Mplus VERSION 7 MUTHEN & MUTHEN 12/01/2012 2:35 PM INPUT INSTRUCTIONS TITLE: Strict Invariance for dichotomous items See Millsap & Tein (2004, p.485) for further details DATA: FILE IS example2c.csv; VARIABLE: NAMES ARE u1-u8 g; USEVARIABLES ARE u1-u8; CATEGORICAL ARE u1-u8; GROUPING IS g (1=male 2=female); ! Theta parameterization is strongly recommended for multiple groups ANALYSIS: PARAMETERIZATION = THETA; ESTIMATOR = WLSMV; ! Put the chi-square values of the model that we wish to compare with this model DIFFTEST=weak2c.dif; ! strict vs. weak MODEL: ! Factor loadings are constrained across groups ! except the marker variables, which are fixed. f1 BY u1@1 u2 (f21) u3 (f31) u4 (f41); f2 BY u5@1 u6 (f62) u7 (f72) u8 (f82); ! Thresholds are constrained across groups [u1$1] (t1); [u2$1] (t2); [u3$1] (t3); [u4$1] (t4); [u5$1] (t5); [u6$1] (t6); [u7$1] (t7); [u8$1] (t8); ! Factor variance/covariance are free across groups f1*; f2*; f1 WITH f2*; ! Factor mean of the first group are fixed to zeros [f1@0]; [f2@0]; ! Unique variances of the all groups are fixed as 1 u1@1; u2@1; u3@1; u4@1; u5@1; u6@1; u7@1; u8@1; MODEL female: ! Factor loadings are constrained across groups ! except the marker variables, which are fixed. f1 BY u1@1 u2 (f21) u3 (f31) u4 (f41); f2 BY u5@1 u6 (f62) u7 (f72) u8 (f82); ! Thresholds are constrained across groups [u1$1] (t1); [u2$1] (t2); [u3$1] (t3); [u4$1] (t4); [u5$1] (t5); [u6$1] (t6); [u7$1] (t7); [u8$1] (t8); ! Factor variance/covariance are free across groups f1*; f2*; f1 WITH f2*; ! Factor mean of the second group are free [f1*]; [f2*]; ! Unique variances are fixed to 1 (equal to the first group) u1@1; u2@1; u3@1; u4@1; u5@1; u6@1; u7@1; u8@1; OUTPUT: TECH1; STDYX; ! Save the chi-square values for difference testing with other nested models SAVEDATA: DIFFTEST=strict2c.dif; INPUT READING TERMINATED NORMALLY Strict Invariance for dichotomous items See Millsap & Tein (2004, p.485) for further details SUMMARY OF ANALYSIS Number of groups 2 Number of observations Group MALE 1000 Group FEMALE 1000 Number of dependent variables 8 Number of independent variables 0 Number of continuous latent variables 2 Observed dependent variables Binary and ordered categorical (ordinal) U1 U2 U3 U4 U5 U6 U7 U8 Continuous latent variables F1 F2 Variables with special functions Grouping variable G Estimator WLSMV Maximum number of iterations 1000 Convergence criterion 0.500D-04 Maximum number of steepest descent iterations 20 Parameterization THETA Input data file(s) example2c.csv Input data format FREE UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES Group MALE U1 Category 1 0.519 519.000 Category 2 0.481 481.000 U2 Category 1 0.503 503.000 Category 2 0.497 497.000 U3 Category 1 0.529 529.000 Category 2 0.471 471.000 U4 Category 1 0.507 507.000 Category 2 0.493 493.000 U5 Category 1 0.514 514.000 Category 2 0.486 486.000 U6 Category 1 0.525 525.000 Category 2 0.475 475.000 U7 Category 1 0.533 533.000 Category 2 0.467 467.000 U8 Category 1 0.506 506.000 Category 2 0.494 494.000 Group FEMALE U1 Category 1 0.652 652.000 Category 2 0.348 348.000 U2 Category 1 0.647 647.000 Category 2 0.353 353.000 U3 Category 1 0.655 655.000 Category 2 0.345 345.000 