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WarpPLS 1.0 User Manual

1. WarpPLS 3 0 User Manual 5 OOO aD O OMBO aba cap D gt ER MONO CK CC gt gt CORED ER ane CEES G gt T ae C fore KENA OO xe Ce QOQ WarpPLS 3 0 User Manual WarpPLS 3 0 User Manual Ned Kock IN ScriptWarp Systems TM Laredo Texas USA WarpPLS 3 0 User Manual WarpPLS 3 0 User Manual February 2012 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 software
2. Exit option the software will WarpPLS 3 0 User Manual 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 an SEM analysis and then discard that project You can do this by simply not saving the project before exiting The Settings menu option You can view or change general SEM analysis settings through the Settings menu option Here you can select the analysis algorithm 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 This menu option is discussed in more detail later The Help menu options There are several help menu options available on the main window as well as on several other windows displayed by the software The Open help file for this window PDF option opens a PDF file with help topics that are context specific in this case specific to the main window The Open User Manual file PDF option opens this document 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 which case specific to the main window The Open Web page with links to
3. WarpPLS 3 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 in addition to helping avoid discriminant validity problems 44 WarpPLS 3 0 User Manual H x 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 that is for each latent variable block Here each VIF is associated with one predictor and relates to the link between that predictor and its latent variable criterion Or criteria when one predictor latent variable points at two or more different latent variables in the model Figure H 11 Block variance inflation factors window Close Help ECUVar i Effi Proc ECUVar Proc Effi 1 007 1 007 __ Efe 1 231 Effi Proc In this context a VIF is a measure of the degree of vertical collinearity or redundancy amo
4. and the path coefficient will be relatively high possibly high enough to yield a statistically significant effect The plots 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 48 WarpPLS 3 0 User Manual related However caution must be taken in the interpretation of these plots especially when the distribution of data points is very uneven An extreme example would be a warped plot in which all of the data points would be concentrated on the right part of the plot with only one data point on the far left part of the plot That single data point called an outlier could strongly influence the shape of the nonlinear relationship In these cases 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 an 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 se
5. 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 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 29 WarpPLS 3 0 User Manual H i View general SEM analysis results General SEM analysis results see Figure H 2 include the version of WarpPLS used in the SEM analysis project file details such as the project file name and when the file was last saved model fit indices 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 2 General SEM analysis results window Close Help General project information Version of WarpPLS used 3 0 Project path directory C Users nedkock Dog Project file W2B_ECU Twk_4LVsMod prj Last changed 25 Jan 2012 10 15 05 Last saved 28 Mar 2011 11 22 33 Raw data path directory C Users nedkock D Raw data file Data_ECUTwk xlsx Model fit indices and P values APC 0 198 P lt 0 001 ARS 0 165 P lt 0 001 AVIF 1
6. 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 an 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 22 WarpPLS 3 0 User Manual unbalanced For example you may move variables around so that they are all accidentally 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
7. excludes the outliers without having to modify and re read a dataset 14 WarpPLS 3 0 User Manual B v Ranked data Users can 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 original data is retained in unranked format When data is ranked typically the value distances that typify outliers are significantly reduced effectively eliminating outliers without any decrease in sample size 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 15 WarpPLS 3 0 User Manual C Step 1 Open or create a project file to save your work Through 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 an SEM analysis That is they contain the original data used in the analysis the graphical model the inner
8. for each of the options can have a dramatic effect on the results of a SEM analysis As such they should be used with caution and normally after a new project file with a unique name is created and the previous one saved so that users can revert back to project files with previously selected settings At the same time the right combinations of settings can provide major insights into the data being analyzed 10 WarpPLS 3 0 User Manual B iii Analysis algorithm 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 it 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 analysis algorithms available are Warp3 PLS Regression Warp2 PLS Regression PLS Regression and Robust Path A
9. inverted Sometimes a Warp3 PLS Regression 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 PLS Regression s results 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 For moderating relationships two plots are shown side by side see Figure H 14 Moderating relationships involve three latent variables the moderating variable and the pair of variables that are connected through a direct link Figure H 14 Plot of a moderating relationship involving three latent variables Low Effi The plots shown for moderating relationships refer to low and high values of the moderating variable and display the relationships of the variables connected through the direct link in those ranges The sign and strength of a path coefficient for a moderating relationship refers to the effect of the moderating variable on the strength of the direct relationship If the relationship becomes significantly stronger as one moves from the low to the high range of the moderating variable left to right plot then the sign of the path coefficient for the corresponding moderating relationship will be positive
10. 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 are expected to 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 iii WarpPLS 3 0 User Manual Table of contents A SOFTWARE INSTALLATION AND UNINSTALLATIION 66000000000000 0000000 000000000000 00000000000000 00000000000000 0000000 0e000e 1 A 1 NEW FEATURES IN VERSION 3 05 ian a Ng a San EE GK EEN RNB Na BA Bag DENE AN NGE vvvvovsseseescosoescevesdeaduesentnsn sn esevssessess 2 B THE M
11. options allow you to save unstandardized pre processed indicator data These options 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 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 WarpPLS 3 0 User Manual Two related menu options allow you to 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 The options that refer to unstandardized data allow you to view and save pre processed data prior to standardization The options that refer to standardized data allow you to view and 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 Save grouped descriptive statistics option is a special option that allows you to save descriptive statistics means and standard deviations organized by
12. 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 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 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 in 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
