Structural Equation Modeling – Rakenneyhtälömallinnus
Contents
1. Format Visibility Font size and style Onentation 4 kad Regular Horizontal Encouraging leadership Set Default Undo Psychic stress of the work Build up of work requirements 0 g o 1 Encouraging e7 leadership Psychic stress of the work V45 0 m V44 eea e45 Build up of work requirements 37 Save the model File Save Ctrl S 38 Click the Calculate estimates Ctrl F9 button Hii to perform the analysis of the model with the data Petri Nokelainen University of Tampere Finland v2 5 20 39 Click the View the output path diagram button HHH If the button is not enabled the analysis was not conducted for some usually technical reason The three most common error sources are 1 The model is not identifiable I Solution You need to fix one or more parameter constraints see section 27 on page 13 2 You have given the same name for two or more error sources and the program gives a following error message There is more than one variable named xx Solution Check that each circle has a unique name e g e1 e2 etc 3 There are one or more I accidentally drawn objects inside or outside the drawing area resulting for an error message for example 1 variable is unnamed Solution Click the Resize the path I diagram tool button to fit all the objects on the drawing area and remove any unnecessary objec2. Go to http www uta fi laitokset aktk lectures sem_en data and save the datal sav file to your working computer s hard drive e g c temp sem Open AMOS Graphics Choose File Data Files Click File Name button and open the datal sav file that is located in your computer Check that the N column shows 447 447 and click the OK button Save the model with the File Save As Ctrl S command to your work folder using name datal 1 Select View Set Interface Properties and click the Page Layout divider Choose Orientation Landscape and click the Apply button Close the Interface Properties window Choose Estimation divider from View Set Analysis Properties window Select Estimate means and intercepts This selection allows missing values eee Petri Nokelainen University of Tampere Finland v2 5 12 Analysis Properties Permutations Random Tithe Output formatting Output Bootstrap Estimation Numerical Bias Discrepancy 7 Estimate means Maximum likelihood and intercepts Generalized least 12 Choose Output divider and select Squared multiple correlations Standardized estimates and Indirect direct amp total effects Analysis Properties Estimation Numerical Bias Permutations Random Tithe Output formatting Output Bootstrap d ren z indirect direct amp total effects 7 Squared multiple M Covariances of estimates correlations
3. 13 Close the Analysis Properties window 14 Select the Draw unobserved variables F4 tool I Note that the AMOS toolbar works like an old radio that has push buttons You select a tool by clicking its button icon once and deselect the tool by clicking the same button once again No mouse dragging from the toolbar to the drawing area is needed but most of the drawing tools assume that you specify the size of the object by mouse dragging inside l the drawing area 15 Draw an ellipse with the tool on the drawing area by dragging with your mouse RS o 16 Select Draw a latent variable tool and click inside the ellipse you just draw three times Petri Nokelainen University of Tampere Finland v2 5 Now you have specified the first latent variable in Figure 1 Encouraging leadership and 3 three observed variables that is three questions in the questionnaire v5 v7 and v17 see Table 1 for details 17 Select the Rotate tool E and click inside the ellipse as many times as needed to rotate the group of three observed variables to the left hand side of the latent variable 19 Click Move objects button ii and drag all the selected 1 e blue objects to the upper left hand part of the drawing area Petri Nokelainen University of Tampere Finland v2 5 14 20 Click Duplicate objects button E part of the drawing area I Turning something on means that t
