume that an unstandardized variable called Country stores the values 1 for Brazil 2 for New Zealand and 3 for the USA To run the analysis only with data from Brazil one can set the range restriction variable as Country after setting its type as Unstandardized indicator and then set both the minimum and maximum values as 1 for the range This range restriction feature is also useful in situations where outliers are causing instability in a resample set which can lead to abnormally high standard errors and thus inflated P values Users can remove outliers by restricting the values assumed by a variable to a range that excludes the outliers without having to modify and re read a dataset Users can also select an option to conduct their analyses with only ranked data whereby all of the data is automatically ranked prior to the SEM analysis the origin
126. ights and loadings end up being negative after an analysis is conducted In this case paths associated with the latent variable may end up being reversed leading to conclusions that are the opposite of what is hypothesized The solution here would normally be a change in sign for starting value of weights and loadings usually from to 1 31 WarpPLS 5 0 User Manual B 10 Grouped descriptive statistics When the Save grouped descriptive statistics option is selected a data entry window is displayed see Figure B 10 1 There you can choose a grouping variable number of groups and the variables to be grouped This option is useful if one wants to conduct a comparison of means analysis using the software where one variable the grouping variable is the predictor and one or more variables are the criteria the variables to be grouped Figure B 10 1 Save grouped descriptive statistics window Save Close Help Grouping variable ECUEmail Variables to be Variables in grouped data file ECUEmailist a sEmail_Elist ECUBoard ECUFiles ECULotusNotes ECuUEnewslet ECUAutoRout ECUFTP ECUWebPage F G H l J K L M Effe1 ECU 0 5 4 676 6 ECU 5 10 5 903 T 8 Effe1 9 Mean 4 676 10 SD 3 572 11 12 Interval 5 000 to 10 000 Eee eerie eee er ae Effet 14 15 Effet T 16 Mean 5 903 6 17 SD 3 639 18 19 k 20 3 21 2 22 23 i 24 0 25 ECU 0 5 ECU 5 10 L26
127. iginally a text file or try to create a tab delimited text file with it if it is originally a spreadsheet file If you try to do either of these things and the data looks corrupted e g missing column names with misplaced columns containing unrecognized symbols then it is likely that the original file has problems which may be hidden from view For example a spreadsheet file may be corrupted but that may not be evident based on a simple visual inspection of the contents of the file 37 WarpPLS 5 0 User Manual E Step 3 Pre process the data for the SEM analysis In Step 3 the raw data will be pre processed for the SEM analysis This is mostly an automatic process requiring only a few button clicks from you This step will correct problems with the data such as identical column names columns with zero variance and missing data The View or change missing data imputation settings option allows you to set the missing data imputation method to be used by the software in this step Missing data imputation can be redone after this step if you later decide to use a different imputation method To accomplish that you should use the option Redo missing data imputation via data pre processing under the Modify menu option Kock 2014c provides a detailed discussion of missing data imputation methods as well as of a Monte Carlo simulation comparing the methods relative performances This step will also let you know
128. in whether the effects indicated by path coefficients are small medium or large The values usually recommended are 0 02 0 15 and 0 35 respectively Cohen 1988 Values below 0 02 suggest effects that are too weak to be considered relevant from a practical point of view even when the corresponding P values are statistically significant a situation that may occur with large sample sizes Additional types of analyses that may be conducted with standard errors are tests of the significance of any mediating effects using the approach discussed by Kock 2013 This approach consolidates the approaches discussed by Preacher amp Hayes 2004 for linear relationships and Hayes amp Preacher 2010 for nonlinear relationships The latter discussed by 56 WarpPLS 5 0 User Manual Hayes amp Preacher 2010 assumes that nonlinear relationships are force modeled as linear which means that the equivalent test using this software would use warped coefficients with the earlier linear approach discussed by Preacher amp Hayes 2004 Again for the consolidated version of these approaches see Kock 2013 The classic approach used for testing mediating effects is discussed by Kock 201 1b This approach is a concise version of Baron amp Kenny s 1986 classic approach which does not rely on standard errors An alternative approach to the analysis of mediating effects which is arguably much less time consuming and prone to error than the
129. ing lines or curves for high and low values of the moderating variable and the data points used to produce the best fitting lines or curves These options show all the data points and thus do not provide the effect of zooming in on the area comprising the best fitting lines or curves The options available are View graph with low high values of moderating variable and data points standardized scales and View graph with low high values of moderating variable and data points unstandardized scales The View moderating relationship in two graphs with data points options allow users to view 2D moderating effect graphs with the best fitting lines or curves for high and low values of the moderating variable and the data points used to produce the best fitting lines or curves in two graphs shown side by side These options show all the data points and thus do not provide the effect of zooming in on the areas comprising the best fitting lines or curves The options available are View two graphs with low high values of moderating variable and data points standardized scales and View two graphs with low high values of moderating variable and data points unstandardized scales The graphs of relationships between pairs of latent variables and between latent variables and links moderating relationships provide a much more nuanced view of how latent variables are related However caution must be taken in the interpretati
130. ion editing all editing is lost immediately after clearing the model Cancel model creation editing all editing is lost This option cancels the model creation or editing essentially undoing all of the model changes you have made Save model into jpg file This option allows you to save the model graph into a jpg file You will be asked to select the file name and the folder where the file will be saved After saved this file can then be viewed and edited with standard picture viewers as well as included as a picture into reports in other files e g a Word file Users can also generate model graph files by copying the model screen into a picture editing application e g Paint cropping it to leave out unnecessary or unneeded areas saving it into a picture file e g jpg or png and then importing that file into reports Create latent variable This option allows you to create a latent variable and is discussed in more detail below Once a latent variable is created it can be dragged and dropped anywhere within the window that contains the model Edit latent variable This option allows you to edit a latent variable that has already been created and thus that is visible on the model graph Delete latent variable This option allows you to delete an existing latent variable All links associated with the latent variable are also deleted Move latent variable This option is rarely used since once a latent variable is created it c
131. ionships between pairs of latent variables that is those relationships best described by a line are relatively easy to interpret They suggest that an increase in one variable either leads to an increase if the slope of the line is positive or decrease if the slope is negative in the other variable Nonlinear relationships provide a much more nuanced view of the data but at the same time are much more difficult to interpret Figure I 2 shows what could be seen as a distorted S curve that is fitted to the data points The latent variables are Proc the extent to which various teams charged with developing new products kept track of their work and costs i e engaged in procedural structuring and Effe the effectiveness of the teams measured as the market success in terms of sales and profits of the new products that the teams developed Figure I 2 Example of warped relationship Data points and regression line or curve standardized values The distorted S can in turn be seen as a combination of two distorted U curves or J curves one straight and the other inverted connected at an inflection point The inflection point is the point at the curve where the curvature changes direction i e the second derivative of the S curve changes sign The inflection point is located at around minus 1 standard deviations from the Proc mean That mean is at the zero mark on the horizontal axis since the data shown is standardized
132. is Viewing and accepting data You are now in St analysis Raw data can be read from a file or from the clipboard If the source of the labels is a file its type can be any of the following xis or xlsx An Excel file txt A tab delimited or comma delimited text file For Excel workbooks with multiple sheets the sheet with the data must be either the first in the workbook or selected manually The file must have the names of the variables latent construct indicators in the first row and the values associated with those variables in the following rows Press the Read from file button or the Read from clipboard button when you are ready to read the raw data Press the Go back button to go back to the main window For more help click on the Help menu option at the top of this window The buttons Read from file and Read from clipboard allow you to read raw data into the project file from a file or from the clipboard respectively This software employs an import wizard that avoids most data reading problems even if it does not entirely eliminate the possibility that a problem will occur Click only on the Next and Finish buttons of the file import wizard and let the wizard do the rest Soon after the raw data is imported it will be shown on the screen and you will be given the opportunity to accept or reject it If there are problems with the data such as missing column names