13. the main course and I am satisfied with the dessert Here the meal comprises the main course say filet mignon and a dessert a fruit salad Both main course and dessert make up the meal 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 MV a convention that is used here Thus see the latter for a definition More technically though indicators are MVs that are actually used in the measurement model as direct measures 51 WarpPLS 3 0 User Manual of LVs As such there can be MVs that are not indicators if the MVs 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 between the latent variables that make up the model In this sense the path coefficients are inner model parameter estimates Latent variable LV A latent variable is a variable that is measured through multiple variables called indicators or manifest variables MVs For example satisfaction with a meal may be a LV measured through
14. to which no other restrictions apply The latent variable name may contain letters numbers and even special characters such as or Then you 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 the latent variable score 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 definition are the following two Tam 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 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 expected to be correlated with each other For example l
15. variables and suggest that the latent variables measure the same construct which calls for the removal of one of the latent variables from the block or the model 45 WarpPLS 3 0 User Manual H xi 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 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 For saving correlations among all indicators including those indicators not included in the model use the menu option Data and the sub options therein This menu option is available from the main software window after Step 3 is completed This option is generally more meaningful for users who want to include the correlations among indicators in their research reports as part of a descriptive stat
16. we are talking about the number of resamples here not the original data sample size 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 in fact 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 presence 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 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 Bootstrapping tends to generate more stable resample path coefficients and th
17. 216 Good if lt 5 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 The model fit indices Three model fit indices are provided average path coefficient APC average R squared ARS and average variance inflation factor A VIF For the APC and ARS P values are also provided These P values are calculated through a complex process that involves resampling estimations coupled with Bonferroni like corrections Rosenthal amp Rosnow 1991 This is necessary since both fit indices are calculated as averages of other parameters The interpretation of the model fit 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 indices are of little 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 indices are a useful set of measures related to model quality When assessing the model fit with the data the following criteria are recommended First it is recommended that the P values for the APC and ARS be both lower than 0 05 that is significant at the 0 05 level Second it is recommended that the
18. AIN WINDOW siscsssessesscssescacessovacsossevtessocessesievssesesesosbestntsosdestadssbesbeusosseseasedbssbassessesessosedbesiensesnsscecssbeneerss 5 B I SAVE GROUPED DESCRIPTIVE STATISTICH tte Ettr ere En ESES eer ES ESE Ee Eeee EErEE eneee renen Ee 8 B IL VIEW OR CHANGE SETTINGS ccccccccccecececeseseessssssesesesecececececsceesesseseecuusussssssssesesesececececececeseusuaueusesssesenensesesess 10 B II ANALYSIS ALGORITHM cccccccceccccccccceceseceususeesssessceeeecececececscecsceueusususssssssssssssesesesecececeseceseseueususususesgensneneeeess 11 B IV RESAMPLING METHODEN 12 B V RANGE RESTRICTION tets te tettette t t t terser es eses ESE ee ere e EEE EEEEEES ENESES PERES ESEESE EEEEEEEEEE EEEE E EEE EEEa 14 B V RANKED E 15 C STEP 1 OPEN OR CREATE A PROJECT FILE TO SAVE YOUR WORK e essseseccssececessccsssosseosssoceessse 16 D STEP 2 READ THE RAW DATA USED IN THE SEM ANALYSIS 600000000000000000000 0000000 00000000000000 00000000000000 18 E STEP 3 PRE PROCESS THE DATA FOR THE SEM ANALYSIS sseoeeessecssssscesssecceesssecessssecsssscseesssoceese 20 F STEP 4 DEFINE THE VARIABLES AND LINKS IN THE SEM MODEL 6000000000000000000000000000000 000000000000 21 F I CREATE OR EDIT THE SEM MODEL ccsesssssssesessseececececccccccccsceceueususususesescsesesececececesecscsseseseseuaususssnensesesesess 22 F I CREATE OR EDIT LATENTVARIARBLE 25 G STEP 5 PERFORM THE SEM ANALYSIS AND VIEW THE RESULTS sseess
19. AVIF be lower than 5 Typically the addition of new latent variables into a model will increase the ARS even if those latent variables 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 30 WarpPLS 3 0 User Manual The AVIF index will increase if new latent variables are added to the model in such a way as to add multicollinearity to the model which 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 thing those should be combined into one single latent variable Thus the AVIF brings in a new dimension that adds to a comprehensive assessment of a model s overall predictive and explanatory quality 31 WarpPLS 3 0 User Manual H ii View path coefficients and P values Path coefficients and respective P values are shown together as can be seen in Figure H 3 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 cons
20. For example Step 5 which is to perform the SEM analysis and view the results cannot be carried out before Step takes place which is to open or create a project file to save your work Therefore unavailable steps have their push buttons grayed out and deactivated until it is time for them 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 project as and Exit Through the Save project option you can choose a folder and file name and save a project that is currently open or has just been created 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 This option is useful in the SEM analysis of multiple models where each 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
21. Procl i 0 037 0 034 0 844 0 029 Proc2 0 073 0 130 0 885 0 006 Proc3 lo 0 041 0 106 0 814 0 036 Procl Effil lo 0 113 0 068 0 133 0 794 Procl Effi2 lo 0 082 0 019 0 068 0 791 Procl Effi3 lo 0 053 0 035 0 113 0 765 Procl Effid lo 0 089 0 033 0 050 0 732 Proc1 Effis lo 0 064 0 059 0 180 0 729 Proc2 Effil 0 0 007 0 818 Since loadings are from a structure matrix and unrotated they are always within the 1 to 1 range 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 loadings which are shown within parentheses will be high and cross loadings will be low P values are also provided for indicators associated with all latent variables These P values are often referred to as validation parameters of a confirmatory factor analysis 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 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 classical factor analysis For research reports users will typically use the table of combined load
22. VE A measure associated with a latent variable which is used in the assessment of the discriminant validity of a measurement instrument Composite reliability coefficient This is a measure of reliability associated with a latent variable 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 latent 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 ins
23. Var Proc i Effi Proc ECUVari 1 000 0 222 0 040 Procl 0 185 0 844 0 304 Proc2 0 178 0 885 0 308 Proc3 0 202 0 814 0 236 Effil 0 028 0 394 0 140 Effi2 0 026 0 402 0 115 Effi3 0 045 0 406 0 126 Effi4 0 061 0 306 0 100 Gu 0 045 0 413 0 252 Effel 0 093 0 347 0 168 Effe2 0 141 0 312 0 134 Effe3 0 107 0 325 0 139 Effe4 0 126 0 333 0 170 Effe5 0 126 0 264 0 147 Effe6 0 133 0 282 0 167 Effe7 0 049 0 334 0 178 Effil Procl 0 014 0 292 0 794 Effil Proc2 0 030 0 301 i 0 818 Effil Proc3 0 058 0 220 0 781 Effi2 Procl 0 031 0 250 0 791 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 Still some researchers recommend using this 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 same as those provided in the combined loadings and cross loadings table The cross loadings however are different 38 WarpPLS 3 0 User Manual H vii View indicator weights Indi