4. file into your computers temporary file folder s sub folder sem_data e g c temp sem 2 Open the data with SPSS and examine if all the variables meet the univariate normal distribution a variable is normally distributed if its graphical shape follows bell curve assumption In SPSS Analyze Descriptive Statistics Frequencies Charts gt Histograms with normal curve Note that both the shape of the phenomena under investigation and its operationalizations the data shape must resemble each other e Are there any variables that meet the univariate normal distribution assumption e Are there any variables that do not meet the univariate normal distribution assumption 3 Examine if two variables that meet the univariate normal distribution UND assumption also meet the multivariate normal distribution assumption by plotting them together a statistical dependency between two variables must be linear in SPSS Graphs Interactive Dot e How the different type of variable pairs meet the multivariate normal distribution assumption Both meet the UND One is UND the Neither is UND assumption other is not UND amp amp amp linear non linear linear non linear linear non linear 4 Examine the correlation matrix Table 3 Usually correlations between 3 9 are considered usable in multivariate analysis Too low correlations indicate weak inter item dependency too high correlations might indicate
5. fix the values more limited the analysis becomes and the df is getting smaller Chi square y value and the models probability level so called p value is reported According to Arbuckle and Wothke 1999 P is the probability of getting as large a discrepancy as occurred with the present sample under appropriate distributional assumptions and assuming a correctly specified model That is P is a p value for testing the hypothesis that the model fits perfectly in the population P value should usually be greater than pre set probability level usually 05 If the value is 05 or less the departure of the data from the model is significant at the 05 level model does not fit into data However the appropriateness of hypothesis testing in model fitting even when the necessary distributional assumptions are met is routinely questioned One approach to model selection employs statistical hypothesis testing to eliminate from consideration those models that are inconsistent with the available data Hypothesis testing is a widely accepted procedure and there is a lot of experience in its use However its unsuitability as a device for model selection was pointed out early in the development of analysis of moment structures J reskog 1969 It is generally acknowledged that most models are useful approximations that do not fit perfectly in the population In other words the null hypothesis of perfect fit is not credible to begin with an
6. per cent Model Fit There is such a great number of indices available that next we will consider only the most important ones to report on a scientific work that involves structural equation modeling o TLI NNFI Tucker Lewis Index Non Normed Fit Index compare the proposed model to a baseline model that all other models should be expected to exceed Hair Anderson Tatham amp Black 1995 p 685 Values close to one indicate a very good fit e CFI RNI Comparative fit index Relative Noncentrality Index are similar measures to TLI and RNI Values close to one indicate a very good fit e NFI Normed Fit Index is also similar to preceding model fit indices telling how big discrepancy there is between the model being evaluated default model and the baseline model terribly fitting independence model According to Bentler amp Bonett 1980 p 600 referring to both the NFI and the TLI Since the scale of the fit indices is not necessarily easy to interpret e g the indices are not squared multiple correlations experience will be required to establish values of the indices that are associated with various degrees of meaningfulness of results In our experience models with overall fit indices of less than 90 can usually be improved substantially These indices and the general hierarchical comparisons described previously are best understood by examples NFI values close to one indicate a very good fit e RMSEA Ro
7. psyl1 The model should look like this Petri Nokelainen University of Tampere Finland v2 5 16 23 Select View Set Variables in dataset 24 Click the Deselect all objects button W to make sure that nothing 1s selected 26 Close the Variables in dataset window 27 Double click AMOS 16 Right mouse click on the uppermost left latent variable ellipse to open the Object properties window Petri Nokelainen University of Tampere Finland v2 5 17 28 Select the Text divider if not selected and write Encouraging ENTER leadership on the Variable Name field DO NOT use the Variable label field I If the text is too big to fit into the ellipse adjust the text size in the Font size field of the Object Properties window or resize the ellipses with the Change the shape of objects Encouraging leadership sE V17 e y 29 Click on the other two latent variable ellipses and feed the requested variable name information into them lowest left latent variable Build up of work ENTER requirements right hand sided latent variable Psychic stress ENTER of the work Object Properties Colors Text Parameters Format Visibility Font size Font stile hai Regular T Yariable name Psychic stress of the work Variable label Set Default Psychic stress of the work Encouraging leadership Build up of work requirements 30 Use Draw covarianc