133. ith each cell referring to an indicator latent variable link Latent variable names are listed at the top of each column and indicator names at the beginning of each row In this table both the loadings and cross loadings are from a pattern matrix 1 e rotated Since these loadings and cross loadings are from a pattern matrix they are obtained after the transformation of a structure matrix through a widely used oblique rotation frequently referred to as Promax The structure matrix contains the Pearson correlations between indicators and latent variables which are not particularly meaningful prior to rotation in the context of measurement instrument validation Because an oblique rotation is employed in some cases loadings may be higher than 1 Rencher 1998 This could be a hint that two or more latent variables are collinear although this may not necessarily be the case better measures of collinearity among latent variables are the full collinearity VIFs reported with other latent variable coefficients In the normalized version of this table typically there will be no loadings higher than 1 The main difference between oblique and orthogonal rotation methods is that the former assume that there are correlations some of which may be strong among latent variables Arguably oblique rotation methods are the most appropriate in a SEM analysis because by definition latent variables are expected to be correlated Otherwise no path coefficient wou
134. ld be significant Technically speaking it is possible that a research study will hypothesize only neutral relationships between latent variables which could call for an orthogonal rotation However this is rarely if ever the case Structure loadings and cross loadings are provided in a table with each cell referring to an indicator latent variable link Latent variable names are listed at the top of each column and indicator names at the beginning of each row In this table both the loadings and cross loadings 60 WarpPLS 5 0 User Manual are from a structure matrix i e unrotated Often these are the only loadings and cross loadings provided by other PLS based SEM software systems As the structure matrix contains the Pearson correlations between indicators and latent variables this matrix is not particularly meaningful or useful prior to rotation in the context of collinearity or measurement instrument validation Here the unrotated cross loadings tend to be fairly high even when the measurement instrument passes widely used validity and reliability tests This is generally true for the normalized version of this matrix Still some researchers recommend using the structure loadings and cross loadings table as well to assess convergent validity by following two criteria that the cross loadings be lower than 0 5 and that the loadings be equal to or greater than 0 5 Hair et al 1987 2009 Note that the loadings here are the sam
135. ld be reflected in the hypothesis that refers to the corresponding association Kock 2014d Hence this software reports one tailed P values for path coefficients from which two tailed P values can be easily obtained if needed Kock 2014d One puzzling aspect of many publicly available PLS based SEM software systems is that they have historically avoided providing P values instead providing standard errors and T values and leaving the users to figure out what the corresponding P values are Often users have to resort to 54 WarpPLS 5 0 User Manual tables relating T to P values or other software e g Excel to calculate P values based on T values This is puzzling because typically research reports will provide P values associated with path coefficients which are more meaningful than T values for hypothesis testing purposes This is due to the fact that P values reflect not only the strength of the relationship which is already provided by the path coefficient itself but also the power of the test which increases with sample size The larger the sample size the lower a path coefficient has to be to yield a statistically significant P value 55 WarpPLS 5 0 User Manual H 3 View standard errors and effect sizes for path coefficients Standard errors and effect sizes for path coefficients are provided in two tables where one standard error and effect size is provided for each path coefficient see Figure H 3 The effect si
136. ll shows 0 225 the column refers to the latent variable ECUVar and the row to the latent variable Proc This means that the path coefficient associated with the arrow that points from ECUVar to Proc is 0 225 Figure H 2 Path coefficients and P values window Close Help Path coefficients ECUVar i Effi Proc ECUVar Proc Effi Effe Effi Proc P values ECUVar Proc i Effi Proc ECUVar Proc lt 0 001 Effi 0 406 lt 0 001 Effe lt 0 001 Effi Proc Since the results refer to standardized variables a path coefficient of 0 225 means that in a linear analysis a 1 standard deviation variation in ECUVar leads to a 0 225 standard deviation variation in Proc In a nonlinear analysis the meaning is generally the same except that it applies to the overall linear trend of the transformed or warped relationship However it is important to note that in nonlinear relationships the path coefficient at each point of a curve varies In nonlinear relationships the path coefficient is given by the first derivative of the nonlinear function that describes the relationship The P values shown are calculated through one of several methods available and are thus method specific i e they change based on the P value calculation method chosen In the calculation of P values a one tailed test is generally recommended if the coefficient is assumed to have a sign positive or negative which shou
137. ll of the indicators are expected to be highly correlated with the latent variable score and also highly correlated with one another For example the answers to certain question statements by a group of people measured on a 1 to 7 scale 1 strongly disagree 7 strongly agree and answered after a meal are expected to be highly correlated with the latent variable satisfaction with a meal The question statements are I am satisfied with this meal and After this meal I feel full Therefore the latent variable satisfaction with a meal can be said to be reflectively measured through these two indicators These indicators store answers to the two question statements This latent variable could be represented in a model graph as Satisf and the indicators as Satisf1 and Satisf2 Reliability of a measurement instrument Reliability is a measure of the quality of a measurement instrument the instrument itself is typically a set of question statements A measurement instrument has good reliability if the question statements or other measures associated with each latent variable are understood in the same way by different respondents R squared coefficient This is a measure calculated only for endogenous latent variables and that reflects the percentage of explained variance for each of those latent variables The higher the R squared coefficient the better is the explanatory power of the predictors of the laten
138. methods are available Arithmetic Mean Imputation the software s default Multiple Regression Imputation Hierarchical Regression Imputation Stochastic Multiple Regression Imputation and Stochastic Hierarchical Regression 16 WarpPLS 5 0 User Manual Imputation Kock 2014c provides a detailed discussion of these methods and of a Monte Carlo simulation that assesses the methods relative performances Latent variable scores can be easily added to the dataset via the options Add one or more latent variable a k a factor scores as new standardized indicators and Add all latent variable a k a factor scores as new standardized indicators These options allow users after Step 5 is completed to add one or more latent variables to the model as new standardized indicators and also to add all latent variables as new indicators Adding one or more latent variables at a time may be advisable in certain cases for example in hierarchical analyses using selected latent variables as indicators of second third etc order latent variables at each level In such cases adding all latent variables at once may soon clutter the set of indicators available to be used in the SEM model 17 WarpPLS 5 0 User Manual B 4 Settings The Settings menu options allow you to view or change general SEM analysis settings see Figure B 4 Here you can select the analysis algorithm used in the SEM analysis the resampling method used t
139. n each resample equals the sample size divided by the number of resamples For example if the sample size is 200 and the number of resamples selected is 100 then each resample will have 2 rows modified If a user chooses a number of resamples that is greater than the sample size the number of resamples is automatically set to the sample size as with Jackknifing The default number of resamples for Bootstrapping and Blindfolding is 100 It can be modified by entering a different number in the appropriate edit box Please note that we are talking about the number of resamples here not the sample size of the original dataset Leaving the number of resamples for Bootstrapping as 100 is recommended because it has been shown that higher numbers of resamples lead to negligible improvements in the reliability of P values see e g Goodhue et al 2012 In fact according to the original developer of the Bootstrapping method even setting the number of resamples at 50 is likely to lead to fairly reliable P value estimates Efron et al 2004 Conversely increasing the number of resamples well beyond 100 leads to a higher computation load on the software making the software look like it is having a hard time coming up with the results In very complex models a high number of resamples may make the software run very slowly Some researchers have suggested in the past that a large number of resamples can address problems with the data such as the presenc
140. n the graph e g reliability measures and also save the results into tab delimited text files Collinearity is estimated before the SEM analysis is run If collinearity appears to be too high users are warned about it A table with estimated latent variable correlations is shown allowing users to identify the possible offending latent variables If users so choose they can proceed with the analysis anyway but in most not all cases the full collinearity a k a multicollinearity measures will confirm that collinearity is too high in their models for the analysis results to be considered credible Measurement error and composite weights are estimated before the SEM analysis is run whenever Factor Based PLS algorithms are used Measurement error and composite weights play a key role in these algorithms If at least one measurement error weight is greater than the corresponding composite weight the user is warned about possible unreliability of results This happens usually when at least one of the Cronbach s alpha coefficients associated with the latent variables is lower than 0 5 Foundational aspects of the Factor Based PLS algorithms are discussed by Kock 2014 who lays out the mathematical basis of these algorithms from which the importance of measurement error and composite weights can be gleaned New options become available from the main window after Step 5 is completed under the Modify menu option These options allow users to