24. alysis literature in connection with VIFs 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 likelihood that one or more will be redundant increases This will be reflected in high VIFs 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 use
25. and outer model structures and the results Figure C 1 Step 1 window Trter the name of a file to save your work E ie 2 H GUGU E b ie 4 You are now in Step 1 Open or create a project file tc work lt Ze HI gt When you press the Open project file button you 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 windasa 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 but it will no longer use it 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 o
26. as 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 can be easily dragged and dropped with the pointing device e g mouse anywhere within the 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 equals 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 Given tha
27. ased 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 moderating 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 Keil et al 2000 and thus ensure that any observed between group differences in structural model coefficients are not due to measurement model differences 36 WarpPLS 3 0 User Manual H v View pattern loadings and cross loadings Pattern loadings and cross loadings are provided in a table with each cell referring to an indicator latent variable link see Figure H 6 Latent variable names are listed at the top of each column and indic
28. atent variables are created to store information about those moderating effects using a procedure described and validated by Chin et al 2003 The more moderating links there are in a model the longer this sub step will take 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 with significantly more indicators than reflective variables 24 WarpPLS 3 0 User Manual F ii 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 the 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 sl sTele_Voice ECU Effe Effi Proc Rand10 Remove Add Measurement model o Reflective You create a latent variable by entering a name for it which may have no more than 8 characters but
29. ator names at the beginning of each row In this table both the loadings and cross loadings are from a pattern matrix 1 e rotated Figure H 6 Pattern loadings and cross loadings window Close Help ECUVar Proc Effi Effi Proc ECUVari 1 000 0 000 0 000 0 000 Proci 0 006 0 830 0 036 0 027 Pog 0 035 0 876 0 076 0 008 Broch 0 045 0 838 0 046 0 037 Effil 0 010 0 008 0 914 0 013 Effi2 0 072 0 055 0 937 0 043 Effi3 0 009 0 069 0 811 0 035 Effi4 0 079 0 114 0 871 0 012 EFS 0 002 0 007 0 667 0 111 Effel 0 044 0 062 0 050 0 005 Effe2 0 028 0 005 0 054 0 029 Effe3 0 004 0 029 0 082 0 021 Effed 0 010 0 017 0 038 0 003 Effe5 0 040 0 077 0 006 0 009 Effe6 0 028 0 035 0 066 0 026 Effe7 0 068 0 001 0 134 0 016 Effil Procl 0 085 0 119 0 117 0 764 Effil Proc2 0 011 0 003 0 012 0 808 Effil Proc3 0 138 0 021 0 054 0 799 Effi2 Proc1 0 040 0 057 0 083 0 784 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 Renche
30. bles including moderating latent variables These can be used for indicator 39 WarpPLS 3 0 User Manual 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 One example would be the removal of only 2 indicators out of 16 by the use of this rule of thumb Otherwise the criteria below should be employed Two criteria one more conservative and one more relaxed are recommended by the multivariate an
31. can assume negative values Acceptable predictive validity in connection with an endogenous latent variable is suggested by a Q squared coefficient greater than zero 42 WarpPLS 3 0 User Manual H ix View correlations among latent variables Among the results generated by this software are tables containing latent variable correlations and the P values associated with those correlations see Figure H 10 On the diagonal of the latent variable correlations table are the square roots of the average variances extracted for each latent variable These results are used for the assessment of the measurement instrument s discriminant validity Figure H 10 Correlations among latent variables window Close Help Latent variable correlations ECUVar Proc Effi Effe Effi Proc ECUvar 1 000 0 222 0 035 0 122 0 040 Proc 0 222 0 848 0 456 0 344 0 334 Effi 0 035 0 456 0 843 0 525 0 172 Effe 0 122 0 344 0 525 0 912 0 173 Effi Proc 0 040 0 334 0 172 0 173 0 760 Note Square roots of average variances extracted AVE sl shown on diagonal P values for correlations ECUVar i Effi Proc ECUVar 1 000 0 502 Proc lt 001 lt 001 Effi 0 551 0 003 Effe 0 038 0 003 Effi Proc 0 502 1 000 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 pa
32. cator weights are provided in a table much in the same way as indicator loadings are see Figure H 8 All cross weights are zero because of the way they are calculated through PLS regression Each latent variable score is calculated as an exactly linear combination of its indicators where the weights are multiple regression coefficients linking the indicators to the latent variable Figure H 8 Indicator weights window Close Help Effi i Effe T Proc Effi WE Pk EII E 0 252 U_UUU U_UUU U_ UUU p ZU UU Effi2 j 0 249 0 000 0 000 0 000 i lt 0 001 Effi i 0 231 0 000 0 000 0 000 i lt 0 001 Effi4 i 0 229 0 000 0 000 0 000 lt 0 001 pes i 0 224 0 000 0 000 0 000 lt 0 001 Effel i 0 000 0 160 0 000 0 000 i lt 0 001 Effe2 i 0 000 0 163 0 000 0 000 i lt 0 001 Effe3 0 000 0 143 0 000 0 000 lt 0 001 Effed f 0 000 0 163 0 000 0 000 g lt 0 001 Effe5 i 0 000 0 158 0 000 0 000 lt 0 001 Effe6 i 0 000 0 156 0 000 0 000 f lt 0 001 Effe7 Jo 0 000 0 154 0 000 0 000 j lt 0 001 Procl lo 0 000 0 000 0 391 0 000 lt 0 001 Brech 0 000 0 000 0 410 0 000 7 lt 0 001 0 000 0 000 0 377 0 000 i lt 0 001 0 000 0 000 0 000 0 092 7 lt 0 001 Procl Effi2 i 0 000 0 000 0 000 0 091 4 lt 0 001 Procl Effi3 i 0 000 0 000 0 000 0 088 f lt 0 001 Procl Effid i 0 000 0 085 aa nen A WL LL WA ECHTEN P values are provided for weights associated with all latent variables Th
33. 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 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 on 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 When 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 cases the full collinearity measures will confirm that collinearity is too high in their models for the analysis results to be considered credible Once Step 5 is completed two new options become available from the main window One of the new options is actually a sub option under the Data menu option which becomes available after Step 3 is completed this new sub option allows users to save latent variable a k a factor scores This option is provided on the main window for completeness as it is also available under the Save menu option on the results windo
34. curve may also be seen as a combination of two U curves one of which on the right is inverted Figure H 13 Plot of a relationship between pair of latent variables Close Save Data points and regression line or curve standardized values T T In some cases nonlinear relationship shapes may be at odds with the corresponding path coefficients For example a path coefficient may be negative while the corresponding relationship shape may appear to be suggestive of an overall positive relationship Some Statisticians believe that this may suggest a cause effect inference error made at the model 47 WarpPLS 3 0 User Manual design stage of the type that characterizes a phenomenon known as Simpson s paradox Wagner 1982 As mentioned earlier in this manual the Warp2 PLS Regression algorithm tries to identify a U curve relationship between latent variables and if that relationship exists the algorithm 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 model The Warp3 PLS Regression algorithm the default algorithm used by this software tries 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
