Mplus VERSION 7 MUTHEN & MUTHEN 12/01/2012 2:35 PM INPUT INSTRUCTIONS TITLE: Weak 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=configural2c.dif; ! weak vs. configural 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 of the marker variables are fixed but others are free. u1@1; u2*; u3*; u4*; u5@1; u6*; u7*; u8*; OUTPUT: TECH1; STDYX; ! Save the chi-square values for difference testing with other nested models SAVEDATA: DIFFTEST=weak2c.dif; INPUT READING TERMINATED NORMALLY Weak 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 28 Chi-Square Test of Model Fit Value 33.401* Degrees of Freedom 44 P-Value 0.8776 Chi-Square Contributions From Each Group MALE 15.037 FEMALE 18.365 Chi-Square Test for Difference Testing Value 4.264 Degrees of Freedom 6 P-Value 0.6411 * 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 0.011 Probability RMSEA <= .05 1.000 CFI/TLI CFI 1.000 TLI 1.004 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 0.783 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 0.826 0.127 6.531 0.000 U3 0.952 0.149 6.374 0.000 U4 0.805 0.122 6.585 0.000 F2 BY U5 1.000 0.000 999.000 999.000 U6 0.832 0.123 6.761 0.000 U7 0.907 0.134 6.764 0.000 U8 0.871 0.128 6.786 0.000 F1 WITH F2 0.668 0.113 5.916 0.000 Means F1 0.000 0.000 999.000 999.000 F2 0.000 0.000 999.000 999.000 Thresholds U1$1 0.066 0.051 1.288 0.198 U2$1 0.023 0.045 0.517 0.605 U3$1 0.104 0.051 2.040 0.041 U4$1 0.010 0.043 0.239 0.811 U5$1 0.053 0.054 0.984 0.325 U6$1 0.081 0.047 1.741 0.082 U7$1 0.078 0.050 1.555 0.120 U8$1 0.070 0.048 1.451 0.147 Variances F1 1.060 0.227 4.665 0.000 F2 1.336 0.276 4.834 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 0.826 0.127 6.531 0.000 U3 0.952 0.149 6.374 0.000 U4 0.805 0.122 6.585 0.000 F2 BY U5 1.000 0.000 999.000 999.000 U6 0.832 0.123 6.761 0.000 U7 0.907 0.134 6.764 0.000 U8 0.871 0.128 6.786 0.000 F1 WITH F2 0.578 0.098 5.897 0.000 Means F1 -0.494 0.075 -6.588 0.000 F2 0.262 0.065 4.042 0.000 Thresholds U1$1 0.066 0.051 1.288 0.198 U2$1 0.023 0.045 0.517 0.605 U3$1 0.104 0.051 2.040 0.041 U4$1 0.010 0.043 0.239 0.811 U5$1 0.053 0.054 0.984 0.325 U6$1 0.081 0.047 1.741 0.082 U7$1 0.078 0.050 1.555 0.120 U8$1 0.070 0.048 1.451 0.147 Variances F1 1.035 0.204 5.068 0.000 F2 1.140 0.244 4.667 0.000 Residual Variances U1 1.000 0.000 999.000 999.000 U2 0.670 0.280 2.394 0.017 U3 1.151 0.466 2.470 0.014 U4 0.466 0.197 2.359 0.018 U5 1.000 0.000 999.000 999.000 U6 0.774 0.332 2.330 0.020 U7 0.876 0.376 2.332 0.020 U8 0.765 0.329 2.327 0.020 STANDARDIZED MODEL RESULTS STDYX Standardization Two-Tailed Estimate S.E. Est./S.E. P-Value Group MALE F1 BY U1 0.717 0.037 19.220 0.000 U2 0.648 0.039 16.523 0.000 U3 0.700 0.038 18.444 0.000 U4 0.638 0.039 16.164 0.000 F2 BY U5 0.756 0.033 22.579 0.000 U6 0.693 0.036 19.142 0.000 U7 0.724 0.035 20.598 0.000 U8 0.709 0.035 19.994 0.000 