8. students Model 1 Model 1 n 447 n 332 62 25 11 5 66 gt 001 102 078 128 945 953 882 31 References Arbuckle J amp Wothke W 1999 Amos 4 0 User s Guide Chicago SPSS Inc Bentler P M amp Bonett D G 1980 Significance tests and goodness of fit in the analysis of covariance structures Psychological Bulletin 88 588 606 Bollen K 1989 Structural Equations with Latent Variables New York John Wiley amp Sons Byman R 2001 Curiosity and Exploration Four Dimensions of Gender Free Exploration A Methodological Example Study Retrieved from http www edu helsinki fi oppimateriaalit byman2003 htm Hair J F Anderson R E Tatham R L amp Black W C 1995 Multivariate Data Analysis Fourth edition Englewood Cliffs NJ Prentice Hall Joreskog K G 1969 A general approach to confirmatory maximum likelihood factor analysis Psychometrika 34 183 202 Kaplan D 2000 Structural Equation Modeling Thousand Oaks Sage Marsh H W amp Hocevar D 1985 Application of confirmatory factor analysis to the study of self concept First and higher order factor models and their invariance across groups Psychological Bulletin 97 562 582 Muth n L amp Muth n B 2000 MPLUS User Manual Los Angeles Muth n amp Muth n Nokelainen P 2007 Introduction to Structural Equation Modeling Retrieved from http www uta fi laitokset aktk lecture
9. to http www uta fi laitokset aktk lectures sem_en data and save the datalfactors sav file to your working computer s hard drive e g c temp sem I The data consists of the thirteen growth oriented atmosphere factors means of the items specified in Table 2 The sample is the same as in datal 447 staff members of Finnish polytechnic institute for higher education The sample was collected in 2000 Select File New Select File Data Files Click the File Name button and select the datalfactors sav file Check that the N column reads 447 447 and click the OK button Select View Set Interface Properties and click the Page Layout divider Choose Orientation Landscape and click the Apply button Close the Interface Properties window Select View Set Analysis Properties and activate the Estimation divider 10 Select Estimate means and intercepts Petri Nokelainen University of Tampere Finland v2 5 Analysis Properties Permutations Random Tithe Output formatting Output Bootstrap Estimation Numerical Bias Discrepancy Estimate means Cs oe ie ealharn Maximum likelihood W and intercepts Generalized least 11 Activate the Output divider and select Standardized estimates Squared multiple correlations and Indirect direct amp total effects Analysis Properties Estimation Numerical Bias Permutations Random Title Output formatting Output Bootstrap
10. 0 is in the upper bound of the mediocre fit level 08 10 indicating that the model over simplifies the reality Also the upper limit of the 90 per cent confidence interval 12 supports this assumption The lower section of the table incremental fit measures compares the proposed model default model to a baseline model independence model that all other models should be expected to exceed Both NFI and CFI are above the expected 90 level Tucker amp Lewis 1973 For example the NFI value of 945 is calculated with the minimum discrepancy values CMIN of the default and independence models VFI 1 62 250 1129 189 945 It shows that the tested model has a discrepancy that is 94 5 per cent of the way between the terribly fitting independence model and the perfectly fitting saturated model Table 4 Goodness of fit Values of the Exercise 2 Model Finnish polytechnic institute of higher Growth oriented atmosphere questionnaire education students 22 items n 447 Measures of Absolute Fit yo 62 25 df 11 x1 df 5 66 Pp lt 001 RMSEA 102 90 per cent C I 078 128 Incremental Fit Measures NFI 945 CFI 933 TLI 882 50 Save the model by selecting File Save 51 Run Windows Explorer and examine the AMOS files in your work folder e g c temp sem Petri Nokelainen University of Tampere Finland v2 5 23 dae AGEBSSEA AmosP KE AMOSPF File a datal 1 4mosQutput 105 KB AMOSOUTPUT File fedatal_1 am