35. d 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 Keil et al 2000 and thus ensure that any observed between group differences in structural model coefficients particularly in path coefficients are not due to measurement model differences 40 WarpPLS 3 0 User Manual H viii 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 9 R squared and Q squared coefficients are provided only for endogenous latent variables and reflect the percentage 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 these are measures of reliability Average variances extracted AVE 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 Figure HO Latent variable coefficients window Close Help Proc Effi R squared Composite reliab 0 953 Cronbach s alpha 0 947 Avg var ext
36. dow 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 possible problems in future versions of the software The software s main window see Figure B 1 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 Figure B 1 The main window Settings Hel y eae Open help file for this window PDF l Save project Open User Manual file PDF Save project as View or change settings Exit 4 Open Web page with video for this window Open Web page with links to various videos Open Web page with WarpPLS blog f Ce farpPLS 3 0 Project file not yet d fined um wen wW a Project Settings Help Welcome to WarpPLS 3 0 a software developed by Ned Kock using MATLAB C and Java Proceed This software will help you conduct a structural equation modeling SEM analysis using the method of warped partial least squares regression The analysis will be conducted through the following steps Proceed Step 1 Open or create a project file to save your work Dase ROSS ee E E The steps must be carried out in the proper sequence
37. e Erlbaum 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 Diamantopoulos A amp Winklhofer H 2001 Index construction with formative indicators An alternative scale development Journal of Marketing Research 37 1 269 177 Efron B Rogosa D amp Tibshirani R 2004 Resampling methods of estimation In N J Smelser amp P B Baltes Eds International Encyclopedia of the Social amp Behavioral Sciences pp 13216 13220 New York NY Elsevier 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 Giaquinta M 2009 Mathematical analysis An introduction to functions of several variables New York NY Springer 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 Q
38. e 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 data 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 column averages in a later step Users may want to employ different approaches to handle missing values such as deleting the rows where they appear or manually replacing them with the average of nearby values on the same column The most widely used approach and also generally the most reliable is replacing the missing values with column averages While this is done automatically by the software you 18 WarpPLS 3 0 User Manual 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 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 i
39. efficients that were not available before WarpPLS 3 0 User Manual Indirect and total effects Indirect and total effects are now calculated and shown together with the corresponding P values standard errors and effect sizes The calculation of 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 mediating effects that have traditionally relied on non automated and thus time consuming calculations based on linear Preacher amp Hayes 2004 and nonlinear Hayes amp Preacher 2010 assumptions P values for all weights and loadings P values are now shown for all weights and loadings including those associated with indicators that make up moderating variables With these P values users can check whether moderating latent variables satisfy validity and reliability criteria for either reflective or formative measurement This can help users demonstrate validity and reliability in hierarchical analyses involving moderating effects where double triple etc moderating effects are tested For instance moderating latent variables can be created added to the model as standardized indicators and then their effects modeled as being moderated by other latent variables an exa
40. ernative approach to the analysis of mediating effects which is arguably much less time consuming and prone to error than the 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 33 WarpPLS 3 0 User Manual effects with more than one mediating variable Indirect and total effects are discussed in more detail later 34 WarpPLS 3 0 User Manual H iv View combined loadings and cross loadings Combined loadings and cross loadings are provided in a table with each cell referring to an indicator latent variable link see Figure H 5 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 e rotated Figure H 5 Combined loadings and cross loadings window Close Help Effe Proc Proc Effi Eris la o uz 17 MH H VUE HM U UST Effid I 0 813 0 008 0 106 0 011 pes 0 796 0 193 0 014 0 114 Effel I 0 044 0 931 0 051 0 004 Effe2 l 0 056 0 947 0 009 0 029 Effe3 l 0 081 0 831 0 031 0 021 Drei 0 040 0 952 0 023 0 002 Effe5 I 0 001 0 917 0 064 0 006 Effe6 0 069 0 906 0 030 0 026 Effe7 i 0 143 0 894 0 020 0 020
41. ese 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 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 instance moderating latent variables can be created added to the model as standardized indicators and then their effects modeled as being moderated by other latent variables an example of double moderation In addition to P values variance inflation factors VIFs are also provided for the indicators of all latent varia
42. estion 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 52 WarpPLS 3 0 User Manual 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 latent variable in the model especially if the number of predictors is small Structural equation modeling SEM A general term used to refer to a class of multivariate statistical methods where relationships between latent variables are estimated usually as path coefficients or standardized partial regression coefficients In an 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 Variance inflation factor VIF This is a measure of the degree of multicollinearity among variables including both indicator
43. et us assume that the latent variable Satis 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 a fruit salad Both main course and dessert make up the meal Oe 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 25 WarpPLS 3 0 User Manual 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 each other they cannot be expected to be highly correlated with their latent variable s score So 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 then the measurement model should be set as reflective If the indicators are not expected to be highly correlated even though they clearly refer to the same latent variable then the measurement model should be set as formative 26 WarpPLS 3 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
44. ew York NY McGraw Hill Nunnaly J C 1978 Psychometric theory New York NY McGraw Hill 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 Rencher A C 1998 Multivariate statistical inference and applications New York NY John Wiley amp Sons Rosenthal R amp Rosnow R L 1991 Essentials of behavioral research Methods and data analysis Boston MA McGraw Hill Stone M 1974 Cross validatory choice and assessment of statistical predictions Journal of the Royal Statistical Society Series B 36 1 111 147 Wagner C H 1982 Simpson s paradox in real life The American Statistician 36 1 46 48 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 55
45. f 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 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 28 WarpPLS 3 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 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 each latent va
46. f 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 analysis 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 KB 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 software objects normally previous versions of the software cannot properly reuse project files created with more recent versions 16 WarpPLS 3 0 User Manual 17 WarpPLS 3 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 an SEM software application will abort or freeze