F1 WITH F2 0.562 0.041 13.607 0.000 Means F1 0.000 0.000 999.000 999.000 F2 0.000 0.000 999.000 999.000 Thresholds U1$1 0.046 0.036 1.293 0.196 U2$1 0.018 0.034 0.517 0.605 U3$1 0.074 0.036 2.061 0.039 U4$1 0.008 0.033 0.239 0.811 U5$1 0.035 0.035 0.989 0.323 U6$1 0.059 0.033 1.754 0.079 U7$1 0.054 0.034 1.565 0.118 U8$1 0.049 0.034 1.458 0.145 Variances F1 1.000 0.000 999.000 999.000 F2 1.000 0.000 999.000 999.000 Residual Variances U1 0.485 0.054 9.066 0.000 U2 0.580 0.051 11.412 0.000 U3 0.510 0.053 9.601 0.000 U4 0.593 0.050 11.758 0.000 U5 0.428 0.051 8.453 0.000 U6 0.519 0.050 10.341 0.000 U7 0.476 0.051 9.364 0.000 U8 0.497 0.050 9.870 0.000 Group FEMALE F1 BY U1 0.713 0.035 20.627 0.000 U2 0.717 0.035 20.507 0.000 U3 0.670 0.036 18.704 0.000 U4 0.768 0.033 23.008 0.000 F2 BY U5 0.730 0.037 19.970 0.000 U6 0.711 0.036 19.561 0.000 U7 0.719 0.036 19.719 0.000 U8 0.728 0.036 20.491 0.000 F1 WITH F2 0.533 0.041 12.891 0.000 Means F1 -0.486 0.059 -8.213 0.000 F2 0.245 0.060 4.109 0.000 Thresholds U1$1 0.046 0.036 1.271 0.204 U2$1 0.020 0.038 0.521 0.603 U3$1 0.072 0.035 2.078 0.038 U4$1 0.010 0.040 0.240 0.811 U5$1 0.036 0.037 0.985 0.325 U6$1 0.065 0.039 1.675 0.094 U7$1 0.058 0.038 1.500 0.134 U8$1 0.055 0.039 1.401 0.161 Variances F1 1.000 0.000 999.000 999.000 F2 1.000 0.000 999.000 999.000 Residual Variances U1 0.491 0.049 9.965 0.000 U2 0.487 0.050 9.716 0.000 U3 0.551 0.048 11.477 0.000 U4 0.410 0.051 7.983 0.000 U5 0.467 0.053 8.762 0.000 U6 0.495 0.052 9.583 0.000 U7 0.483 0.052 9.200 0.000 U8 0.470 0.052 9.074 0.000 R-SQUARE Group MALE Observed Two-Tailed Scale Variable Estimate S.E. Est./S.E. P-Value Factors U1 0.515 0.054 9.610 0.000 0.697 U2 0.420 0.051 8.262 0.000 0.762 U3 0.490 0.053 9.222 0.000 0.714 U4 0.407 0.050 8.082 0.000 0.770 U5 0.572 0.051 11.290 0.000 0.654 U6 0.481 0.050 9.571 0.000 0.721 U7 0.524 0.051 10.299 0.000 0.690 U8 0.503 0.050 9.997 0.000 0.705 Group FEMALE Observed Two-Tailed Scale Variable Estimate S.E. Est./S.E. P-Value Factors U1 0.509 0.049 10.314 0.000 0.701 U2 0.513 0.050 10.253 0.000 0.852 U3 0.449 0.048 9.352 0.000 0.692 U4 0.590 0.051 11.504 0.000 0.938 U5 0.533 0.053 9.985 0.000 0.684 U6 0.505 0.052 9.781 0.000 0.800 U7 0.517 0.052 9.860 0.000 0.742 U8 0.530 0.052 10.245 0.000 0.783 QUALITY OF NUMERICAL RESULTS Condition Number for the Information Matrix 0.194E-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 18 U3 0 0 19 U4 0 0 0 20 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 21 U7 0 22 U8 0 0 23 ALPHA F1 F2 ________ ________ 1 24 25 BETA F1 F2 ________ ________ F1 0 0 F2 0 0 PSI F1 F2 ________ ________ F1 26 F2 27 28 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 weak2c.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\weak2c.dgm Beginning Time: 14:35:33 Ending Time: 14:35:33 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