U4 Category 1 0.646 646.000 Category 2 0.354 354.000 U5 Category 1 0.443 443.000 Category 2 0.557 557.000 U6 Category 1 0.455 455.000 Category 2 0.545 545.000 U7 Category 1 0.442 442.000 Category 2 0.558 558.000 U8 Category 1 0.463 463.000 Category 2 0.537 537.000 THE MODEL ESTIMATION TERMINATED NORMALLY MODEL FIT INFORMATION Number of Free Parameters 22 Chi-Square Test of Model Fit Value 40.739* Degrees of Freedom 50 P-Value 0.8219 Chi-Square Contributions From Each Group MALE 18.657 FEMALE 22.082 Chi-Square Test for Difference Testing Value 6.637 Degrees of Freedom 6 P-Value 0.3558 * 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. RMSEA (Root Mean Square Error Of Approximation) Estimate 0.000 90 Percent C.I. 0.000 0.013 Probability RMSEA <= .05 1.000 CFI/TLI CFI 1.000 TLI 1.003 Chi-Square Test of Model Fit for the Baseline Model Value 3726.800 Degrees of Freedom 56 P-Value 0.0000 WRMR (Weighted Root Mean Square Residual) Value 0.905 MODEL RESULTS Two-Tailed Estimate S.E. Est./S.E. P-Value Group MALE F1 BY U1 1.000 0.000 999.000 999.000 U2 0.915 0.095 9.621 0.000 U3 0.918 0.095 9.706 0.000 U4 0.971 0.101 9.627 0.000 F2 BY U5 1.000 0.000 999.000 999.000 U6 0.887 0.095 9.390 0.000 U7 0.937 0.100 9.382 0.000 U8 0.928 0.099 9.361 0.000 F1 WITH F2 0.602 0.084 7.175 0.000 Means F1 0.000 0.000 999.000 999.000 F2 0.000 0.000 999.000 999.000 Thresholds U1$1 0.057 0.049 1.175 0.240 U2$1 0.027 0.046 0.579 0.563 U3$1 0.088 0.046 1.893 0.058 U4$1 0.026 0.047 0.556 0.579 U5$1 0.052 0.053 0.990 0.322 U6$1 0.083 0.048 1.712 0.087 U7$1 0.079 0.050 1.573 0.116 U8$1 0.067 0.050 1.350 0.177 Variances F1 0.933 0.149 6.275 0.000 F2 1.231 0.199 6.176 0.000 Residual Variances U1 1.000 0.000 999.000 999.000 U2 1.000 0.000 999.000 999.000 U3 1.000 0.000 999.000 999.000 U4 1.000 0.000 999.000 999.000 U5 1.000 0.000 999.000 999.000 U6 1.000 0.000 999.000 999.000 U7 1.000 0.000 999.000 999.000 U8 1.000 0.000 999.000 999.000 Group FEMALE F1 BY U1 1.000 0.000 999.000 999.000 U2 0.915 0.095 9.621 0.000 U3 0.918 0.095 9.706 0.000 U4 0.971 0.101 9.627 0.000 F2 BY U5 1.000 0.000 999.000 999.000 U6 0.887 0.095 9.390 0.000 U7 0.937 0.100 9.382 0.000 U8 0.928 0.099 9.361 0.000 F1 WITH F2 0.644 0.091 7.043 0.000 Means F1 -0.531 0.069 -7.712 0.000 F2 0.266 0.065 4.121 0.000 Thresholds U1$1 0.057 0.049 1.175 0.240 U2$1 0.027 0.046 0.579 0.563 U3$1 0.088 0.046 1.893 0.058 U4$1 0.026 0.047 0.556 0.579 U5$1 0.052 0.053 0.990 0.322 U6$1 0.083 0.048 1.712 0.087 U7$1 0.079 0.050 1.573 0.116 U8$1 0.067 0.050 1.350 0.177 Variances F1 1.178 0.193 6.091 0.000 F2 1.242 0.203 6.110 0.000 Residual Variances U1 1.000 0.000 999.000 999.000 U2 1.000 0.000 999.000 999.000 U3 1.000 0.000 999.000 999.000 U4 1.000 0.000 999.000 999.000 U5 1.000 0.000 999.000 999.000 U6 1.000 0.000 999.000 999.000 U7 1.000 0.000 999.000 999.000 U8 1.000 0.000 999.000 999.000 STANDARDIZED MODEL RESULTS STDYX Standardization Two-Tailed Estimate S.E. Est./S.E. P-Value Group MALE F1 BY U1 0.695 0.029 24.265 0.000 U2 0.662 0.030 22.103 0.000 U3 0.664 0.029 22.765 0.000 U4 0.684 0.030 22.999 0.000 F2 BY U5 0.743 0.027 27.561 0.000 U6 0.702 0.028 24.761 0.000 U7 0.721 0.028 25.922 0.000 U8 0.717 0.028 25.835 0.000 F1 WITH F2 0.562 0.041 