47. fending latent variables If users so choose they can proceed with the analysis anyway but in most cases the full collinearity measures will confirm that collinearity is too high in their models for the analysis results to be considered credible Full collinearity VIFs VIFs are now shown for all latent variables separately from the VIFs calculated for predictor latent variables in individual latent variable blocks These new VIFs are calculated based on a full collinearity test 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 blocks Lateral collinearity is a new term 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 Lindell amp Whitney 2001 bias tests that are more conservative than and arguably superior to the traditionally used tests relying on exploratory factor analyses Incremental code optimization At several points the code was optimized for speed stability and coefficient estimation precision This led to incremental gains in speed even as a significant number of new features were added Several of these new features required new and complex calculations mostly to generate co
48. fficients ECU Effi Proc Effi ECU efi ona Effe 0 015 0 284 Proc Proc Effi The effect sizes are calculated as the absolute values of the individual contributions of the corresponding predictor latent variables to the R square coefficients of the criterion latent variable in each latent variable block With the effect sizes users can ascertain 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 One of the 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 Preacher amp Hayes 2004 for linear relationships and Hayes amp Preacher 2010 for nonlinear relationships The latter discussed by 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 The classic approach used for testing mediating effects is the one discussed by Baron amp Kenny 1986 which does not rely on standard errors An alt
49. figure out what the corresponding P values are Often users have to resort to 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 32 WarpPLS 3 0 User Manual H iii 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 4 The effect sizes are 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 4 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 0 056 0 055 Proc Proc Effi Effect sizes for path coe
50. groups defined based on certain parameters this option is discussed in more detail below WarpPLS 3 0 User Manual B i Save grouped descriptive statistics When the Save grouped descriptive statistics option is selected a data entry window is displayed see Figure B 3 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 3 Save grouped descriptive statistics window Save Close Help Grouping variable ECUEmail Variables to be Variables in grouped data file jsEmail_Elist ECUBoard ECUFiles ECULotusNotes ECUEnewslet ECUAutoRout ECUFTP ECUWebPage Add Figure B 4 shows the grouped statistics data saved through the window shown in Figure B 3 The tab delimited txt file was opened with a spreadsheet program and contained the data on the left part of the figure Figure B 4 Grouped descriptive statistics bar chart ECU 0 5 ECU 5 10 ECU S 10 That data on the left part of Figure B 4 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 WarpPLS 3 0 User Manual means analysis
51. iable Create moderating link Cancel model creation editing all editing is lost Move latent variable ene E P Delete moderating link Save model into jpg file 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 dr 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 option 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 1617 The F refers to the measurement model where F means formative and 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
52. ider the case in which the cell shows 0 225 and the column refers to the latent variable ECU Var 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 Since the results refer to standardized variables this 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 Figure H 3 Path coefficients and P values window Close Help Path coefficients _ E ECUVar i Effi Proc ECUVar Proc Effi E Effi Proc P values _ EEN EE Proc Effi Effe Effi Proc ECUVar Proc lt 0 001 Effi 0 406 lt 0 001 Effe lt 0 001 Effi Proc The P values shown are calculated by resampling and thus are specific to the resampling method and number of resamples selected by the user As mentioned earlier the choice of number of resamples is only meaningful for the bootstrapping and blindfolding methods and numbers higher than 100 add little to the reliability of the P value estimates when bootstrapping is used One puzzling aspect of many publicly available PLS based SEM software systems is that they do not provide P values instead providing standard errors and T values and leaving the users to
53. 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 Step 2 window Viewing and accepting data File import wizard WB aaa kaanan rar EEr OOO ae Does the dats look correct Yee e v meaa me raw Gata usea In me oom ead raw data file button you will be asked the data for the analysis is a file whose type can be any of the ha Read raw data file ile comma delimited text file Go back ith multiple sheets the sheet with the data torkbook names of the variables latent construct 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 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 th
54. ings 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 convergent validity that the P values associated with the loadings be lower than 0 05 and that the loadings be equal to or greater than 0 5 Hair et al 1987 2009 35 WarpPLS 3 0 User Manual 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 Effil Proc1 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 b
55. istics table This option also generates means and standard deviations for each of the indicators Indicators that are not used in the model may simply be deleted prior to the inclusion in a research report 46 WarpPLS 3 0 User Manual H xii View plot linear and nonlinear relationships among latent variables The software shows a table with the types of relationships warped or linear between latent variables that are linked in the model see Figure H 12 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 12 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 Plots with the points as well as the regression curves that best approximate the relationships 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 See Figure H 13 for an example of one of these plots In this example the relationship takes the form of a distorted S curve The
56. lections under the Settings options to a range that excludes the outlier This allows for the 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 can 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 the SEM analysis steps again 49 WarpPLS 3 0 User Manual H xiii View indirect and total effects The software allows users to view indirect and total effects associated with all latent variables that are linked via one or more paths with more than one segment see Figure H 15 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
57. means of the respective columns The number of rows modified in this way in 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 Effect sizes Cohen s 1988 f squared effect size coefficients are now calculated and shown for all path coefficients These are calculated as the absolute values of the individual contributions of the corresponding predictor latent variables to the R square coefficients of the criterion latent variable in each latent variable block With these effect sizes users can ascertain 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 Estimated collinearity Collinearity is now estimated before the SEM analysis is ran When 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 of
58. minating outliers 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 Thus a concomitant increase in collinearity may be observed but typically not to the point of threatening the credibility of the results This option 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 Restricted ranges Users can now run their analyses with subsamples defined by a range restriction variable which may be standardized or unstandardized This option is useful in multi group analyses whereby separate analyses are conducted for each subsample and the results then compared with 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 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 WarpPLS 3 0 User Manual 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 Standard errors for all weights and loadings Standard errors are now sh