11. 32 is collected in 2003 from another Finnish polytechnic for I higher education It includes the same items as the first data see Tables 1 and 2 Open the datal_1 amw model and save it as data2_1 amw Select File Data Files Click the File Name button and select the data2 sav file Check that the N column reads 332 332 and click the OK button Calculate the regression estimates for this new data How do the two IV s differ as predictors for the DV The first strongest predictor for Psychic stress of the work 1s r The second predictor for Psychic stress of the work is r How well the two IV s predict the DV Squared Multiple Correlations SmMCgata2 1 that equals to per cent 11 Fill in the model fit indices into the Table 5 and compare them to the original indices with the first data n 447 You have just conducted a validation of generalizability for your model exercise 1 by switching the data but keeping the model the same Why 1s this kind of model testing Petri Nokelainen University of Tampere Finland v2 5 30 Table 5 Cross validation of the Model 1 with Two Different Samples from the same Domain Growth oriented atmosphere questionnaire Measures of Absolute Fit 2 X af x Iaf p RMSEA 90 per cent C I Incremental Fit Measures NFI CFI TLI Petri Nokelainen University of Tampere Finland v2 5 Finnish polytechnic institute of higher education
12. 9 0 8 0 7 0 4 0 2 0 2 0 1 0 3 0 2 0 2 v30 0 7 0 4 0 3 0 2 0 1 0 3 0 2 0 2 v31 0 4 0 4 0 3 0 1 0 3 0 2 0 2 v33 v34 0 7 0 2 0 2 00 0 1 0 1 0 1 0 3 0 2 0 2 0 2 0 2 0 2 v42r 0 4 0 5 03 03 0 4 v43 05 0 2 0 1 0 2 w44 0 5 0 4 0 5 v45 0 7 0 6 v46 0 7 v Those variables that are unable to meet univariate normal distribution and or do not correlate with other variables may become problematic ones in the later analysis stages Petri Nokelainen University of Tampere Finland v2 5 Exercise 1 Path analysis In this exercise we will build a model of observed variables path analysis The statistical calculations are based on multiple linear regressions These calculations do not need a special program like AMOS but it allows an easy way of building the model visually instead of programming by hand series of regression analyses in SPSS The model that we build here examines four predictors IV s of valuation of the work DV The predictors are Encouraging leadership Know how rewarding Incentive value of the job Clarity of the job Figure 2 1 Encouraging leadership 3 Know how rewarding 9 Incentive value of the work 6 Clarity of the work T7 Valuation of the work Figure 1 Predictors of valuation of the job in Finnish polytechnic institute of higher education path oe oe ee aa model 2 Go
13. Indirect direct amp total Minimization history w oe 7 Squared multiple Covarances of estimates correlations 12 Close the Analysis Properties window 13 Save the model as datalfactors_1l amw 14 Select View Set Variables in Dataset 15 Drag the four IV and one DV variable from the Variables in Dataset window to the drawing area In order to make the rectangles the same size you can use the Change the shape of l objects tool i after selecting all the objects with that you wish to reshape Petri Nokelainen University of Tampere Finland v2 5 1 Encouraging leadership 3 Know how rewarding 7 Valuation of the work 5 Incentive value of the work 6 Clarity of the work 16 Add an error term to the DV variable with Add a unique variable Ka button y TT 5 17 Double click inside the error term circle and name it as err 18 Add covariance between IV s and variance arrows from each IV to the DV to the model Petri Nokelainen University of Tampere Finland v2 5 1 Encouraging leadership 3 Know how rewarding 7 Valuation of the work 5 Incentive value of the work 6 Clarity of the work 19 Click the Calculate estimates Ctrl F9 button Hit to perform the analysis of the model with the data 20 Click the View the output path diagram button II to see the results of the analysis 21 Select Standardized
14. Structural Equation Modeling with AMOS Petri Nokelainen Research Centre for Vocational Education University of Tampere Finland petri nokelainen uta fi LAE OGUCTION wcasiticd uiehnnhe a a lcd adden utile bere y tea ied ate l SPIE da ea A a a Re te T l DTD er a O a A E E E ate 3 Exerce t Paranal y SUS ea E E TE 5 Exerce Tasen sia hala N 9 Exercise l Dennen a a a aitadia ahdasoaea lend ae Raamaateadiae 10 Exerce 2 Laten yanable mode lenan tah alatinpstian halademner ass aahnnetapeeuan hicad ape ie 11 ES or e E O A tasted 26 Eer e Deae a N 29 RE TNE e a a a a a a R P Introduction This learning material is a tutorial that shows how to design and analyze path observed variables and structural equation latent variables models for more details see Nokelainen amp Ruohotie 1999 This material supports the lectures http www uta fi aktkk lectures sem_en and research literature Arbuckle amp Wothke 1999 Bollen 1989 Byman 2003 Kaplan 2000 We use here an AMOS Analysis of Moment Structures program developed by James Arbuckle http www spss com amos but these exercises work naturally also with other SEM programs such as LISREL http www ssicentral com lisrel MPLUS Muthen amp Muthen 2000 and EQS http www mvsoft com I have selected AMOS for two reasons Firstly its graphical user interface is quite intuitive and secondly it has been merged since year 2000 into the most popular statistical software package for s
