SR MODELS REX B KLINE PSYCHOLOGY, CONCORDIA UNIVERSITY

Transcription

1 SEM SR MODELS REX B KLINE PSYCHOLOGY, CONCORDIA UNIVERSITY E

2 Latents CFA: Exogenous only L M only SR: Exogenous or endogenous L M or M L E2

3 Fully latent SR EX EX2 EY EY2 EY3 EY4 X X2 Y Y2 Y3 Y4 A B C DB DC E3

4 Partially latent SR () EX EX2 EY3 EY4 X X2 Y3 Y4 A Y C DY DC E4

5 Partially latent SR (2) EY EY2 EY3 EY4 Y Y2 Y3 Y4 X B C D B D C E5

6 identify two parts measurement structural E6

7 2-step (sufficient) rule measure as cfa structure as path E7

8 (a) Original SR (b) Respecified as a CFA EX EX 2 EY EY 2 EY 3 EY 4 EX EX 2 EY EY 2 EY 3 EY 4 X X2 Y Y2 Y3 Y4 X X2 Y Y2 Y3 Y4 A B C A B C DB DC (c) Structural A B C DB DC E8

9 analyze -step original model E9

10 EX EX2 EY EY2 EY3 EY4 X X2 Y Y2 Y3 Y4 A B C DB DC E0

11 analyze 2-step respecify as cfa then structural E

12 (a) Original SR Model (b) Respecified as a CFA Model EX EX 2 EY EY 2 EY 3 EY 4 EX EX 2 EY EY 2 EY 3 EY 4 X X2 Y Y2 Y3 Y4 X X2 Y Y2 Y3 Y4 A B C A B C DB DC E2

13 analyze 4-step efa, cfa, structural (2) 4 indicators/l E3

14 R 2 size indicators factors E4

15 Single indicators () EX EX2 EY3 EY4 X X2 Y3 Y4 A Y C DY DC E5

16 Single indicators (2) EY EY2 EY3 EY4 Y Y2 Y3 Y4 X B C D B D C E6

17 Single indicators. Proportion error variance ( rxx) s 2 2. Fixed parameters E7

18 2.30s Y EX EX2 EY EY3 EY4 X X2 Y Y3 Y4 A B C D B D C E8

19 2.20s X EX EY EY2 EY3 EY4 X Y Y2 Y3 Y4 A B C D B D C E9

20 X DY Y X2 E20

21 ( r ) 2 s ( r YY ) 2 s Y E EY X Y A C ( r 22 ) 2 s 2 E2 DY X2 B E2

22 Hayduk, L. A. & Littvay, L. (202). Should researchers use single indicators, best indicators, or multiple indicators in structural equation models? BMC Medical Research Methodology, 2(59). E22

23 EAS EGS EPL EInt EJo Acculturation Scale General Status Percent Life U.S. Interpersonal Job Acculturation Stress DSt SES Depression Scale DDS Education Income EEd EInc E23

24 EAS EGS EPL EInt EJo Acculturation Scale General Status Percent Life U.S. Interpersonal Job Acculturation Stress DSt SES Depression DDe Education Income EEd EInc Depression Scale EDS 2.30 s DS E24

25 v = 8; 8(9)/2 = 39 dfm = = 9 E25

26 Model Direct effects Variances Covariances Total Acc GS Acc %L SES Inc Str Job Acc Str Str Dep SES Dep Acc, SES E (7) D (2) Acc GS SES %Li 20 E26

27 LISREL title: shen and takeuchi (200) error term for depression scale observed variables acculscl genstat perlife educ income interper job depscale latent variables: Accultur Ses Stress Depressi correlation matrix E27

28 standard deviations sample size is 983 relationships acculscl = *Accultur genstat perlife = Accultur educ = *Ses income = Ses interper = *Stress job = Stress depscale = *Depressi! depscale as single indicator Stress = Accultur Depressi = Ses Stress E28

29 set error variance of depscale to 3.06! fixes the error variance of the single indicator! rxx =.70, proportion of error variance =.30! sample variance is 0.200;.30 * = 3.06 let the errors of genstat and perlife correlate path diagram LISREL output: ND = 3 SC RS end of program E29

30 Covariance Matrix interper job depscale acculscl genstat perlife interper job depscale acculscl genstat perlife educ income Covariance Matrix educ income educ income Total Variance = Generalized Variance = Largest Eigenvalue = Smallest Eigenvalue =.972 Condition Number = E30

31 Parameter Specifications LAMBDA-Y Stress Depressi interper 0 0 job 0 depscale 0 0 LAMBDA-X Accultur Ses acculscl 0 0 genstat 2 0 perlife 3 0 educ 0 0 income 0 4 Loadings, indicators Endogenous factors Loadings, indicators Exogenous factors E3

32 BETA Stress Depressi Stress 0 0 Depressi 5 0 Endogenous factor Exogenous factor GAMMA Accultur Ses Stress 6 0 Depressi 0 7 Exogenous factor Endogenous factor E32

33 PHI Accultur Ses Accultur 8 Ses 9 0 PSI Stress Depressi Variances, covariances Exogenous factors Disturbance variances, Endogenous factors E33

34 THETA-EPS interper job depscale THETA-DELTA Errors, indicators Endogenous factors Errors, indicators Exogenous factors acculscl genstat perlife educ income acculscl 5 genstat 0 6 perlife educ income E34

35 Number of Iterations = 9 LISREL Estimates (Maximum Likelihood) LAMBDA-Y Stress Depressi interper job (0.23).863 depscale E35