59. 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 21 WarpPLS 3 0 User Manual F i 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 and to a context specific help file 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 Model options Latent variable options Direct link of Latent variable options Di Save model and close Conese wed ah Create latent variable bie link options Mc Moderating link options Hel Show hide indicators Edit latent variable Elte E Clear model deletes all latent variables Delete latent var
60. 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 creation 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 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 other files e g a Word file 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 h
61. mple of double moderation Predictive validity Stone Geisser Q squared coefficients Geisser 1974 Stone 1974 are now calculated and shown for each endogenous variable in an SEM model 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 Sometimes referred to as a resampling analog of the R squared it is often similar in value to that measure even though unlike the R squared coefficient the Q squared coefficient can assume negative values Acceptable predictive validity in connection with an endogenous latent variable is suggested by a Q squared coefficient greater than zero Project files for previous versions 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 Ranked data Users can now select an option to conduct their analyses with only ranked data whereby all the data is automatically ranked prior to the SEM analysis the original data is retained in unranked format When data is ranked typically the value distances that typify outliers are significantly reduced effectively eli
62. nalysis The Warp2 PLS Regression algorithm tries to identify a U curve relationship between latent variables and if that relationship exists the algorithm 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 model The Warp3 PLS Regression algorithm the default algorithm used by the software tries to identify a relationship between latent variables 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 The PLS Regression algorithm does not perform any warping of relationships It is essentially a standard PLS regression algorithm whereby indicators weights loadings and factor scores a k a latent variable scores are calculated based on an algorithm that maximizes the variance explained in the latent variable scores by the latent variable indicators after which path coefficients are estimated using a robust path analysis algorithm A key criterion for the calculation of the weights observed in virtually all PLS based algorithms is that the regression equation expressing the relationship between the indicators and the factor scores has an error term that equals zero In other words the factor scores are calculated as exact linear c
63. nd 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 which 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 17 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
64. ng the latent variables that are hypothesized to affect another latent variable This classic type of collinearity refers to predictor predictor collinearity in a latent variable block containing one or more latent variable predictors and one latent variable criterion 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 suggests that VIFs of 3 3 or lower suggest the existence of no vertical multicollinearity in a latent variable block 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 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 VIFs be lower than 5 a more relaxed criterion is that they be lower than 10 Hair et al 1987 2009 Kline 1998 These latter criteria may be particularly relevant in the context of path analyses where all latent variables are measured through single indicators High VIFs usually occur for pairs of predictor latent
65. nging 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 even though unlike the R squared coefficient the Q squared coefficient can assume negative values Reflective latent variable A reflective latent variable is one in which all of the indicators are expected to be highly correlated with the latent variable score 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 two indicators Those indicators store answers to the two qu
66. not proceed with the SEM analysis but the results may be unstable and in some cases completely unreliable It is not uncommon for rank problems to be reported and the results of the ensuing SEM analysis still remain 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 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 usually assuming values toward the left or right end of those extremes sometimes beyond 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 relationship from positive to negative 1 e changing the association 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 it is apparent that they are due to data collection er
67. oefficient 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 instability is a marked difference between the P values estimated through bootstrapping and jackknifing P values can be easily estimated using two or more resampling methods by following this simple procedure Run an 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 13 WarpPLS 3 0 User Manual B v Range restriction Users can 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 Two range restriction variable types are available standardized a
68. ombinations of their indicators PLS regression is the underlying weight calculation algorithm used in both Warp3 and Warp2 PLS Regression The warping takes place during the estimation of path coefficients and after the estimation of all weights and loadings in the model The weights and loadings of a model with latent variables make up what is often referred to as the outer 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 Finally the Robust Path Analysis algorithm is a simplified algorithm in which factor scores are calculated by averaging all of the indicators associated with a latent variable that is in this algorithm weights are not estimated through PLS regression This algorithm is called Robust Path Analysis because as with most robust statistics methods the P values are calculated through resampling If all latent variables are measured with single indicators the Robust Path Analysis and the PLS Regression algorithms will yield identical results 11 WarpPLS 3 0 User Manual B iv Resampling method One of a few resampling methods may be selected bootstrapping jackknifing and blindfolding Bootstrapping the software s default 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
69. own for all loadings and weights 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 using a multi group comparison technique such as the one documented by Keil et al 2000 and thus ensure that any observed differences in structural model coefficients are not due to measurement model differences VIFs for all indicators VIFs are now shown for all indicators including those associated with moderating latent variables With these VIFs users can check whether moderating latent variables satisfy criteria for formative measurement in case they do not satisfy validity and reliability criteria for reflective measurement This can be particularly helpful in hierarchical analyses involving moderating effects where formative latent variables are frequently employed including cases where double triple etc moderating effects are tested Here moderating latent variables can be created added to the model as standardized indicators and then their effects modeled as being moderated by other latent variables with this process being repeated at different levels WarpPLS 3 0 User Manual B The main window Prior to displaying the software s main window a command prompt window is shown and kept open for the duration of the SEM analysis session Do not try to close this command prompt win