15. d will in the end be accepted only 1f the sample is not allowed to get too big Arbuckle amp Wothke 1999 Estimates These indices show the unstandardized original scale and standardized normalized scale where M 0 0 and SD 1 0 regression estimates the same values are presented in the graphical path models above For example unstandardized estimate between Encouraging leadership and Psychic stress of the work are interpreted as follows When Encouraging leadership goes up by 1 Psychic stress of the work goes down by 10 Petri Nokelainen University of Tampere Finland v2 5 23 When we examine the Regression Weights table a bit closer we see from the P column that the probability of getting a critical ratio C R is calculated by dividing the regression weight estimate by the estimate of its standard error z 104 063 1 651 as large as 1 651 in absolute value is p 099 In other words the regression weight for Encouraging leadership in the prediction of Psychic stress of the work is not significantly different from zero at the 05 level two tailed On the other hand the similar p value for the difference between Build up of work requirements and Psychic stress of the work is significantly different from zero p lt 001 The last part of the estimates Squared multiple correlation R 785 shows how much the two predictors IV s explain the variance of the DV Psychic stress of the work that is 79
16. er as predictors for the DV e The first strongest predictor for Psychic stress of the work 1s r e The second predictor for Psychic stress of the work is r e The third predictor for Psychic stress of the work is r SmMmCgatal 2 that equals to per cent Complete the following sentences e When Encouraging leadership goes up by 1 Psychic stress of the work goes up down by e When Build up of work requirements goes up by 1 Psychic stress of the work goes up down by l e When Rewarding of know how goes up by 1 Psychic stress of the work goes up down by Complete the following Table 5 Petri Nokelainen University of Tampere Finland v2 5 28 Table 5 Comparison of the Goodness of fit Values of the Exercise 2 and 2a Models Finnish polytechnic institute of higher education students n 447 Growth oriented atmosphere questionnaire Model 1 Model la Measures of Absolute Fit x 62 25 df 11 x l df 5 66 P gt 001 RMSEA 102 90 per cent C I 078 128 Incremental Fit Measures NFI 945 CFI 953 TLI 882 9 Compare the goodness of fit values of the models 2 and 2a which model fits better to the data Why Petri Nokelainen University of Tampere Finland v2 5 29 Exercise 2b l e Oe a ae oe a 10 Go to http www uta fi laitokset aktk lectures sem_en data and save the data2 sav file to your working computer s hard drive e g c temp sem I The second data file n 3
17. es F6 tool gt to draw a double headed arrow between Encouraging leadership and Build up of work requirements latent variables 31 Use Draw paths F5 tool to draw a single headed arrow from both aforementioned latent variables to Psychic stress of the work variable Petri Nokelainen University of Tampere Finland v2 5 18 Encouraging leadership Psychic stress of the work Build up of work requirements lt as 32 Select Add a unique variable button and add an error source to the Psychic stress of the work variable by clicking it once with the tool Psychic stress of the work N 33 Deselect the Add a unique variable button Z 34 Name all the empty circles 1 e error sources in the model by double clicking one of them and then filling the Object properties window s Variable Name field as follows Object Properties Colors Text Parameters Format Visibility Eont size Font style Varlable name ca Variable label Set Default Encouraging O B Undo leadership lt j Psychic stress of the work T T P2 lt T hs pU Build up of work requirements D a Ca lt gt QJ Petri Nokelainen University of Tampere Finland 19 35 Using the same Object properties window make sure that at least one arrow departing from each variable has a regression weight of 1 Object Properties x Parameters