141. n you choose guiding you through the sub steps related to each option For example if you choose the option Create latent variable the guiding text box will change color and tell you to select a location for the latent variable on the model graph Direct links are displayed as full arrows in the model graph and moderating links as dashed arrows Each latent variable is displayed in the model graph within an oval symbol where its name is shown above a combination of alphanumerical characters with this general format F 16i The F refers to the measurement model where F means formative and 41 WarpPLS 5 0 User Manual R reflective The 161 reflects the number of indicators of the latent variable which in this case is 16 Save model and close This option saves the model within the project and closes the model editing and creation window This option does not however save the project file That is the project file has to be saved for a model to be saved as part of it This allows you to open a project file change its model run a SEM analysis and discard all that you have done if you wish to do so reverting back to the previous project file Centralize model graph This option centralizes the model graph and is useful when you are building complex models and in the process of doing so end up making the model visually unbalanced For example you may move variables around so that they are all ac
142. ng indicator or indicators and consider removing them 68 WarpPLS 5 0 User Manual Second to latent variables involved in moderating effects formative latent variables are the most likely to lead to discriminant validity problems This is one of the reasons why formative latent variables are not used as often as reflective latent variables in empirical research In fact it is wise to use formative variables sparingly in models that will serve as the basis for SEM analysis Formative variables can in many cases be decomposed into reflective latent variables which themselves can then be added to the model Often this provides a better understanding of the empirical phenomena under investigation Edwards 2011 in addition to helping avoid discriminant validity problems A table with correlations among latent variable error terms containing VIFs associated with the error terms on the diagonal is also provided This table may be useful in identifying error terms that are highly correlated which suggest the existence of confounders More specifically if a latent variable A points at a latent variable B and the error terms e A and e B are strongly correlated then this may be an indication of the existence of a hidden confounder This hidden confounder may be the real cause behind a significant association between A and B suggesting a causality problem namely one in which a link may in fact not be a true causal link but rather be due to
143. no guarantee that the functions FI LVp1 F2 LVp2 discovered by this software will match perfectly that true underlying functions As mentioned earlier this level of perfection is one that should be strived for but that is essentially impossible to achieve due to one key factor measurement error The more measurement error exists i e the greater is its magnitude the more likely it is that the functions F1 LVp1 F2 LVp2 discovered by this software will be distorted by error In fact the existence of significant measurement error may lead this software to model relationships that are actually linear as nonlinear With the above caveats in mind users can check through simple visual inspection tests whether the functions discovered by this software are at least good approximations of the true underlying functions To do so users can divide the dataset into a number of quantiles e g 3 and then build graphs containing the mean values of each criteria latent variable for each of the quantiles These graphs can be simple bar charts or scatter plots 87 WarpPLS 5 0 User Manual This allows users to check whether the shapes of the plots are similar to the shapes of the best fitting curves generated by this software The best fitting curves are representations of the functions Fl LVp1 F2 LVp2 discovered by this software 88 WarpPLS 5 0 User Manual 1 2 Interpreting warped relationships Linear relat
144. nparametric estimation techniques do not require the data to be normally distributed which is a requirement of other comparison of means techniques e g ANOVA Another advantage of conducting a comparison of means analysis using this software is that the analysis can be significantly more elaborate than with traditional comparison of means methods even nonparametric ones For example the analysis may include control variables or covariates which would make it equivalent to an ANCOVA test Finally the comparison of means analysis may include latent variables as either predictors or criteria This is not usually possible with ANOVA or commonly used nonparametric comparison of means tests e g the Mann Whitney U test An even more extreme situation is that discussed by Kock 2013b where data on only one group and one condition is available This situation is illustrated through a scenario in which a researcher obtains empirical data by asking questions to gauge the effect of a technology on task performance but does not obtain data on the extent to which the technology is used Because of this the researcher ends up with only one column of data to analyze Two other scenarios are also discussed by Kock 2013b These two scenarios are discussed to set the stage for the discussion of the one group and one condition scenario The first is a typical study scenario in which the researcher measures the degree to which the technology is
145. o calculate standard errors and P values as well as other elements that will define how the SEM analysis will be conducted These menu options are discussed individually below Several of them are discussed in more detail later in this document Figure B 4 Settings menu options View or change missing data imputation settings View or change general settings View or change data modification settings View or change individual inner model analysis algorithm settings View or change individual latent variable weight and loading starting value settings The View or change missing data imputation settings option allows you to set the missing data imputation method to be used by the software from among the following methods Arithmetic Mean Imputation the software s default Multiple Regression Imputation Hierarchical Regression Imputation Stochastic Multiple Regression Imputation and Stochastic Hierarchical Regression Imputation The missing data imputation method chosen will be used prior to execution of Step 3 and also after that when the option Redo missing data imputation via data pre processing under the Modify menu option is selected Kock 2014c provides a detailed discussion of these methods as well as of a Monte Carlo simulation whereby the methods relative performances are investigated The View or change general settings option allows you to set the outer model analysis algorithm default inner mod
146. o the Control Panel click on Add or Remove Programs or Programs and Features and uninstall the MATLAB Compiler Runtime The MATLAB Compiler Runtime 7 14 is used in this version of WarpPLS This is the same MATLAB Compiler Runtime as the one used in versions 2 0 4 0 The MATLAB Compiler Runtime used in version 1 0 is a different one and thus will not work properly with this version of WarpPLS In most cases previous versions of WarpPLS and of the MATLAB Compiler Runtime may be retained on a user s computer Different versions of WarpPLS and of the MATLAB Compiler Runtime generally do not interfere with one other To uninstall the main software program simply delete the main software installation folder This folder is usually C Program Files WarpPLS 5 0 or C Program Files x86 WarpPLS 5 0 unless you chose a different folder for the main software program during the installation process Then delete the shortcut created by the software from the desktop Both programs the MATLAB Compiler Runtime and the main software may be retained without harm to your computer They will not normally interfere with other programs not even with MATLAB the main MATLAB program if you have it installed on your computer WarpPLS 5 0 User Manual A 2 Stable version notice This version was initially released as a beta version and was later upgraded to stable As you will see below it incorporates a large number of new
147. ock amp Verville 2012 The table of correlations among indicators used in the model is usually much larger with many more columns and rows than that of the correlations among latent variables For this reason the P values for the correlations are not shown in the screen view option together with the correlations but are saved in the related tab delimited text file To save correlations among all indicators and respective P values including those indicators not included in the model use the menu option Data and the appropriate sub options therein It should be noted that indicators that are not included in the model are not technically true indicators Nevertheless they do fall under the general term manifest variables as they are directly measured and thus not latent variables They refer to the columns of the original dataset The menu option for saving correlations among all manifest variables which refer to all columns of the original dataset is available from the main software window under Data after Step 3 is completed This option is generally more meaningful for users who want to include the correlations among manifest variables in their research reports as part of a descriptive statistics table and for users employing the anchor variable procedure developed by Kock amp Verville 2012 This option also generates means standard deviations and other descriptive statistics for each of the manifest
148. on of these graphs especially when the distribution of data points is very uneven An extreme example would be a warped graph in which all of the data points would be concentrated on the right part of the graph with only one data point on the far left part of the graph That single data point called an outlier could strongly influence the shape of the nonlinear relationship In cases such as this the researcher must decide whether the outlier is good data that should be allowed to shape the relationship or is simply bad data resulting from a data collection error If the outlier is found to be bad data it can be removed from the analysis even as it remains in the dataset by a simple procedure The user should first add the latent variable score to the set of standardized indicators used in a SEM analysis using the appropriate menu option under the option Modify from the main software window after Step 5 is completed The user can then remove the outlier by restricting the values assumed by the latent variable using the appropriate selections under the Settings options to a range that excludes the outlier This allows for the 78 WarpPLS 5 0 User Manual exclusion of the outlier without the user having to modify and re read a dataset This procedure may lead to a visible change in the shape of the nonlinear relationship and significantly affect the results An outlier that is found to be bad data c
