ADVANCED SEM REX B KLINE CONCORDIA A. POWER, ORDINAL CFA

Transcription

1 ADVANCED SEM REX B KLINE CONCORDIA A1 A. POWER, ORDINAL CFA

2 A2

3 A3

4 topics power ordinal cfa means A4

5 topics latent growth cfa invariance moderation A5

6 A6

7 A7

8 power proper a priori (planning) improper A8

9 power applications model level effect level A9

10 Input (1) H0: parameter0, α, N, dfm H1: parameter1 A10

11 Output (1) p (reject H0 H1) 1 β A11

12 Input (2) Target power (e.g.,.85) H0, α, statistic, dfm, H1 A12

13 Output (2) Target N E.g., if power.85, then N 500 A13

14 MacCallum et al. RMSEA, 0 1 Type of H0, H1 A14

15 ˆ df M ˆ ( N 1) ˆ max (0, 2 df ) M M A15

16 ˆ, 90% CI [ ˆ, ˆ ] L U E.g., ˆ =.02 [0,.15] A16

17 H0 Accept support Reject support Exact fit Close fit Not close fit A17

18 Accept-support Logically weak Power, model A18

19 Reject-support Conventional logic Power, model A19

20 Low power Exact fit, close fit p (reject false model) A20

21 Low power Not close fit p (detect close model) A21

22 Test Null Exact fit H0: = 0 0 Close fit H0:.05 0 Not close fit H0: >.05 0 * A22

23 Close fit * Given ˆ, 90% CI [ ˆ, ˆ ] L U ˆ >.05, reject H0:.05 L 0 A23

24 Test H0 H1 Close fit.05 = Not close fit >.05 = A24

25 N = 373, dfm = 5 A25

26 Goodness of Fit Statistics Degrees of Freedom for (C1)-(C2) 5 Maximum Likelihood Ratio Chi-Square (C1) (P = ) Browne's (1984) ADF Chi-Square (C2_NT) (P = ) Estimated Non-centrality Parameter (NCP) Percent Confidence Interval for NCP ( ; ) Minimum Fit Function Value Population Discrepancy Function Value (F0) Percent Confidence Interval for F0 (0.000 ; ) Root Mean Square Error of Approximation (RMSEA) Percent Confidence Interval for RMSEA ( ; 0.103) P-Value for Test of Close Fit (RMSEA < 0.05) A26

27 Close but failing Exact-fit H0 rejected Close-fit H0 retained Inspect residuals A27

28 semtools for R A28

29 semtools for R A29

30 date() library(semtools) # power for test of close fit hypothesis for N = 373 findrmseapower(.05,.08, 5, 373,.05, 1) # sample size for target power =.80 for close fit hypothesis findrmseasamplesize(.05,.08, 5,.80,.05, 1) # power for test of not close fit hypothesis for N = 373 findrmseapower(.05,.01, 5, 373,.05, 1) # sample size for target power =.80 for not close fit hypothesis findrmseasamplesize(.05,.01, 5,.80,.05, 1) A30

31 Statistic N 373 dfm 5 Power Close fit a.317 Not close fit b.229 a H0:.05, 0 =.08, α =.05 1 b H0: >.05, 0 =.01, α =.05 1 A31

32 Target power.80 Target N Close fit a 1,464 Not close fit b 1,216 a H0:.05, 0 =.08, α =.05 1 b H0: >.05, 0 =.01, α =.05 1 A32

33 STATISTICA Power Analysis Generate SPSS, R syntax SAS/STAT syntax A33

34 Power Sample Size (N) A34

35 Minimum N for power.80 dfm N 1, A35

36 Bandalos, D. L., & Leite, W. (2013). Use of Monte Carlo studies in structural equation modeling. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (2nd ed.) (pp ). Charlotte, NC: IAP. A36

37 A37

38 ordinal likert scale 5 levels skewed A38

39 ordinal robust wls thresholds polychoric A39

40 ordinal global fit stats interpretation? residuals A40

41 (a) Histogram of observed item X responses with cumulative probabilities Proportion Disagree 2 Neutral 3 Agree Response Category A41

42 (b) Latent response variable X* with threshold estimates 25% 35% 40% ˆ 1=.67 ˆ 2=.25 X* A42

43 .45 Probability * X1 * X2 A43

44 X1 X2 X3 1 E X * 1 1 E X * 2 1 E X * 3 X * 1 X * 2 X * 3 A A44

45 Delta scaling Var (X*) = 1.0 Correlation metric A45

46 Delta standardized Simple indicator, r Threshold, z ~ND (0, 1) A46

47 Theta scaling Var (EX*) = 1.0 Probit metric A47

48 Theta unstandardized Indicators, probit z Thresholds, z ~ND (0, 1) A48

49 ordinal delta vs. theta 1 sample simplicity A49

50 ordinal delta vs. theta 2 samples error testing A50

51 Mplus WLSM Mean-adjusted A51

52 Mplus WLSMV Mean- and variance-adjusted Estimated dfm A52

53 LISREL RDWLS Robust diagonally-weighted A53

54 LISREL PRELIS: Thresholds Polychoric r LISREL Asymptotic cov A54

55 Example 5 items, CES-D 0 = < 1 day 1 = 1 2 days 2 = 3 4 days 3 = 5 7 days A55

56 Example N = 2,004 White men A56

57 A57

58 X2 X2 X3 X4 X5 τ 11 τ 13 τ 21 τ 23 τ 31 τ 33 τ 41 τ 43 τ 51 τ 53 X * 1 X * 2 X * 3 X * 4 X * 5 1 λ 2 λ 3 λ 4 λ 5 φ A A58