18. estimates and answer to the following questions a How much DV s variance the four IV s predict Smc J b Order the IV s in the following rows best predictor comes first o The first strongest predictor for Valuation of the work 1s rs o The second predictor for Valuation of the work is r o The third predictor for Valuation of the work is r o The fourth predictor for Valuation of the work is r 22 Select Unstandardized estimates and complete the following sentences o When Encouraging leadership goes up by 1 Valuation of the work goes up down by o When Know how rewarding goes up by 1 Valuation of the work goes up down by Petri Nokelainen University of Tampere Finland v2 5 Exercise la 1 Save the datalfactors_1l amw model as datalfactors 2 amw 2 Modify the datalfactors_2 amw model as follows We add in this exercise an indirect path from Know how rewarding via Incentive value of the work to Valuation of the work 1 Encouraging leadership 3 Know how rewarding 9 Incentive value of the work 5 6 Clarity of the work 3 Calculate the estimates and answer to the following questions T Valuation of the work 4 How much DV s variance the four IV s predict SMC rode t e Compare this finding to the previous model s smc SMCmodel_2 o How does the indirect path affect the regression model Petri Nokelainen Univer
19. he button is on downwards position 1 e the button is pressed down 21 Use the Delete button A to remove the lowest observed variable and its error from the copied ee variable The reason for doing this is simply that if we aim to build a model according to the Figure 1 we only need two observed variables for the last two latent variables Petri Nokelainen University of Tampere Finland v2 5 15 E E X ai ON BEE 22 Click the Deselect all objects button al to make sure that nothing 1s selected 23 Click the Select one object at a time button Wi to select all components of the second latent wee cluster this means that you need to click everything in the cluster to make it blue 1 The first latent variable cluster stays black and the new copy of it except that the copy I has one observed variable less becomes blue 24 Repeat the duplication procedure for the third and last latent and observed variable cluster in the model It is wise to duplicate the selected blue cluster as it already has the right number of observed variables 20 Use the Rotate tool C to adjust the two observed variables to the right hand side of the third latent variable 21 Click the Resize the path diagram tool button e to fit all the objects on the drawing area 22 Now we have defined the templates for all three variable clusters kj_enc1 tv_bui12 and tr
20. in a variety of ways My work consists of various differing tasks Factor 6 Clarity of the job CLA A clear division of tasks exists between members of teaching staff The organization s decision making structure 1s transparent The organization s goals are transparent Factor 7 Valuation of the job VAL My manager appreciates my work I am given encouraging feedback on my work I feel that my work is valued Factor 10 Psychic stress of the job PSY I feel that I am beginning to dislike my work I feel that it is getting more difficult for me to take the initiative I find it difficult to concentrate Factor 11 Build up of work requirements BUI My workplace has too few employees to cope with the workload My workload has increased during the past years My working pace has increased in recent years Petri Nokelainen University of Tampere Finland v2 5 Data prerequisites The sample data for this exercise datal sav is downloadable from http www uta fi laitokset aktk lectures sem_en data The data is in SPSS sav format as we first examine its technical properties for structural equation modeling AMOS 1s able to read SPSS data as an input For the other software packages mentioned earlier the data must be saved into a different format usually all programs are able to read tabulator delimited text files In SPSS File Save As Tab delimited dat 1 Download and save the datal sav
21. multicollinearity Petri Nokelainen University of Tampere Finland v2 5 v1 v1 v2 0 7 v3 0 6 w4 0 6 vw O35 v6 03 vi 0 4 v8 03 v9 0 4 w12 0 4 v13 0 4 vid 0 4 v15 0 4 v16 03 wif 03 v18 03 v29 0 4 v30 05 v31 0 4 v33 0 2 v34 0 2 v4 42r 0 2 v43 0 1 w44 0 2 w45 02 v46 0 1 w47 0 1 v2 v3 Table 3 Correlation Matrix of the GOAQ items v4 v v6 vi v6 v9 03 03 0 8 04 06 0 6 04 06 06 0 7 0 6 03 05 05 05 05 Of 04 03 03 04 04 04 04 04 04 05 O4 OS 04 05 05 06 05 0 6 03 Of Of Of 06 Of 04 07 08 07 06 06 03 06 06 06 05 0 6 04 05 06 06 O05 0 6 04 05 06 0 6 05 0 6 03 03 04 05 04 0 4 02 03 03 04 O03 03 0 2 0 2 0 2 03 03 03 0 1 0 1 0 1 0 1 0 1 0 1 0 1 03 O2 03 02 0 2 0 1 0 2 0 2 03 03 03 00 0 1 01 02 0 2 0 2 0 1 02 02 03 02 03 v12 v13 0 6 0 6 0 4 0 4 0 4 0 4 0 4 0 4 0 2 0 2 0 3 0 2 0 3 0 3 0 1 0 1 vid 0 6 05 05 0 4 04 0 4 03 03 0 2 0 1 0 1 0 2 0 1 0 0 v15 0 6 0 6 0 6 0 5 0 5 0 5 0 4 03 0 3 0 1 0 3 0 1 0 1 w16 0 8 0 7 0 6 0 5 0 5 0 4 0 4 0 2 0 1 0 2 0 3 0 2 0 2 vif 0 8 0 7 0 6 0 6 os 03 0 2 00 0 3 0 2 0 2 What is the strength of linear dependencies lowest r R highest r R Mr 0 4 SDr 0 2 v18 0 7 0 6 0 6 05 0 4 0 2 0 1 0 2 0 1 0 2 v2