149. on the same column The most widely used approach and also a reasonably reliable one in the context of PLS based SEM is replacing the missing values with column averages This missing data imputation method is called Arithmetic Mean Imputation and is automated by the software It is in fact the software s default missing data imputation method Kock 2014c provides a detailed discussion of various missing data imputation methods as well as of a Monte Carlo simulation whereby the methods relative performances are investigated While missing data imputation is done automatically by the software you should not use datasets with too many missing values as this will distort the results A general rule of thumb is that your dataset should not have any column with more than 10 percent of its values missing a more relaxed rule would be to set the threshold to 20 percent Hair et al 1987 2009 On the other hand Kock 2014c shows that even 30 percent of missing data will still not lead to significant bias from the perspective of theory testing with any of the missing data imputation methods employed by this software One can reduce the percentage of missing values per column by deleting rows in the dataset where the deleted rows are the ones that refer to the columns with missing values One simple test can be used to try to find out if there are problems with a raw data file Try to open it with a spreadsheet software e g Excel if it is or
150. ontribution to the R squared of a criterion latent variable note the predictor points at the criterion this means that the predictor is actually reducing the percentage of variance explained in the criterion Such a reduction takes into consideration the contributions of all predictors plus that of the residual This index is similar to the SPR The key difference is that it is calculated based on the actual values of the R squared contributions not on the number of paths where these contributions have specific signs The RSCR index is calculated by dividing the sum of positive R squared contributions in a model by the sum of the absolute R squared contributions be they negative or positive in the model At the time of this writing the RSCR was an experimental index and thus the following recommendations should also be treated as experimental Ideally the RSCR should equal 1 meaning that there are no negative R squared contributions in a model acceptable values of RSCR are equal to or greater than 0 9 meaning that the sum of positive R squared contributions in a model makes up at least 90 percent of the total sum of the absolute R squared contributions in the model SSR The SSR index is a measure of the extent to which a model is free from statistical suppression instances MacKinnon et al 2000 An instance of statistical suppression occurs when a path coefficient is greater in absolute terms than the corresponding correlation associated wit
151. or two tailed P values in PLS SEM Laredo TX ScriptWarp Systems Kock N amp Gaskins L 2014 The mediating role of voice and accountability in the relationship between Internet diffusion and government corruption in Latin America and Sub Saharan Africa Information Technology for Development 20 1 23 43 Kock N amp Lynn G S 2012 Lateral collinearity and misleading results in variance based SEM An illustration and recommendations Journal of the Association for Information Systems 13 7 546 580 Kock N amp Verville J 2012 Exploring free questionnaire data with anchor variables An illustration based on a study of IT in healthcare International Journal of Healthcare Information Systems and Informatics 7 1 46 63 Lee D T amp Schachter B J 1980 Two algorithms for constructing a Delaunay triangulation International Journal of Computer amp Information Sciences 9 3 219 242 Lindell M amp Whitney D 2001 Accounting for common method variance in cross sectional research designs Journal of Applied Psychology 86 1 114 121 Lohmdller J B 1989 Latent variable path modeling with partial least squares Heidelberg Germany Physica Verlag MacKinnon D P Krull J L amp Lockwood C M 2000 Equivalence of the mediation confounding and suppression effect Prevention Science 1 4 173 181 106 WarpPLS 5 0 User Manual Miller R B amp Wichern D W 1977 Intermediate
152. ot change in linear relationships segmentation only occurs in nonlinear relationships This graph segmentation option allows for the identification of unobserved heterogeneity Sarstedt amp Ringle 2010 without a corresponding reduction in sample size providing an alternative to data segmentation approaches such as FIMIX PLS Hahn et al 2002 The View relationship graphs with data points options allow users to view graphs with the best fitting lines or curves and the data points used to produce the best fitting lines or curves These options show all the data points and thus do not provide the effect of zooming in on the best fitting line or curve area The options available are View multivariate relationship graph with data points standardized scales View multivariate relationship graph with data points unstandardized scales View bivariate relationship graph with data points standardized scales and View bivariate relationship graph with data points unstandardized scales The View relationship graphs with data points and legends options allow users to view graphs with the best fitting lines or curves the data points used to produce the best fitting lines or curves and legends associated with data labels These options show all the data points and thus do not provide the effect of zooming in on the best fitting line or curve area They are useful in cases where many data points are available becaus
153. ou w to provide the path and name of the project file Such project file will only exist if you created it before using this software Project files are saved with the extension prj When you press the Create project file button you will be asked to provide the path and name for a new project file Press the Open project file button when you are ready to open an existing project file Press the Create project file button when you are ready to create a new project file Drace tha Aa hasl hittan ta an hack ta tha main windaw Once an original data file is read into a project file the original data file can be deleted without effect on the project file The project file will store the original location and file name of the data file so that this information is available in case it is needed in the future but the project file will no longer use the data file Project files may be created with one name and then renamed using Windows Explorer or another file management tool Upon reading a project file that has been renamed in this fashion the software will detect that the original name is different from the file name and will adjust accordingly the name of the project file that it stores internally Different users of this software can easily exchange project files electronically if they are collaborating on a SEM analysis project This way they will have access to all of the original data intermediate data and SEM analy
154. phs with segments options allow users to view graphs that focus on the best fitting line or curve that exclude data points to provide the effect of zooming in on the best fitting line or curve area and that show curves as linear segments The segments are shown with their respective beta coefficients and with or without P values The options available are View focused multivariate relationship graph with segments standardized scales View focused multivariate relationship graph with segments standardized scales P values View focused multivariate relationship graph with segments unstandardized scales View focused bivariate relationship graph with 74 WarpPLS 5 0 User Manual segments standardized scales View focused bivariate relationship graph with segments standardized scales P values and View focused bivariate relationship graph with segments unstandardized scales The number of segments shown in the graphs above depends on the absolute effect segmentation delta chosen by the user through the Settings menu option This absolute effect segmentation delta is the change or delta threshold in the first derivative of the nonlinear function depicting the relationship before a new segment is started For example a delta of 0 1 means that in each segment the first derivative of the nonlinear function depicting the relationship does not vary more than 0 1 Since the first derivative does n
155. project as and Exit Through the Save project option you can save the project file that has just been created or that has been created before and is currently open To open an existing project or create a new project you need to execute Step 1 by pressing the Proceed to Step 1 push button The Save project as option allows you to save an existing project with a different name and in a different folder from ones for the project that is currently open or has just been created This option is useful in the SEM analysis of multiple models where each 12 WarpPLS 5 0 User Manual model is a small variation of the previous one Finally the Exit option ends the software session If your project has not been saved and you choose the Exit option the software will ask you if you want to save your project before exiting In some cases you will not want to save your project before exiting which is why a project is not automatically saved after each step is completed For example you may want to open an existing project change a few things and then run a SEM analysis and then discard that project You can do this by simply not saving the project before exiting After Step 3 is completed whereby the data used in the SEM analysis is pre processed three sets of menu options become available from the main window Data Modify and Settings The Data menu options These menu
156. rametric characteristics of classic PLS algorithms Moreover factor based PLS algorithms address head on a problem that has been discussed since the 1920s the factor indeterminacy problem Classic PLS algorithms yield composites as linear combinations of indicators which can be seen as factor approximations Factor based PLS algorithms on the other hand provide estimates of the true factors as linear combinations of indicators and measurement errors All of the features provided have been extensively tested with both real data collected in actual empirical studies as well as simulated data generated through Monte Carlo procedures Robert amp Casella 2010 Future tests however may reveal new properties of these features and clarify the nature of existing properties WarpPLS 5 0 User Manual A 1 Software installation and uninstallation The software installs automatically from a self extracting executable file There are two components to the software the MATLAB Compiler Runtime and the main software i e WarpPLS The first is a set of free distribution MATLAB libraries with code that is called by the main software Because the MATLAB Compiler Runtime is used you do not have to have MATLAB the main MATLAB program installed on your computer to run WarpPLS Minimal and harmless changes to the operating system registry are made by the MATLAB Compiler Runtime which are easily reversed upon uninstallation To uninstall g