70. pPLS 3 0 or C Program Files x86 WarpPLS 3 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 interfere with other programs not even with MATLAB the main MATLAB program if you have it installed on your computer WarpPLS 3 0 User Manual A i New features in version 3 0 Addition of latent variables as indicators Users now have the option of adding latent variable scores to the set of standardized indicators used in an SEM analysis This option 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 This option is also useful in hierarchical analysis where users define second order and higher order latent variables and then conduct analyses with different models including latent variables of different orders Blindfolding Users now have the option of using a third resampling algorithm namely blindfolding in addition to bootstrapping and jackknifing Blindfolding is a resampling algorithm that creates a number of resamples a number that can be selected by the user where each resample has a certain number of rows replaced with the
71. r 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 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 would 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 37 WarpPLS 3 0 User Manual H vi View structure loadings and cross loadings Structure loadings and cross loadings are provided in a table with each cell referring to an indicator latent variable link see Figure H 7 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 structure matrix i e unrotated Often these are the only loadings and cross loadings provided by other PLS based SEM software systems Figure H 7 Structure loadings and cross loadings window Close Help ECU
72. rac 0 578 Full collin VIF 1 138 Q squared 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 latent 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 compositive 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 Ifa 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 con
73. riable these can be useful in some specialized applications e g users may want to generate customized graphs based on those scores Just to be clear the factor scores are the latent variable scores The term factor is often used in this context The reason is that factor analysis can be seen as a special case of SEM analysis Figure H 1 View and save results window View Save Close Help Save all model estimates into a tab delimited txt file Save Close Help Save correlations among indicators into a tab delimited txt file Save latent variable a k a factor scores into a tab delimited txt file View general results Save model into jpg file View path coefficients and P values View standard errors and effect sizes for path coefficients effi View combined loadings and cross loadings y View pattern loadings and cross loadings ECH o R 0 22 View structure loadings and cross loadings View indicator weights p 0 19 View latent variable coefficients P 4 02 View correlations among latent variables View variance inflation factors View correlations among indicators View plot linear and nonlinear relationships among latent variables View indirect and total effects The path coefficients are noted as beta coefficients Beta coefficient is another term often used to refer to path coefficients in PLS based SEM analysis this term is commonly used in multiple regression analysis The P values are displayed
74. ror 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 try 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 20 WarpPLS 3 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 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 an SEM
75. s and latent variables With latent variables collinearity can take two main forms vertical and lateral collinearity Vertical or classic collinearity is predictor predictor latent variable collinearity in individual blocks Lateral collinearity is a new term 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 an SEM model 53 WarpPLS 3 0 User Manual J References 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 Cenfetelli R amp Bassellier G 2009 Interpretation of formative measurement in information systems research MIS Quarterly 33 4 689 708 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 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 Lawrenc
76. s 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 analysis where 27 WarpPLS 3 0 User Manual 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 is 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 this software calculates model fit 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 many indicators even if they are reflective moderating effects particularly if they associate latent variables with many indicators setting the number o
77. s 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 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 19 WarpPLS 3 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 values This step will also let you know 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 that does not mean that you can
78. sbesdecsesustassouses 54 iv WarpPLS 3 0 User Manual A 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 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 go 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 version 2 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 which is usually C Program Files War
79. sececcssececssseccssssseesssoceessse 27 H VIEW AND SAVE RESULTS sicssseccestscsscecvssvesessobssovecssswesesesssesvosecetchscdessesessecsouuvoussesssuvesveseisesaetinsveavcsvcantvesseoxeds 29 H I VIEW GENERAL SEM ANALYSIS RESULTS si nsireie srece etice isaidrisriees osetite tr Enida dedsr ine ieri read si ikert S rsd tsei sasi 30 H 11 VIEW PATH COEFFICIENTS AND DNALUES 32 Hm VIEW STANDARD ERRORS AND EFFECT SIZES FOR PATH COEFRICIENTS 33 H mW VIEW COMBINED LOADINGS AND CROSS LOADINOS 35 H v VIEW PATTERN LOADINGS AND CROSS LOADINOS 37 H VI VIEW STRUCTURE LOADINGS AND CROSS LOADINGS sesesesesesesesrsesrsrtrtrerrrerrresrersressssesrerestetererereerseeeeeesests 38 FL Vil VIEW INDICATOR WEIGHTS 35 cc3 ssi sai cee AN a Na Ga E Bagel es buen Gs lec A A E Aa SE AE SEA een 39 H vum VIEW LATENT VARIABLE CORBPRICIENTg tetette trer ttt ttt ttrt rtr PESES ESE EE eSEE E Eere E EE EEeEeE eneren Ee 41 HG VIEW CORRELATIONS AMONGLATENTVARIABLES 43 HX VIEW BLOCK VARIANCE INFLATION FACTORS scsscseeececececcccccccceccecucuseeesssersesesesececececeseseseseususssusessenssseseeeess 45 H XI VIEW CORRELATIONS AMONG INDICATORS ttrt ttt Stees erer rE Eeee etete eese eree enee 46 H vm VIEW PLOT LINEAR AND NONLINEAR RELATIONSHIPS AMONGLATENTVARIABLES 47 H vm VIEW INDIRECT AND TOTAL ERPRCTS 50 Tc GLOSSARY EE 51 Je REFERENCES isccsssieisscsestecssinsiensestecceseossebecsessevnseossvsavcessouss sed cesbessecsosusseadesseutecsessesossssbevuscacsbsesicsi
80. ss widely accepted criteria for discriminant validity assessment 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 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 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 offending indicator or indicators and consider removing them 43
81. t the underlying algorithm used for outer model estimation is PLS 23 WarpPLS 3 0 User Manual regression both formative and reflective latent variables can be part of moderating links This is not possible with some variations of the PLS regression algorithm often defined by modes see Lohm ller 1989 which are implemented through other PLS based SEM software tools Moderating links are usually 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 equals 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 and thus may make some model parameter estimates unstable 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 l
82. ted 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 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 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 It is often similar in value to that measure even though unlike the R squared coefficient the Q squared coefficient