22. ocial sciences SPSS http www spss com Sample data Our sample material consists of two sub samples that are collected from Finnish polytechnics of higher education in 2000 n 447 datal sav and 2003 n 332 data2 sav The respondents in both samples are the staff of the organizations e g leaders teachers clerks cleaners etc The original measurement instrument Growth oriented Atmosphere Questionnaire GOAQ has 13 factors and 92 items Ruohotie 1996 Ruohotie Nokelainen amp Tirri 2002 but for the purposes of this exercise I have selected the following factors and sample items see Table 1 Five point Likert scale from 1 totally disagree to 5 totally agree was applied Petri Nokelainen University of Tampere Finland v2 5 Table 1 Growth oriented Atmosphere Questionnaire items Ruohotie 1996 Ruohotie Nokelainen amp Tirri 2002 Nokelainen amp Ruohotie 2009 Factor 1 Encouraging leadership ENC My manager is friendly and easily approachable My manager pays attention to my suggestions and wishes My manager works with a team to find solutions Factor 3 Know how rewarding REW It is rewarding to achieve my goals The organization rewards its employees professional knowledge and skills Employees with increased knowledge are given extra responsibility Factor 5 Incentive value of the job INV I can work independently and without restrictions I can use my skills at work
23. ot Mean Square Error of Approximation The RMSEA is designed to evaluate the approximate fit of the model in the population Kaplan 2000 p 112 This indice is getting smaller as the df increases In practice this means that models with large RMSEA values e g 0 12 default model simplify the reality This error could be estimated as follows Browne amp Cudeck 1993 Kaplan 2000 p 113 lt 0 05 close fit 0 05 0 08 fair fit 0 08 0 10 mediocre fit gt 0 10 poor fit RMSEA should always be reported with confidence intervals C 1 that in AMOS describe the population RMSEA for the default model your model with approximately 90 per cent confidence However with C I certain statistical distribution assumptions should be met First observations must be independent Second the IV must meet multivariate normal distribution requirement Petri Nokelainen University of Tampere Finland v2 5 24 49 Table 4 shows how these indices are reported in practice The upper section of the table measures of absolute fit determine the degree to which the model predicts the observed correlation matrix Hair et al 1995 p 683 First relative y is calculated by dividing the y with df resulting in 5 66 Usually values less than five are considered adequate Marsh amp Hocevar 1985 However some researchers argue that the value should be less than two Byrne 1989 Second the RMSEA estimate of 1
24. p 6KE AmosTableviewer Document eeDatal_1 Anos TTY FEB AMOSTN File eedatal_1 amy SEB Amos Graphics Document datal_1 amw AMOS Graphics file This is the model you just drawed so do not loose it datal_l amosOutput AMOS Text Output file Here you have the analysis results in a text file These you may easily reproduce by estimating the model once again Petri Nokelainen University of Tampere Finland v2 5 26 Exercise 2a l 0 Save the datal_l amw model as datal_ 2 amw Modify the datal_2 amw model as follows Before you start the work note two things First due to limitation of maximum number of observed variables 8 in AMOS student version we need to drop one encouraging leadership indicator namely v7 from the model Second all the V s in the model are 0 0 Encouraging leadership Build up of work requirements Psychic stress of the work Rewarding of know how Figure 2 Measurement model 1b of predictors of psychic stress of the work in Finnish polytechnic institute of higher education structural equation model 1b 3 Before calculating the estimates consider in theory should the new IV behave as a negative or 4 positive promotor for psychic stress of the work Petri Nokelainen University of Tampere Finland v2 5 How well the three IV s predict the DV Squared Multiple Correlations 27 How do the three IV s diff