157. raph title is the text shown at the top of the graph The M axis label is the text shown next to the moderating variable axis The X axis label is the text shown next to the X axis or the predictor variable axis The Y axis label is the text shown next to the Y axis or the criterion variable axis The View moderating relationship in one smooth 3D graph with data points options allow users to view 3D graphs where the surfaces are generated through Delaunay triangulations Chew 1989 Lee amp Schachter 1980 with smoothing Because the surfaces are generated with smoothing they sometimes resemble more bed sheets than rocky mountain formations Surfaces can be viewed with data points excluded or included The options to view surfaces with data points excluded are View smooth 3D graph for moderating effect standardized scales and View smooth 3D graph for moderating effect unstandardized scales The options to view surfaces with data points included are View smooth 3D graph for moderating effect with data points standardized scales and View smooth 3D graph for moderating effect with data points unstandardized scales In addition to 3D graphs this software also provides various 2 dimensional 2D graphs of moderating relationships The 2D graphs shown for moderating relationships refer to low and high values of the moderating variable and display the relationships of the variables connected through the moderated di
158. re also provided In windows showing normalized loadings and cross loadings a Kaiser normalization is employed to calculate them Ferguson 1981 Kaiser 1958 Ogasawara 1999 Through a Kaiser normalization each row of a table of loadings and cross loadings is divided by the square root of its communality This has the effect of making the sum of squared values in each row add up to 1 Using a Kaiser normalization is reasonably standard practice Ferguson 1981 Ogasawara 1999 Sometimes the normalization is followed by a de normalization which is not the case with this software The normalized values are useful in situations where the PLS Regression algorithm is used and some of the latent variables have only 2 indicators particularly with respect to options displaying unrotated loadings In such cases the unrotated loadings in the combined loadings and cross loadings window that are associated with each of the 2 indicators are the same because with the PLS Regression algorithm the inner model does not influence the outer model A Kaiser normalization will usually make indicator loadings diverge in value in these cases in a way that is consistent with standard practice and that some researchers argue frequently leads to more conservative estimates of loadings and cross loadings For a more detailed discussion and a review of different perspectives on this topic see Ogasawara 1999 Pattern loadings and cross loadings are provided in a table w
159. re available to be aggregated in the calculation of latent variable scores GoF Similarly to the ARS the GoF index referred to as Tenenhaus GoF in honor of Michel Tenenhaus is a measure of a model s explanatory power Tenenhaus et al 2005 defined the GoF as the square root of the product between what they refer to as the average communality index and the ARS The communality index for a given latent variable is defined as the sum of the squared loadings for that latent variable each loading associated with an indicator divided by the number of indicators The average communality index for a model is defined similarly and takes all latent variables into account in its calculation The loadings referred to here are the unrotated loadings which are available from the structure loadings and cross loadings table It is also worth noting that the definition of the communality index used by Tenenhaus et al 2005 does not match the typical definition of communality at least as it is normally stated in the context of factor analysis As noted by Wetzels et al 2009 the average variance extracted AVE for each latent variable equals the corresponding communality index Wetzels et al 2009 also proposed the following thresholds for the GoF small if equal to or greater than 0 1 medium if equal to or greater than 0 25 and large if equal to or greater than 0 36 They did so by assuming a minimum acceptable average AVE of 0 5 and using Cohen
160. read from the clipboard or from a file but only one column of labels can be read at a time Data label cells cannot be empty contain spaces or contain only numbers they must be combinations of letters or of letters and numbers Valid examples are the following Age gt 17 Y2001 AFR and HighSuccess These would normally be entered without the quotation marks which are used here only for clarity Some invalid examples 123 Age gt 17 and Y 2001 Through the menu options Add raw data from clipboard and Add raw data from file users can add new data from the clipboard or from a file This data then becomes available for use in models without users having to go back to Step 2 These options relieve users from having to go through nearly all of the steps of a SEM analysis if they find out that they need more data after they complete Step 5 of the analysis Past experience supporting users suggests that this is a common occurrence These options employ the same data checks and data correction algorithms as in Step 2 please refer to the section describing that step for more details The option Redo missing data imputation via data pre processing allows users to redo the missing data imputation process after choosing a method through the View or change missing data imputation settings option which is available under the Settings menu options The following missing data imputation
161. rect links in those ranges 77 WarpPLS 5 0 User Manual The View moderating relationship in one focused graph options allow users to view 2D moderating effect graphs that focus on the best fitting lines or curves for high and low values of the moderating variable and that exclude data points to provide the effect of zooming in on the area comprising the best fitting lines or curves The options available are View focused graph with low high values of moderating variable standardized scales and View focused graph with low high values of moderating variable unstandardized scales Through the Settings menu option the user can also set the following 2D moderating effect graph options the graph title the labels associated with high and low values of the moderating variable and the location of the legend box containing these labels These options allow users to create more informative 2D moderating relationship graphs For example instead of Low Exp and High Exp more informative labels such as Novices and Veterans could be used Setting the location of the legend box e g from East to Northwest allows users to move the legend box from more to less crowded areas of the graph giving the graph a more balanced and cleaner appearance The View moderating relationship in one graph with data points options allow users to view 2D moderating effect graphs with the best fitt
162. relationship type description These cells are the same as those that contain path coefficients in the path coefficients table that was shown earlier Their column labels are displayed on the table as product latent variables e g Effi Proc In this example namely Effi Proc the latent variable Effi is hypothesized to moderate the relationship between Proc and another latent variable where Proc points at the third latent variable The third latent variable is listed in the corresponding row label Among the options available are 3 dimensional 3D graphs showing the points as well as the surfaces that best approximate the relationships see Figure H 10 3 Figure H 10 3 Graph options for moderating effects including 3D graph with points and best fitting surface View Rotate Save Settings Close Help View moderating relationship in one rocky 3D graph gt View rocky 3D graph for moderating effect standardized scales View moderating relationship in one smooth 3D graph View rocky 3D graph for moderating effect unstandardized scales View moderating relationship in one focused graph View rocky 3D graph for moderating effect with data points standardized scales View moderating relationship in one graph with data points gt View rocky 3D graph for moderating effect with data points unstandardized scales View moderating relationship in two graphs with data points gt a o ae 148 ier oo Mo ou O 281s _ oh AN EColl
163. rom Job performance to Age in a more reasonable and intuitively appealing way 85 WarpPLS 5 0 User Manual I Concluding remarks and additional issues This software provides users with a wide range of features including experimental features and also other features that are not available from other SEM software For example this software is the first and only at the time of this writing to explicitly identify nonlinear functions connecting pairs of latent variables in SEM models and calculate coefficients of association accordingly A wide range of features means that there are many coefficients graphs and other elements that users can choose to include in research reports and many possible interpretations of those elements This user manual does not cover all possible interpretations Users are strongly advised to keep abreast of the latest developments on methodological issues employing this software particularly those from research published in academic outlets e g academic journals Multivariate statistical analysis software systems like this software are inherently complex sometimes yielding results that are biased and disconnected with the reality of the phenomena being modeled Users are strongly cautioned against accepting the results provided by this software as a completely unbiased representation of the underlying reality that the software attempts to unveil No multivariate statistical analysis software yi
164. rovided by this software seem to be an improvement over them as indicated by Monte Carlo simulations Kock 2014b Blindfolding tends to perform somewhere in between Jackknifing and Bootstrapping If the number of resamples is set as very close to the sample size particularly with small sample sizes lower than 100 and with samples containing outliers Blindfolding performs similarly to Jackknifing With larger samples and with samples where the data points are evenly distributed on a scatter plot Blindfolding tends to performs more like Bootstrapping especially when the number of resamples is set as the same for both algorithms Prior to the development of the stable methods a recommendation was usually made in connection with Bootstrapping and Jackknifing Since the warping algorithms are also sensitive to the presence of outliers the recommendation was to estimate P values with both Bootstrapping and Jackknifing which are complementary resampling methods and use the P values associated with the most stable coefficients An indication of instability is a high P value 1 e statistically non significant associated with path coefficients that could be reasonably expected to yield low P values For example with a sample size of 100 a path coefficient of 0 2 could be reasonably expected to yield a P value that is statistically significant at the 0 05 level If that is not the case there may be a stability problem Another indication of ins