13.600 0.000 Means F1 0.000 0.000 999.000 999.000 F2 0.000 0.000 999.000 999.000 Thresholds U1$1 0.041 0.035 1.170 0.242 U2$1 0.020 0.034 0.577 0.564 U3$1 0.065 0.035 1.881 0.060 U4$1 0.019 0.035 0.554 0.579 U5$1 0.035 0.035 0.994 0.320 U6$1 0.059 0.034 1.723 0.085 U7$1 0.055 0.035 1.583 0.113 U8$1 0.047 0.035 1.358 0.175 Variances F1 1.000 0.000 999.000 999.000 F2 1.000 0.000 999.000 999.000 Residual Variances U1 0.517 0.040 12.998 0.000 U2 0.561 0.040 14.131 0.000 U3 0.560 0.039 14.465 0.000 U4 0.532 0.041 13.075 0.000 U5 0.448 0.040 11.192 0.000 U6 0.508 0.040 12.767 0.000 U7 0.480 0.040 11.980 0.000 U8 0.485 0.040 12.179 0.000 Group FEMALE F1 BY U1 0.735 0.028 26.532 0.000 U2 0.705 0.028 25.021 0.000 U3 0.706 0.029 24.324 0.000 U4 0.725 0.027 26.632 0.000 F2 BY U5 0.744 0.027 27.390 0.000 U6 0.703 0.028 25.074 0.000 U7 0.722 0.028 26.018 0.000 U8 0.719 0.028 26.133 0.000 F1 WITH F2 0.533 0.041 12.918 0.000 Means F1 -0.489 0.055 -8.831 0.000 F2 0.239 0.056 4.264 0.000 Thresholds U1$1 0.039 0.033 1.169 0.242 U2$1 0.019 0.033 0.577 0.564 U3$1 0.062 0.033 1.879 0.060 U4$1 0.018 0.033 0.554 0.579 U5$1 0.035 0.035 0.993 0.321 U6$1 0.059 0.034 1.721 0.085 U7$1 0.055 0.035 1.582 0.114 U8$1 0.047 0.034 1.356 0.175 Variances F1 1.000 0.000 999.000 999.000 F2 1.000 0.000 999.000 999.000 Residual Variances U1 0.459 0.041 11.260 0.000 U2 0.503 0.040 12.673 0.000 U3 0.502 0.041 12.245 0.000 U4 0.474 0.040 11.995 0.000 U5 0.446 0.040 11.031 0.000 U6 0.506 0.039 12.821 0.000 U7 0.478 0.040 11.925 0.000 U8 0.483 0.040 12.218 0.000 R-SQUARE Group MALE Observed Two-Tailed Scale Variable Estimate S.E. Est./S.E. P-Value Factors U1 0.483 0.040 12.133 0.000 0.719 U2 0.439 0.040 11.052 0.000 0.749 U3 0.440 0.039 11.382 0.000 0.748 U4 0.468 0.041 11.500 0.000 0.729 U5 0.552 0.040 13.780 0.000 0.669 U6 0.492 0.040 12.381 0.000 0.713 U7 0.520 0.040 12.961 0.000 0.693 U8 0.515 0.040 12.917 0.000 0.697 Group FEMALE Observed Two-Tailed Scale Variable Estimate S.E. Est./S.E. P-Value Factors U1 0.541 0.041 13.266 0.000 0.678 U2 0.497 0.040 12.511 0.000 0.709 U3 0.498 0.041 12.162 0.000 0.708 U4 0.526 0.040 13.316 0.000 0.688 U5 0.554 0.040 13.695 0.000 0.668 U6 0.494 0.039 12.537 0.000 0.711 U7 0.522 0.040 13.009 0.000 0.692 U8 0.517 0.040 13.067 0.000 0.695 QUALITY OF NUMERICAL RESULTS Condition Number for the Information Matrix 0.835E-02 (ratio of smallest to largest eigenvalue) TECHNICAL 1 OUTPUT PARAMETER SPECIFICATION FOR MALE TAU U1$1 U2$1 U3$1 U4$1 U5$1 ________ ________ ________ ________ ________ 1 1 2 3 4 5 TAU U6$1 U7$1 U8$1 ________ ________ ________ 1 6 7 8 NU U1 U2 U3 U4 U5 ________ ________ ________ ________ ________ 1 0 0 0 0 0 NU U6 U7 U8 ________ ________ ________ 1 0 0 0 LAMBDA F1 F2 ________ ________ U1 0 0 U2 9 0 U3 10 0 U4 11 0 U5 0 0 U6 0 12 U7 0 13 U8 0 14 THETA U1 U2 U3 U4 U5 ________ ________ ________ ________ ________ U1 0 U2 0 0 U3 0 0 0 U4 0 0 0 0 U5 0 0 0 0 0 U6 0 0 0 0 0 U7 0 0 0 0 0 U8 0 0 0 0 0 THETA U6 U7 U8 ________ ________ ________ U6 0 U7 0 0 U8 0 0 0 ALPHA F1 F2 ________ ________ 1 0 0 BETA F1 F2 ________ ________ F1 0 0 F2 0 0 PSI F1 F2 ________ ________ F1 15 F2 16 17 PARAMETER SPECIFICATION FOR FEMALE TAU U1$1 U2$1 U3$1 U4$1 U5$1 ________ ________ ________ ________ ________ 1 1 2 3 4 5 TAU U6$1 U7$1 U8$1 ________ ________ ________ 1 6 7 8 NU U1 U2 U3 U4 U5 ________ ________ ________ ________ ________ 1 0 0 0 0 0 NU U6 U7 U8 ________ ________ ________ 1 0 0 0 LAMBDA F1 F2 ________ ________ U1 0 0 U2 9 0 U3 10 0 U4 11 0 U5 0 0 U6 0 12 U7 0 13 U8 0 14 THETA U1 U2 U3 U4 U5 ________ ________ ________ ________ ________ U1 0 U2 0 0 U3 0 0 0 U4 0 0 0 0 U5 0 0 0 0 0 U6 0 0 0 0 0 U7 0 0 0 0 0 U8 0 0 0 0 0 THETA U6 U7 U8 ________ ________ ________ U6 0 U7 0 0 U8 0 0 0 ALPHA F1 F2 ________ ________ 1 18 19 BETA F1 F2 ________ ________ F1 0 0 F2 0 0 PSI F1 F2 ________ ________ F1 20 F2 21 22 STARTING VALUES FOR MALE TAU U1$1 U2$1 U3$1 U4$1 U5$1 ________ ________ ________ ________ ________ 1 0.048 0.008 0.073 0.018 0.035 TAU U6$1 U7$1 U8$1 ________ ________ ________ 1 0.063 0.083 0.015 NU U1 U2 U3 U4 U5 ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 NU U6 U7 U8 ________ ________ ________ 1 0.000 0.000 0.000 LAMBDA F1 F2 ________ ________ U1 1.000 0.000 U2 0.893 0.000 U3 1.024 0.000 U4 0.898 0.000 U5 0.000 1.000 U6 0.000 0.942 U7 0.000 0.945 U8 0.000 0.963 THETA U1 U2 U3 U4 U5 ________ ________ ________ ________ ________ U1 1.000 U2 0.000 1.000 U3 0.000 0.000 1.000 U4 0.000 0.000 0.000 1.000 U5 0.000 0.000 0.000 0.000 1.000 U6 0.000 0.000 0.000 0.000 0.000 U7 0.000 0.000 0.000 0.000 0.000 U8 0.000 0.000 0.000 0.000 0.000 THETA U6 U7 U8 ________ ________ ________ U6 1.000 U7 0.000 1.000 U8 0.000 0.000 1.000 ALPHA F1 F2 ________ ________ 1 0.000 0.000 BETA F1 F2 ________ ________ F1 0.000 0.000 F2 0.000 0.000 PSI F1 F2 ________ ________ F1 0.050 F2 0.000 0.050 STARTING VALUES FOR FEMALE TAU U1$1 U2$1 U3$1 U4$1 U5$1 ________ ________ ________ ________ ________ 1 0.219 0.192 0.236 0.196 -0.054 TAU U6$1 U7$1 U8$1 ________ ________ ________ 1 -0.025 -0.032 -0.039 NU U1 U2 U3 U4 U5 ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 NU U6 U7 U8 ________ ________ ________ 1 0.000 0.000 0.000 LAMBDA F1 F2 ________ ________ U1 1.000 0.000 U2 1.029 0.000 U3 0.930 0.000 U4 1.085 0.000 U5 0.000 1.000 U6 0.000 1.055 U7 0.000 1.003 U8 0.000 1.058 THETA U1 U2 U3 U4 U5 ________ ________ ________ ________ ________ U1 1.000 U2 0.000 1.000 U3 0.000 0.000 1.000 U4 0.000 0.000 0.000 1.000 U5 0.000 0.000 0.000 0.000 1.000 U6 0.000 0.000 0.000 0.000 0.000 U7 0.000 0.000 0.000 0.000 0.000 U8 0.000 0.000 0.000 0.000 0.000 THETA U6 U7 U8 ________ ________ ________ U6 1.000 U7 0.000 1.000 U8 0.000 0.000 1.000 ALPHA F1 F2 ________ ________ 1 0.000 0.000 BETA F1 F2 ________ ________ F1 0.000 0.000 F2 0.000 0.000 PSI F1 F2 ________ ________ F1 0.050 F2 0.000 0.050 SAVEDATA INFORMATION Difference testing Save file strict2c.dif Save format Free DIAGRAM INFORMATION Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram. If running Mplus from the Mplus Diagrammer, the diagram opens automatically. Diagram output c:\users\s044p855.home\desktop\sem\categorical invariance\strict2c.dgm Beginning Time: 14:35:42 Ending Time: 14:35:42 Elapsed Time: 00:00:00 MUTHEN & MUTHEN 3463 Stoner Ave. Los Angeles, CA 90066 Tel: (310) 391-9971 Fax: (310) 391-8971 Web: www.StatModel.com Support: Support@StatModel.com Copyright (c) 1998-2012 Muthen & Muthen