36 LAMBDA-X Accultur Ses acculscl genstat (0.046) perlife (0.043) 2.49 educ income (0.089) E36

37 BETA Stress Depressi Stress Depressi (0.4).634 GAMMA Accultur Ses Stress (0.023) Depressi (0.060) E37

38 Covariance Matrix of ETA and KSI Stress Depressi Accultur Ses Stress Depressi Accultur Ses E38

39 PHI Accultur Ses Accultur (0.825).608 Ses (0.345) (0.732) E39

40 PSI Note: This matrix is diagonal. Stress Depressi (0.354) (0.465) Squared Multiple Correlations for Structural Equations Stress Depressi E40

41 THETA-EPS interper job depscale (0.349) (0.564) Squared Multiple Correlations for Y - Variables interper job depscale E4

42 THETA-DELTA acculscl genstat perlife educ income acculscl 0.53 (0.699) 0.29 genstat (0.420) perlife (0.248) (0.245) educ (0.666) income (0.524) 8.33 E42

43 Squared Multiple Correlations for X - Variables acculscl genstat perlife educ income E43

44 Goodness of Fit Statistics Degrees of Freedom for (C)-(C2) 6 Maximum Likelihood Ratio Chi-Square (C) (P = ) Browne's (984) ADF Chi-Square (C2_NT) (P = ) Root Mean Square Error of Approximation (RMSEA) Percent Confidence Interval for RMSEA ( ; ) P-Value for Test of Close Fit (RMSEA < 0.05) Chi-Square for Independence Model (28 df) Comparative Fit Index (CFI) Root Mean Square Residual (RMR) Standardized RMR E44

45 Fitted Covariance Matrix interper job depscale acculscl genstat perlife interper job depscale acculscl genstat perlife educ income Fitted Covariance Matrix educ income educ income E45

46 Fitted Residuals interper job depscale acculscl genstat perlife interper job depscale acculscl genstat perlife educ income Fitted Residuals educ income educ income E46

47 Summary Statistics for Fitted Residuals Smallest Fitted Residual = Median Fitted Residual = Largest Fitted Residual = 0.78 Stemleaf Plot E47

48 Standardized Residuals interper job depscale acculscl genstat perlife interper job depscale acculscl genstat perlife educ income Standardized Residuals educ income educ income E48

49 Summary Statistics for Standardized Residuals Smallest Standardized Residual = Median Standardized Residual = Largest Standardized Residual = Stemleaf Plot E49

50 E50

51 Standardized Solution LAMBDA-Y Stress Depressi interper job depscale LAMBDA-X Accultur Ses acculscl genstat perlife educ income E5

52 Completely Standardized Solution LAMBDA-Y Stress Depressi interper job depscale LAMBDA-X Accultur Ses acculscl genstat perlife educ income E52

53 BETA Stress Depressi Stress Depressi GAMMA Accultur Ses Stress Depressi E53

54 Correlation Matrix of ETA and KSI Stress Depressi Accultur Ses Stress.000 Depressi Accultur Ses PSI Note: This matrix is diagonal. Stress Depressi E54

55 THETA-EPS interper job depscale THETA-DELTA acculscl genstat perlife educ income acculscl 0.06 genstat perlife educ income E55

56 E56

57 Correlation Residuals (EQS) STANDARDIZED RESIDUAL MATRIX: ACCULSCL GENSTAT PERLIFE EDUC INCOME V V2 V3 V4 V5 ACCULSCL V.000 GENSTAT V PERLIFE V EDUC V INCOME V INTERPER V JOB V DEPSCL V INTERPER JOB DEPSCL V6 V7 V8 INTERPER V6.000 JOB V DEPSCL V E57

58 L M M L E58

59 reflect all cfa models classical theory assumes... E59

60 reflect exchangeable M high, positive rij unidimensional L E60

61 Reflective? Income SES Occupation Education Residence E6

62 M L form heterogeneous L no error, composite E62

63 exchangeable M form high, positive rij any pattern (, 0, +) E63

64 (a) L M (effect indicators) (b) M L (causal indicators) E E2 E3 E4 X X2 X3 X4 X X2 X3 X4 Latent variable Latent variable DLV E64

65 (c) M C (composite indicators) X X2 X3 X4 Composite E65

66 whole model is sr form identified? pls path modeling E66

67 Requirements Formative L emits 2 Formative L cannot receive Indirect effects... E67

68 EAS EGS EPL EInt EJo Acculturation Scale General Status Percent Life U.S. Interpersonal Job Acculturation Stress DSt SES Depression DDe Education Income EEd EInc Depression Scale EDS 2.30 s DS E68

69 construct validity form exogenous M unmodeled, error E69

70 ( r) s 2 ( r22) s 2 2 ( r33) s 2 3 EX EY EY 3 X X2 X3 X4 X X2 X3 Latent variable A B C DLV Latent variable DLV E70

71 Bollen, K. A., & Bauldry, S. (20). Three Cs in measurement models: Causal indicators, composite Indicators, and covariates. Psychological Methods, 6, Diamantopoulos, A. (Ed.). (2008). Formative indicators [Special issue]. Journal of Business Research, 6(2). Grace, J. B., & Bollen, K. A. (2008). Representing general theoretical concepts in structural equation models: The role of composite variables. Environmental and Ecological Statistics, 5, E7

72 regression & pca pls composites prediction E72

73 combine predictors? pls no theory no identification E73

74 E74

75 Henseler, J., & Wang, H. (200) (Eds.) Handbook of partial least squares: Concepts, methods and applications. Berlin: Springer-Verlag. E75

76 E76