165. s 50 100 and 300 We show results for all of the structural paths in the model but restrict ourselves to loadings for one indicator in one factor since all loadings are the same in the true population model used This is also done to avoid repetition as the same general pattern of results for loadings repeats itself for all indicators in all factors As we can see from the summarized results the Factor Based PLS Type CFM1 algorithm yielded virtually unbiased estimates at the sample size of 300 whereas the PLS Mode A algorithm yielded significantly biased estimates at that same sample size One of the reasons for 97 WarpPLS 5 0 User Manual these significantly biased estimates with PLS Mode A are the relatively low loadings in the true population model used as a basis for simulation namely 0 7 for all indicators which tend to be a challenge for algorithms based on Wold s original PLS design Kock 2014 The relatively low loadings in the true population model apparently had little effect on the Factor Based PLS Type CFM1 algorithm s asymptotic convergence to the true values of the model parameters although those loadings probably slowed down that convergence somewhat as sample sizes increased In other simulations we conducted with higher loadings convergence was achieved at smaller sample sizes For several of the path coefficients and loadings the Factor Based PLS Type CFM1 algorithm yielded lower standard errors particularly as
166. s Journal of the Royal Statistical Society Series B 36 1 111 147 Temme D Kreis H amp Hildebrandt L 2006 PLS path modeling A software review Berlin Germany Institute of Marketing Humboldt University Berlin 107 WarpPLS 5 0 User Manual Tenenhaus M Vinzi V E Chatelin Y M amp Lauro C 2005 PLS path modeling Computational Statistics amp Data Analysis 48 1 159 205 Theil H 1958 Economic forecasts and policy Amsterdam Netherlands North Holland Wagner C H 1982 Simpson s paradox in real life The American Statistician 36 1 46 48 Wetzels M Odekerken Schroder G amp van Oppen C 2009 Using PLS path modeling for assessing hierarchical construct models Guidelines and empirical illustration M S Quarterly 33 1 177 196 Wold H 1980 Model construction and evaluation when theoretical knowledge is scarce In J Kmenta and J B Ramsey Eds Evaluation of econometric models pp 47 74 Waltham MA Academic Press Wold S Trygg J Berglund A amp Antti H 2001 Some recent developments in PLS modeling Chemometrics and Intelligent Laboratory Systems 58 2 131 150 Wooldridge J M 1991 A note on computing r squared and adjusted r squared for trending and seasonal data Economics Letters 36 1 49 54 108
167. s can be computationally very taxing With the emergence of the concept of big data the need to analyze large datasets is becoming increasingly common Bootstrapping employs a resampling algorithm that creates a number of resamples a number that can be selected by the user by a method known as resampling with replacement This means that each resample contains a random arrangement of the rows of the original dataset where some rows may be repeated The commonly used analogy of a deck of cards being reshuffled leading to many resample decks is a good one but not entirely correct because in Bootstrapping the same card may appear more than once in each of the resample decks Jackknifing on the other hand creates a number of resamples that equals the original sample size and where each resample has one row removed That is the sample size of each resample is the original sample size minus 1 Thus when Jackknifing is selected the number of resamples is automatically set as the sample size This refers to the most common form of jackknifing also known as delete 1 and classic jackknifing which is the one implemented through this software Blindfolding employs a resampling algorithm that creates a number of resamples a number that can be selected by the user by a method whereby each resample has a certain number of rows replaced with the means of the respective columns The number of rows modified in this way i
168. sample sizes increased This is noteworthy because the Factor Based PLS Type CFM1 algorithm is considerably more computationally complex than the PLS Mode A algorithm Kock 2014 and thus could have been expected to have a greater cost in terms of standard errors Nevertheless standard errors yielded at the sample size of 50 were generally higher for the Factor Based PLS Type CFM1 algorithm Apparently the difference was enough to have a negative effect on power as the ratios of path coefficients to standard errors indicate That is at the sample size of 50 one could argue based on the results that the PLS Mode A algorithm has greater power than the Factor Based PLS Type CFM1 algorithm for this particular model although the ratios of path coefficients to standard errors suggest that both algorithms may struggle to avoid type II errors at this small sample size particularly for the paths whose true coefficients were lower than 0 400 the path with the highest strength 98 WarpPLS 5 0 User Manual J Glossary Adjusted R squared coefficient A measure equivalent to the R squared coefficient with the key difference that it corrects for spurious increases in the R squared coefficient due to predictors that add no explanatory value in each latent variable block Like R squared coefficients adjusted R squared coefficients can assume negative values These are rare occurrences that normally suggest problems with the model in which they oc
169. sing data imputation methods in general Enders 2010 Newman 2014 Our results suggest that such concerns may not be warranted in the context of PLS based SEM 96 WarpPLS 5 0 User Manual 1 6 Factor Based PLS algorithms The Factor Based PLS algorithms available in this software combine the precision of covariance based SEM algorithms under common factor model assumptions Kock 2014 with the nonparametric characteristics of classic PLS algorithms Moreover the Factor Based PLS algorithms address head on a problem that has been discussed since the 1920s the factor indeterminacy problem Classic PLS algorithms yield composites as linear combinations of indicators which can be seen as factor approximations The Factor Based PLS algorithms on the other hand provide estimates of the true factors as linear combinations of indicators and measurement errors A Monte Carlo simulation was conducted to comparatively assess the performance of one of the Factor Based PLS algorithms namely the Factor Based PLS Type CFM1 algorithm against that of the PLS Mode A algorithm Like covariance based SEM algorithms the Factor Based PLS Type CFM1 algorithm is fully compatible with common factor model assumptions including the assumption that all indicator errors are uncorrelated Table I 6 adapted from Kock 2014 summarizes the results of this simulation Table I 6 Summarized Monte Carlo experiment results for composite based and factor based
170. sis results in one single file Project files are relatively small For example a complete project file of a model containing 5 latent variables 32 indicators columns in the original dataset and 300 cases rows in the original dataset will typically be only approximately 200 KB in size Simpler models may be stored in project files as small as 50 If a project file created with a previous version of the software is open the software automatically recognizes that and converts the file to the new version This takes placed even with project files where all of the five steps of the SEM analysis were completed However because each new version incorporates new features with outputs stored within new or modified 34 WarpPLS 5 0 User Manual software objects normally previous versions of the software cannot properly reuse project files created with more recent versions 35 WarpPLS 5 0 User Manual D Step 2 Read the raw data used in the SEM analysis Through Step 2 you will read the raw data used in the SEM analysis see Figure D 1 While this should be a relatively trivial step it is in fact one of the steps where users have the most problems with other SEM software Often a SEM software application will abort or freeze if the raw data is not in the exact format required by the SEM software or if there are any problems with the data such as missing values empty cells Figure D 1 Reading the raw data used in the SEM analys
171. size Af Warp Basic Resampling method Bootstrapping Jackknifing Blindfolding Parametric The settings chosen for each of the options can have a dramatic effect on the results of a SEM analysis At the same time the right combinations of settings can provide major insights into the data being analyzed As such the settings options should be used with caution and normally after a new project file with a unique name is created and the previous one saved This allows users to compare results and if necessary revert back to project files with previously selected settings A key criterion for the calculation of the weights observed in virtually all classic PLS based algorithms is that the regression equation expressing the relationship between the indicators and the latent variable scores has an error term that equals zero In other words in classic PLS based algorithms the latent variable scores are calculated as exact linear combinations of their indicators This is not the case with the new Factor Based PLS algorithms provided by this software as these new algorithms estimate latent variable scores fully accounting for measurement error The warping takes place during the estimation of path coefficients and after the estimation of all weights latent variable scores and loadings in the model The weights and loadings of a 21 WarpPLS 5 0 User Manual model with latent variables make up what is often referred to as the ou
172. standardized scales As mentioned earlier in this manual the Warp2 and the Warp2 Basic algorithms try to identify a U curve relationship between each pair of predictor criterion latent variables and if that relationship exists the algorithm used transforms or warps the scores of the predictor latent variables so as to better reflect the U curve relationship in the estimated path coefficients in the 75 WarpPLS 5 0 User Manual model The Warp3 and the Warp3 Basic algorithms the former being the default algorithm used by this software try to identify a relationship defined by a function whose first derivative is a U curve This type of relationship follows a pattern that is more similar to an S curve or a somewhat distorted S curve and can be seen as a combination of two connected U curves one of which is inverted Sometimes a Warp3 based analysis will lead to results that tell you that a relationship between two latent variables has the form of a U curve or a line as opposed to an S curve Similarly sometimes a Warp2 based analysis will tell you that a relationship has the form of a line This is because the underlying algorithms find the type of relationship that best fits the distribution of points associated with a pair of latent variables and sometimes those types are not S curves or U curves As with direct effects several graphs a k a plots for moderating effects can be viewed by clicking on a cell containing a