25. s sem_en Nokelainen P amp Ruohotie P 1999 Structural Equation Modeling in Professional Growth Research In P Ruohotie H Tirri P Nokelainen amp T Silander Eds Modern Modeling of Professional Growth vol I pp 121 154 H meenlinna Finland RCVE Nokelainen P amp Ruohotie P 2009 Non linear Modeling of Growth Prerequisites in a Finnish Polytechnic Institution of Higher Education Journal of Workplace Learning 21 1 36 57 Ruohotie P 1996 Professional Growth and Development In K Leithwood et al Eds International Handbook of Educational Leadership and Administration pp 419 445 Dordrecht Kluwer Academic Publishers Ruohotie P Nokelainen P amp Tirri H 2002 April Visualization of Growth oriented Atmosphere Paper presented at the Annual Meeting of American Educational Research Association New Orleans USS Raykov T amp Marcoulides G A 2000 A First Course in Structural Equation Modeling Mahwah NJ Lawrence Erlbaum Associates Schumacker R E amp Lomax R G 2004 A Beginner s Guide to Structural Equation Modeling Second edition Mahwah NJ Lawrence Erlbaum Associates Petri Nokelainen University of Tampere Finland v2 5
26. ship goes up by 1 standard 44 Consider on the basis of the standardized estimates of the model how the two IV s explain the DV psychic stress of the work e Best predictor for Psychic stress of the work is e Second best predictor for Psychic stress of the work 1s 45 How well the two IV s predict the DV Squared Multiple Correlations e SmCgatal 1 that equals to per cent Petri Nokelainen University of Tampere Finland v2 5 22 46 Select the Unstandardized estimates view 47 Unstandardized values of an observed indicator v5 and its error variance are explained as follows p CR 4 0 1 15 V5 90 Ar V5 oh K 1 v7 Encouraging V me leadershi F oe mu dg P 1 e17 Viy EED Mean of error e5 for the v5 is O and the variance is 0 47 2 The mean of 3 82 is an estimation of the population mean of the observed variable v5 under the hypothesis that the model is correct I 3 The total effect combined direct and indirect effect of Encouraging leadership on v5 is 90 When Encouraging_leadership goes up by 1 measurement scale value v5 goes up by 0 90 scale values here the scale is from 1 to 5 48 Click View text F10 button to proceed to a more detailed level of model analysis The most important headings in the text output window are as follows Notes for Model Notes display if the model was fitted to the data successfully Minimum was achieved Also degrees of freedom more you
27. sity of Tampere Finland v2 5 10 Exercise 1b l oh a A e oe a Go to http www uta fi laitokset aktk lectures sem_en data and save the data2factors sav file to your working computer s hard drive e g c temp sem i This data2factors shares the same variable structure with datalfactors but is collected from I another Finnish polytechnic institute for higher education in 2003 n 332 Open the datalfactors_l amw model and save it as data2factors_1 amw Select File Data Files Click the File Name button and select the data2factors sav file Check that the N column reads 332 332 and click the OK button Calculate the estimates Ponder if the model is generalizable over the two samples 1 e are the results comparable e SMC datalfactors_1 gt Smc data2factors_2 Petri Nokelainen University of Tampere Finland v2 5 11 Exercise 2 Latent variable model Our first task is to build a latent variable model that is presented in Figure 1 The model examines how encouraging leadership and build up of work requirements together affect on psychical stress of the work Standardized estimates are presented Encouraging leadership Psychic stress of the work Build up of work requirements Figure 1 Predictors of psychic stress of the work in Finnish polytechnic institute of higher education oy E a ee Aa 1 8 9 10 11 structural equation model 1
28. ts 40 Now you are able to examine both unstandardized and standardized estimates of the model Data1_1 Group number 1 OK Default model SEE File Edit View Set Diagram Model Fit Tools Help 0 27 1 Click hete t ve oes 0 1 15 V5 k 90 i AT 1 V7 ia Encouraging V7 l 1 leadersh 32 a eadership J i 0 29 W e17 00 Unstandardized esti gt l V44 44 EEEE Psychic stress V44 8 1 00 N of the work 1 Chi square 62 3 c 0 ie 2 99 V45 e45 1 00 we V42R l T So datal_1 amw a 80 y Build up of work 1 requirements SH e43 v43 Y oes 66 Ha epsw 3 65 gt _V5 N at j bad ii 67 pon Tass ago 8 i E 81 e1 r Psychic stress 0 e44 of the work 45 V45 45 e42 V42R be Build up of work requirements e43 41 Select the Standardized estimates view Petri Nokelainen University of Tampere Finland v2 5 21 42 Standardized estimates view shows the explained variance squared multiple correlation of the model R 785 79 R 2 R squared 1s the explained variance 78 78 Psychic stress of the work Encouraging leadership i 1 Squared multiple correlation SMC of v5 is 66 per cent 2 The standardized total direct and indirect effect of Encouraging leadership on v5 is 81 That is due to both direct unmediated and indirect mediated effects of Encouraging_leadership on v5 when Encouraging leader
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