STRUCTURAL EQUATION MODEL (SEM)

Transcription

1 STRUCTURAL EQUATION MODEL (SEM) V. Čekanavičius, G. Murauskas 1 PURPOSE OF SEM To check if the model of possible variable dependencies matches data. SEM can contain latent (directly unobservable) variables. SEM aggregates confirmatory factor analysis (CFA), path analysis (PA) and linear regression. V. Čekanavičius, G. Murauskas 2 1

2 SEM SEM Path Analysis CFA Regression.. V. Čekanavičius, G. Murauskas 3 Regression Simple model when one normal variable depends on other variables. Exam Attitude Lectures Self-learning V. Čekanavičius, G. Murauskas 4 2

3 Path Analysis (PA) Attitude + Lectures Exam Self-learning V. Čekanavičius, G. Murauskas 5 Confirmatory Factor analysis (CFA) Latent variable appears. Lestures Self-learning Attitude motivation V. Čekanavičius, G. Murauskas 6 3

4 SEM Unifies CFA and PA. Stamina Age Phys. Vigor Swiftness Education Psich. Optimism Soc. aktiv. V. Čekanavičius, G. Murauskas 7 Aims To estimate the general fit of the model. To estimate each variable s significance and importance in the model. To estimate possible correlations. The model is constructed by the researcher according to his understanding of the research problem. V. Čekanavičius, G. Murauskas 8 4

5 Initial data It suffices to have the covariance matrix of variables, their number and means. The values of variables for each respondent are unnecessary. V. Čekanavičius, G. Murauskas 9 The idea of SEM The covariance matrix, reproduced when model s relations are taken into account, is compared to the initial covariance matrix. If both matrices are similar (differences are not statistically significant) we conclude that model fits data. V. Čekanavičius, G. Murauskas 10 5

6 Remark Sometimes it is possible to construct a few very different models fitting the data. Which model is better depends on researcher s decision. SEM is just a tool not a substitute for the researcher. V. Čekanavičius, G. Murauskas 11 General scheme of research 1. Model s specification. 2. Model s identification. 3. Estimation of model s parameters. 4. Model s respecification. V. Čekanavičius, G. Murauskas 12 6

7 Model s specification The researcher constructs model. Applies his theoretical knowledge of the investigated field. Variables are normal. Some variables are endogenous, some exogenous. V. Čekanavičius, G. Murauskas 13 Model s specification Endogenous Kintamieji, kurie variable paaiškinami variable kitais affected by kintamaisiais the model; (turi depends ateinančią on other rodyklę) variables vadinami (has endogeniniais. an incoming arrow). Exogenous Kintamieji, kurie variable tokios affects rodyklės the neturi model but egzogeniniai. is not affected by it, variable without an X1 incoming egzogeninis, arrow. X2 endogeninis. X1 is exogenous, Y is endogenous. X1 Y e X1 Y V. Čekanavičius, G. Murauskas 14 7

8 Model s specification If we think (and usually we do) that endogenous variable is not exclusively determined by the models variables, then we add the residual e. Y = a X1 +e, or graphically a 1 X1 Y e V. Čekanavičius, G. Murauskas 15 Model s specification CFA contains latent variables. They can correlate. No direct arrows between latent variables. V. Čekanavičius, G. Murauskas 16 8

9 Model s identification All parameters are estimated with the help of covariance matrix. If model has k variables, then no more than k(k+1)/2 parameter (path coefficients, variances, correlations) is allowed. V. Čekanavičius, G. Murauskas 17 Parameter estimates All parameters should be statistically significant. Signs of path coefficients must correspond to the theory of investigated field. For example, we expect correlation between exam s mark and self-learning to be positive. V. Čekanavičius, G. Murauskas 18 9

10 Indicators of the good general fit Chi-square test. Good model s fit if p >= GFI (goodnes of fit index). Godd fit if GFI is >= 0,95. RMSEA (root mean square error of approximation). Good fit if RMSEA<0,05. NFI (normed fit index). Good fit if NFI >= 0,95. V. Čekanavičius, G. Murauskas 19 Remark Typically output also contains information about the saturated model, that is, about the model with all possible paths And about the independence model, that is, the model without any path. V. Čekanavičius, G. Murauskas 20 10

11 Parameter estimates Both paths are doubtful (p-values > 0,05). V. Čekanavičius, G. Murauskas 21 Freeware -5 slightly differs from the later versions. (Beware that windows7 and higher versions require additional file) Now is connected to IBM SPSS. We give just some hints and ideas for the work with -21. V. Čekanavičius, G. Murauskas 22 11

12 example Variables: 1. Visual perception. 2. Cubes. 3. Lozenges. 4. Paragraph Comprehension. 5. Sentence Completion. 6. Word meaning. V. Čekanavičius, G. Murauskas 23 Possible CFA model: visperc cubes lozenges paragraph sentence word spatial verbal V. Čekanavičius, G. Murauskas 24 12

13 File -> Data files -> File name -> Grant.sav File name V. Čekanavičius, G. Murauskas 25 push V. Čekanavičius, G. Murauskas 26 13

14 Press left button of the mouse and draw V. Čekanavičius, G. Murauskas 27 Click three times V. Čekanavičius, G. Murauskas 28 14

15 Push V. Čekanavičius, G. Murauskas 29 Click on the picture for a change of direction. V. Čekanavičius, G. Murauskas 30 15

16 Click Then (select all) picture becomes blue, (for a copy). Then press left-hand button of the mouse and move copy of the picture down. V. Čekanavičius, G. Murauskas 31 Then We got V. Čekanavičius, G. Murauskas 32 16

17 Click List of variables appears Each can be moved to empty squares. V. Čekanavičius, G. Murauskas 33 Picture almost finished, but variables do not fit rectangles. Select all Use picture to improve V. Čekanavičius, G. Murauskas 34 17

18 Unselect all. V. Čekanavičius, G. Murauskas 35 Connect latent factors with V. Čekanavičius, G. Murauskas 36 18

19 By twice clicking on latent factors we can name them. V. Čekanavičius, G. Murauskas 37 Similarly, we name residuals as e1,e2, One can also use Plugins -> name unobserved variables V. Čekanavičius, G. Murauskas 38 19

20 Click Choose Output Check Minim.history Stand.est. Squared... V. Čekanavičius, G. Murauskas 39 Click And save file. Then click on (view text). V. Čekanavičius, G. Murauskas 40 20

21 P= Chi-square test shows good model fit. V. Čekanavičius, G. Murauskas 41 GFI=0.991 NFI=0.989 RMSEA=0.00 also prove good general fit. V. Čekanavičius, G. Murauskas 42 21

22 Factorial Weights correlation V. Čekanavičius, G. Murauskas 43 All factor weights and correlation are statistically significant. The model fits data. Regression weights and covariance can be seen in the picture if we click V. Čekanavičius, G. Murauskas 44 22

23 V. Čekanavičius, G. Murauskas 45 By choosing Standardized estimates We get factor loadings And correlation. V. Čekanavičius, G. Murauskas 46 23