173. t variable in the model especially if the number of predictors is small Contrary to popular belief and in spite of what their name implies R squared coefficients are not calculated by squaring a correlation like measure They can assume negative values although these are rare occurrences that normally suggest problems with the model in which they occur e g severe collinearity or model misspecification Structural equation modeling SEM A general term used to refer to a class of multivariate statistical methods where complex relationships among latent variables and indicators are estimated at once In a SEM analysis each latent variable is typically measured through multiple indicators although there may be cases in which only one indicator is used to measure a latent variable Key measures of relationships among latent variables are path coefficients or standardized partial regression coefficients and corresponding P values Key measures of relationships among latent variables and their respective indicators are weights and loadings and corresponding P values 101 WarpPLS 5 0 User Manual Variance inflation factor VIF This is a measure of the degree of collinearity or multicollinearity among variables including both indicators and latent variables With latent variables collinearity can take two main forms vertical and lateral collinearity Kock amp Lynn 2012 Vertical or classic collinearity is predictor predictor laten
174. t covers all noncyclical nonlinear relationships These relationships include the logarithmic hyperbolic decay exponential decay exponential and quadratic relationships among others That is these relationships can be conceptually modeled as variations of U curve relationships The default inner model analysis algorithms available are the following Linear Warp2 Warp Basic Warp3 and Warp3 Basic All of these inner model algorithms share a common characteristic They calculate path coefficients through least squares regression algorithms based on the latent variable scores calculated through one of the outer model analysis algorithms available The Linear algorithm does not perform any warping of relationships The Warp2 algorithm tries to identify U curve relationships among linked latent variables and if those relationships exist the algorithm transforms or warps the scores of the predictor latent variables so as to better reflect the U curve relationships in the estimated path coefficients in the model Here the signs of the path coefficients are initially i e prior to the inner model least squares regressions assigned as the signs of the corresponding path coefficients obtained without any warping Similarly to the outer model basic versions the Warp2 Basic algorithm is a variation of the Warp2 algorithm that tends to reduce the number of instances of Simpson s paradox Wagner 1982 in the final results This happens be
175. t variable collinearity in individual latent variable blocks Lateral collinearity is a term coined by Kock amp Lynn 2012 that refers to predictor criterion latent variable collinearity a type of collinearity that can lead to particularly misleading results Full collinearity VIFs allow for the simultaneous assessment of both vertical and lateral collinearity in a SEM model 102 WarpPLS 5 0 User Manual K Acknowledgements The author would like to thank the users of WarpPLS for their questions comments and suggestions New features are frequently added in response to requests by users Revised text and other materials from previously published documents by the author have been used in the development of this manual 103 WarpPLS 5 0 User Manual L References Adelman I amp Lohmoller J B 1994 Institutions and development in the nineteenth century A latent variable regression model Structural Change and Economic Dynamics 5 2 329 359 Baron R M amp Kenny D A 1986 The moderator mediator variable distinction in social psychological research Conceptual strategic and statistical considerations Journal of Personality amp Social Psychology 51 6 1173 1182 Bera A K amp Jarque C M 1981 Efficient tests for normality homoscedasticity and serial independence of regression residuals Monte Carlo evidence Economics Letters 7 4 313 318 Berglund E Lytsy P amp Westerling R 2012
176. tability is a marked difference between the P values estimated through Bootstrapping and Jackknifing The recommendation above was based on the fact that P values can be easily estimated using two or more resampling methods by following the simple procedure outlined as follows Run a SEM analysis of the desired model using one of the resampling methods and save the project Then save the project again this time with a different name change the resampling method and run the SEM analysis again Then save the second project again Each project file will now have results that refer to one of the resampling methods The P values can then be compared and the most stable ones used in a research report on the SEM analysis While this is a perfectly valid approach for the calculation of P values as the coefficients to which the P values refer do not change across iterations it is very important to fully disclose this to the readers of the research report or reports written based on the SEM analyses An alternative to the above approach is the use one of the stable methods particularly the Stable3 method see e g Kock 2014b as these methods can be seen as yielding P values that are consistent with and often more precise than the P values generated by the software s other resampling methods Using these stable methods has the advantage of requiring much less manual work from the user Based on various tests in the context of PLS based SEM
177. tent variable It usually increases with the number of indicators used and is often slightly lower than the composite reliability coefficient another measure of reliability Discriminant validity of a measurement instrument Discriminant validity is a measure of the quality of a measurement instrument the instrument itself is typically a set of question statements A measurement instrument has good discriminant validity if the question statements or other measures associated with each latent variable are not confused by the respondents in terms of their meaning with the question statements associated with other latent variables Endogenous latent variable This is a latent variable that is hypothesized to be affected by one or more other latent variables An endogenous latent variable has one or more arrows pointing at it in the model graph Exogenous latent variable This is a latent variable that does not depend on other latent variables from a SEM analysis perspective An exogenous latent variable does not have any arrow pointing at it in the model graph Factor score A factor score is the same as a latent variable score see the latter for a definition Formative latent variable A formative latent variable is one in which the indicators are expected to measure certain attributes of the latent variable but the indicators are not expected to be highly correlated with the latent variable score because they i e the indicators are not e
178. ter model a k a measurement model whereas the path coefficients among latent variables make up what is often called the inner model a k a structural model The outer model analysis algorithms available are Factor Based PLS Type CFM1 Factor Based PLS Type REG1 Factor Based PLS Type PTH1 PLS Regression PLS Mode M PLS Mode M Basic PLS Mode A PLS Mode A Basic PLS Mode B PLS Mode B Basic and Robust Path Analysis All of these outer model algorithms share a common characteristic They calculate latent variable scores as exact linear combinations of their indicators or of their indicators and measurement errors With the exception of the Robust Path Analysis algorithm all of these algorithms perform iterations until they converge to a solution There has been a long and in some instances fairly antagonistic debate among proponents and detractors of the use of Wold s original PLS algorithms Adelman amp Lohmoller 1994 Lohmdller 1989 Wold 1980 in the context of SEM This debate has been fueled by one key issue which is analogous to the issue underlying the related principal components versus factor analysis debate Wold s original PLS algorithms do not deal with actual factors as covariance based SEM algorithms do but with composites which are exact linear combinations of indicators Kock 2014d The Factor Based PLS algorithms provided by this software have been developed specifically to address this perceived limitation of Wold
179. ting effects should be included in models with caution Standard errors are also provided for the loadings in the column indicated as SE for indicators associated with all latent variables They can be used in specialized tests Among other purposes these standard errors can be used in multi group analyses with the same model but different subsamples In these cases users may want to compare the measurement models to ascertain equivalence based on loadings and weights using a multi group comparison technique such as the one documented by Kock 2013 and Keil et al 2000 and thus ensure that any observed between group differences in structural model coefficients are not due to measurement model differences Keil et al s 2000 discussion on multi group analyses includes an equation 59 WarpPLS 5 0 User Manual that contains an error the correct form of the equation is used in Kock s 2013 discussion The equation in question is for the calculation of a pooled standard error and is one of the two equations discussed by Kock 2013 in the context of multi group analyses the other implements the alternative Satterthwaite method According to Keil et al 2000 the original proponent of the pooled standard error equation is Wynne Chin one of the world s foremost authorities on PLS based SEM Normalized loadings and cross loadings Normalized versions of the combined pattern and structure loadings and cross loadings tables a
180. tive latent variables can be used with this algorithm In other words using PLS Mode A does not make a formative latent variable become a reflective latent variable In it the inner model influences the outer model through path coefficients and correlations depending on whether the links go into or out from each latent variable respectively In this mode the outer model weights are calculated through a least squares regression where the latent variable is the predictor and the indicators are the criteria PLS Mode A Basic is a variation of 23 WarpPLS 5 0 User Manual PLS Mode A in which the inner model influences the outer model through the signs of the correlations among latent variables PLS Mode B is often referred to as the formative mode This is arguably incorrect for the same reason discussed above namely that both reflective and formative latent variables can be used with this algorithm In other words using PLS Mode B does not turn a reflective latent variable into a formative latent variable However PLS Mode B is often less stable than PLS Mode A and also tends to cause a significant increase in collinearity among linked latent variables In it the inner model influences the outer model through path coefficients and correlations depending on whether the links go into or out from each latent variable respectively In this mode the outer model weights are calculated through a least squares regression where the indicators ar