83. 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 Figure H 15 Indirect and total effects window Close Help Total effects ECU Effi ECU Effi 0 173 Effe 0 180 0 526 Proc Proc Ef Number of paths for total effects Effe P values for total effects Effi ECU Effi 0 057 Effe 0 025 lt 0 001 Proc Proc Ef Indirect effects are aggregated for paths with a certain number of segments So 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 mediating effects that have traditionally relied on non automated and thus time consuming calculations based on linear Preacher amp Hayes 2004 and nonlinear Hayes amp Preacher 2010 assumptions 50 WarpPLS 3 0 User Manual I Glossary Average variance extracted A
84. tors or criteria This is not usually possible with ANOVA or commonly used nonparametric comparison of means tests e g the Mann Whitney U test WarpPLS 3 0 User Manual B ii View or change settings The view or change settings window see Figure B 5 allows you to select an algorithm for the SEM analysis select a resampling method select the number of resamples used if the resampling method selected was bootstrapping or blindfolding select a range restriction variable type select a range restriction variable select a range in the form of minimum and maximum values for the range restriction variable and choose whether to use only ranked data in the analysis or not Figure B 5 View or change settings window Warp2 PLS regression Warp3 PLS regression Warp2 PLS regression PLS regression Resampling method Robust path analysis Bootstrapping No of resamples rec 100 min 7 max 999 100 Analysis algorithm Warp2 PLS regression Bootstrapping Bootstrapping Jackknifing Range restriction variable type Blindfolding None Range restriction variable j Unstandardized indicator None None Range min max for restriction variable Unstandardized indicator Minimum value Maximum value Standardized indicator 0 000 0 000 Use only ranked data in analysis No e a The following subsections provide more details on the options available on the view or change settings window The settings chosen
85. trument 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 an 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 expected to be correlated with each other 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
86. two MVs 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 score A latent variable score is a score calculated based on the indicators defined by the user as associated with the latent variable It is calculated using a partial least squares PLS algorithm This score may be understood as a new column in the data with the same number of rows as the original data and which maximizes the loadings and minimizes the cross loadings of a pattern matrix of loadings after an oblique rotation Manifest variable MV A manifest variable is one of several variables that are used to indirectly measure a latent variable LV For example satisfaction with a meal may be a LV measured through two MVs 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 structural equation modeling analysis the outer model is the part of the model that describes the relationships between 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 excha
87. uantifying and testing indirect effects in simple mediation models when the constituent paths are nonlinear Multivariate Behavioral Research 45 4 627 660 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 Kline R B 1998 Principles and practice of structural equation modeling New York NY The Guilford Press 54 WarpPLS 3 0 User Manual 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 Miller R B amp Wichern D W 1977 Intermediate 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 Nunnally J C amp Bernstein I H 1994 Psychometric theory N
88. us more reliable P values with larger samples and with samples where the data points are evenly distributed on a scatter plot The use of bootstrapping with small sample sizes lower than 100 has been discouraged Nevitt amp Hancock 2001 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 12 WarpPLS 3 0 User Manual 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 Since the warping algorithms are also sensitive to the presence of outliers in many cases it is a good idea 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 Oe statistically non significant associated with path coefficients that could be reasonably expected to have low P values For example with a sample size of 100 a path c
89. 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 4 or a similar bar chart could be added to a report describing the analysis Some may think that it is an overkill to conduct a comparison of means analysis using an 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 estimation techniques These are sometimes referred to as bootstrapping techniques which may lead to confusion since bootstrapping is also the name of a type of resampling technique Nonparametric estimation techniques do not require the data to be normally distributed which is a requirement of other comparison of means techniques eg ANOVA Another advantage of conducting a comparison of means analysis using this software is that the analysis can be significantly more elaborate 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 predic
90. 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 The Data menu options After Step 3 is completed whereby the data used in the SEM analysis is pre processed seven data menu options become available see Figure B 2 These menu options allow you to view or save data 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 Figure B 2 Save menu options on main window available after Step 3 only Project Settings Help View or save indicator correlations means and standard deviations View or save P values for indicator correlations View or save unstandardized pre processed indicator data View or save unstandardized ranked pre processed indicator data View or save standardized pre processed indicator data View or save standardized ranked pre processed indicator data Save grouped descriptive statistics The View or save indicator correlations means and standard deviations option allows you to save general descriptive statistics about the data which are complemented by the option View or save P values for indicator correlations Two menu
91. vergent validity assessment For discriminant validity assessment AVEs are used in conjunction with latent variable correlations in the assessment of a measurement instrument s discriminant validity This is discussed in more detail later together with the discussion of the table of correlations among latent variables For convergent validity assessment the 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 which enables the identification of not only vertical but also lateral 41 WarpPLS 3 0 User Manual 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 new term 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 Lindell amp Whitney 2001 bias tests that are more conservative than and arguably superior to the traditionally used tests relying on exploratory factor analyses A rule of thumb roo
92. w The other new option that becomes available from the main window after Step 5 is completed is the Modify menu option see Figure G 1 This option allows users to 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 as in hierarchical analyses using selected latent variable scores as indicators at each level In such cases adding all latent variable scores at once may soon clutter the set of indicators available to be used in the SEM model Figure G 1 New main window option available after Step 5 is completed Settings Help 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 Project Data Modify Settings Help Welcome to WarpPLS 3 0 a software developed by Ned Kock using MATLAB C and Java This software will help you conduct a structural equation modeling SEM analysis using the method of warped partial least squares regression The analysis will be conducted through the following steps Step 1 Open or create a project file to save your work Step 2 Read the raw data used in the SEM analysis Step 3 Pre process the data for the SEM analysis The option of adding latent variable scores to the model as new standardized indicator

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