59 Observations v = 5, 5(4)/2 = 10 polychoric 5 3 = 15 thresholds A59

60 Parameters 15 thresholds (τ) 4 loadings (λ), 1 variance (φ) dfm = = 5 A60

61 PRELIS, LISREL Sorry, SIMPLIS Mplus A61

62 title: principles and practice of sem (4th ed.), rex kline single-factor model of depression, white sample, figure 13.6 data: file is radloff-white-mplus.dat; variable: names are x1-x5; categorical are x1-x5;! variables correspond to, respectively,! CES Depression scale items 1, 2, 7, 11, and 20 analysis: parameterization is delta;! total variance of latent response variables fixed to 1 model: Conflict by x1-x5; output: sampstat residual standardized tech1; A62

63 SUMMARY OF ANALYSIS Number of groups 1 Number of observations 2004 Number of dependent variables 5 Number of independent variables 0 Number of continuous latent variables 1 Observed dependent variables Binary and ordered categorical (ordinal) X1 X2 X3 X4 X5 A63

64 Continuous latent variables CONFLICT Estimator WLSMV Maximum number of iterations 1000 Convergence criterion 0.500D-04 Maximum number of steepest descent iterations 20 Parameterization DELTA A64

65 UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES X1 Category Category Category Category X2 Category Category Category Category A65

66 X3 Category Category Category Category X4 Category Category Category Category X5 Category Category Category Category A66

67 ESTIMATED SAMPLE STATISTICS MEANS/INTERCEPTS/THRESHOLDS X1$1 X1$2 X1$3 X2$1 X2$ MEANS/INTERCEPTS/THRESHOLDS X2$3 X3$1 X3$2 X3$3 X4$ MEANS/INTERCEPTS/THRESHOLDS X4$2 X4$3 X5$1 X5$2 X5$ A67

68 CORRELATION MATRIX (WITH VARIANCES ON THE DIAGONAL) X1 X2 X3 X4 X5 X1 X X X X A68

69 MODEL FIT INFORMATION Number of Free Parameters 20 Chi-Square Test of Model Fit Value * Degrees of Freedom 5 P-Value The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used for chi-square difference testing in the regular way. MLM, MLR and WLSM chi-square difference testing is described on the Mplus website. MLMV, WLSMV, and ULSMV difference testing is done using the DIFFTEST option. A69

70 RMSEA (Root Mean Square Error Of Approximation) Estimate Percent C.I Probability RMSEA <= CFI/TLI CFI TLI A70

71 MODEL RESULTS Two-Tailed Estimate S.E. Est./S.E. P-Value CONFLICT BY X X X X X Variances CONFLICT A71

72 Two-Tailed Estimate S.E. Est./S.E. P-Value Thresholds X1$ X1$ X1$ X2$ X2$ X2$ X3$ X3$ X3$ X4$ X4$ X4$ X5$ X5$ X5$ A72

73 STDYX Standardization Two-Tailed Estimate S.E. Est./S.E. P-Value CONFLICT BY X X X X X Variances CONFLICT A73

74 Thresholds X1$ X1$ X1$ X2$ X2$ X2$ X3$ X3$ X3$ X4$ X4$ X4$ X5$ X5$ X5$ A74

75 R-SQUARE Observed Two-Tailed Residual Variable Estimate S.E. Est./S.E. P-Value Variance X X X X X A75

76 RESIDUAL OUTPUT ESTIMATED MODEL AND RESIDUALS (OBSERVED - ESTIMATED) Residuals for Means/Intercepts/Thresholds X1$1 X1$2 X1$3 X2$1 X2$ Residuals for Means/Intercepts/Thresholds X2$3 X3$1 X3$2 X3$3 X4$ Residuals for Means/Intercepts/Thresholds X4$2 X4$3 X5$1 X5$2 X5$ A76

77 Model Estimated Covariances/Correlations/Residual Correlations X1 X2 X3 X4 X5 X1 X X X X Residuals for Covariances/Correlations/Residual Correlations X1 X2 X3 X4 X5 X1 X X X X A77

78 Unstandardized Standardized Parameter Estimate SE Estimate SE R 2 Pattern coefficients A X1* A X2* A X3* A X4* A X5* Factor variance A (Depression) Note. Thresholds: X1,.772, 1.420, 1.874; X2, 1.044, 1.543, 1.874; X3,.541, 1.152, 1.503; X4,.288, 1.000, 1.500; X5,.558, 1.252, All results were computed with Mplus in delta parameterization and STDYX standardization. A78

79 Indicator X1* X2* X3* X4* X5* Correlation residuals X1* X2*.041 X3* X4* X5* Note. The correlation residuals were computed by Mplus. A79

80 Indicator X1* X2* X3* X4* X5* Standardized residuals X1* X2* X3* X4* X5* Note. The standardized residuals were computed by LISREL. A80

81 A81