181. to the R squared of the criterion variable in each latent variable block by each of the predictor latent variables in the block The View path correlation ratios option allows users to identify statistical suppression instances MacKinnon et al 2000 by inspecting a table with the absolute path correlation ratios These ratios are calculated by dividing path coefficients by their respective correlation coefficients and taking the absolute values of those divisions An instance of statistical suppression occurs when a path coefficient is greater in absolute terms than the corresponding correlation associated with a pair of linked variables This leads to a path correlation ratio that is greater than 1 Like a Simpson s paradox instance a statistical suppression instance is a possible indication of a causality problem Spirtes et al 1993 suggesting that a hypothesized path is either implausible or reversed The following interpretations are suggested for absolute path correlation ratios ratio gt indicates statistical suppression lt ratio lt 1 3 weak suppression 1 3 lt ratio lt 1 7 medium 1 7 lt ratio strong In the same way that one can distinguish between a statistically significant and non significant direct association one can also distinguish between statistically significant and non significant suppression instances The View path correlation differences option allows users to do just that by inspecting
182. tware minus the licenses That is they are not demo versions Nevertheless they are provided for assessment purposes only and not for production purposes such as to analyze data and subsequently publish it as a consulting or research report Users must purchase licenses of the Software before they use it for production purposes Multivariate statistical analysis software systems are inherently complex sometimes yielding results that are biased and disconnected with the reality of the phenomena being modeled Users are strongly cautioned against accepting the results provided by the Software without double checking those results against past empirical results obtained by other means and or with other software applicable theoretical models and practical commonsense assumptions Under no circumstances is ScriptWarp Systems to be held liable for any damages caused by the use of the Software ScriptWarp Systems does not guarantee in any way that the Software will meet the needs of its users For more information ScriptWarp Systems P O Box 452428 Laredo Texas 78045 USA www scriptwarp com WarpPLS 5 0 User Manual Table of contents B THE MAIN WINDOW sestisssisssecesscsestsstiesesvesnsesincesvesccvessenssoossedebecesdecssent sendsvesecoseesesiesesescasesssieds docbeseebeeccdeecediecsdeesedscsesueceseateases 11 BT THE SEM ANALYSIS STEPS annan arn sveesdovudivenstenesdesestessdunssescessdees Gods deuswne sees eiese t
183. ument has good discriminant validity if the question statements or other measures associated with each latent variable are not confused by the respondents answering the questionnaire with the question statements associated with other latent variables particularly in terms of the meaning of the question statements The following criterion is recommended for discriminant validity assessment for each latent variable the square root of the average variance extracted should be higher than any of the correlations involving that latent variable Fornell amp Larcker 1981 That is the values on the diagonal of the table containing correlations among latent variables which are the square roots of the average variances extracted for each latent variable should be higher than any of the values above or below them in the same column Or the values on the diagonal should be higher than any of the values to their left or right in the same row which means the same as the previous statement given the repeated values of the latent variable correlations table The above criterion applies to reflective and formative latent variables as well as product latent variables representing moderating effects If it is not satisfied the culprit is usually an indicator that loads strongly on more than one latent variable Also the problem may involve more than one indicator You should check the loadings and cross loadings tables to see if you can identify the offendi
184. vailable on the main window as well as on several other windows displayed by the software The Open context sensitive User Manual file PDF option opens this document as a PDF file from a Web location in a context sensitive manner in this case at an area that is specific to the main window The Open User Manual file PDF option opens this document as a PDF file from a Web location and is not context specific The Open Web page with video for this window option opens a Web page with a video clip that is context specific in this case specific to the main window The Open Web page with links to various videos option is not context specific and opens a Web page with links to various video clips The Open Web page with WarpPLS blog option opens a Web page with the WarpPLS blog Similar help options are available from several other windows in this software 13 WarpPLS 5 0 User Manual B 2 Data The Data menu options allow you to view or save data and various statistics mostly descriptive statistics see Figure B 2 These menu options are discussed individually below Some of them are discussed in more detail later in this document Figure B 2 Data menu options Modify Settings Help View or save correlations and descriptive statistics for indicators View or save P values for indicator correlations View or save raw indicator data View or save unstandardized pre processed indicator data View or sa
185. variables Manifest variables that are not used in the model and that thus are not true indicators may simply be deleted prior to the inclusion in a research report 12 WarpPLS 5 0 User Manual H 10 View plot linear and nonlinear relationships among latent variables Choosing the menu option View plot linear and nonlinear relationships among latent variables causes the software to show a table with the types of relationships warped or linear between latent variables that are linked in the model see Figure H 10 1 The term warped is used for relationships that are clearly nonlinear and the term linear for linear or quasi linear relationships Quasi linear relationships are slightly nonlinear relationships which look linear upon visual inspection on plots of the regression curves that best approximate the relationships Figure H 10 1 Linear and nonlinear warped relationships among latent variables window Close Help Click on a Linear or Warped relationship cell to view plot ECUVar Proc Effi Effe Effi Proc ECUVar Proc Warped Effi Warped Warped Effe Warped Effi Proc Figure H 10 2 Graph options for direct effects including one with points and best fitting curve Save Settings Close Help View focused relationship graphs Siem increed SEAE AAE EEA st fitting curve and data points for multivariate relationship standardized scales View relationship graphs with data points and leg
186. ve unstandardized ranked pre processed indicator data View or save standardized pre processed indicator data View or save standardized ranked pre processed indicator data View or save data labels Save grouped descriptive statistics View or save latent variable a k a factor scores The View or save correlations and descriptive statistics for indicators option allows you to view or save general descriptive statistics about the data These include the following which are shown at the bottom of the table that is displayed through this option means standard deviations minimum and maximum values medians modes skewness and excess kurtosis coefficients results of unimodality and normality tests and histograms The unimodality tests for which results are provided are the Rohatgi Sz kely test Rohatgi amp Sz kely 1989 and the Klaassen Mokveld van Es test Klaassen et al 2000 The normality tests for which results are provided are the classic Jarque Bera test Jarque amp Bera 1980 Bera amp Jarque 1981 and Gel amp Gastwirth s 2008 robust modification of this test Since these tests are applied to individual indicators they can be seen as univariate or bivariate unimodality and normality tests These descriptive statistics are complemented by the option View or save P values for indicator correlations This option may be useful in the identification of candidate indicators for latent variables throug
187. xpected to be correlated with one another For example let us assume that the latent variable Satisf satisfaction with a meal is measured using the two following question statements I am satisfied with the main course and I am satisfied with the dessert Here the meal 99 WarpPLS 5 0 User Manual comprises the main course say filet mignon and a dessert a fruit salad Both main course and dessert make up the meal i e they are part of the same meal but their satisfaction indicators are not expected to be highly correlated with each other The reason is that some people may like the main course very much and not like the dessert Conversely other people may be vegetarians and hate the main course but may like the dessert very much Indicator The term indicator is frequently used as synonymous with that of manifest variable a convention that is used here Thus see the latter for a definition More technically though indicators are manifest variables that are actually used in the measurement model as direct measures of latent variables As such technically speaking there can be manifest variables that are not indicators if the manifest variables in question are part of the original dataset but not included in the measurement model Inner model In a structural equation modeling analysis the inner model is the part of the model that describes the relationships among the latent variables that make up the model
188. zes provided are similar to Cohen s 1988 f squared coefficients Standard errors and effect sizes are provided in the same order as the path coefficients so that users can easily visualize them and in certain cases use them to perform additional analyses Figure H 3 Standard errors and effect sizes for path coefficients window Close Help Standard errors for path coefficients ECU Effi Effe Proc Effi ECU Effi 0 109 Effe l0 056 0 055 Proc Proc Effi Effect sizes for path coefficients ECU Effi Proc Effi ECU Effi 0 030 Effe 0 015 0 284 Proc Proc Effi Even though the effect sizes provided are similar to Cohen s 1988 f squared coefficients they are calculated using a different procedure The reason for this is that the stepwise regression procedure proposed by Cohen 1988 for the calculation of f squared coefficients is generally not compatible with PLS based SEM algorithms The removal of predictor latent variables in latent variable blocks used in the stepwise regression procedure proposed by Cohen 1988 tends to cause changes in the weights linking latent variable scores and indicators thus biasing the effect size measures The effect sizes are calculated by this software as the absolute values of the individual contributions of the corresponding predictor latent variables to the R squared coefficients of the criterion latent variable in each latent variable block With the effect sizes users can ascerta

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