Mplus VERSION 5.1 MUTHEN & MUTHEN 05/01/2008 5:08 PM INPUT INSTRUCTIONS TITLE: this is an example of multiple-group EFA with continuous factor indicators with intercept and loading measurement invariance and factor covariance matrix invariance DATA: FILE IS example4.dat; VARIABLE: NAMES ARE y1-y10 group; GROUPING IS group (1 = g1 2 = g2); MODEL: f1-f2 by y1-y10 (*1); f1 WITH f2 (1); f1-f2@1; OUTPUT: TECH1; INPUT READING TERMINATED NORMALLY this is an example of multiple-group EFA with continuous factor indicators with intercept and loading measurement invariance and factor covariance matrix invariance SUMMARY OF ANALYSIS Number of groups 2 Number of observations Group G1 500 Group G2 500 Number of dependent variables 10 Number of independent variables 0 Number of continuous latent variables 2 Observed dependent variables Continuous Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10 Continuous latent variables EFA factors *1: F1 F2 Variables with special functions Grouping variable GROUP Estimator ML Rotation GEOMIN Row standardization COVARIANCE Type of rotation OBLIQUE Epsilon value Varies Information matrix OBSERVED Maximum number of iterations 1000 Convergence criterion 0.500D-04 Maximum number of steepest descent iterations 20 Optimization Specifications for the Exploratory Factor Analysis Rotation Algorithm Number of random starts 30 Maximum number of iterations 10000 Derivative convergence criterion 0.100D-04 Input data file(s) example4.dat Input data format FREE THE MODEL ESTIMATION TERMINATED NORMALLY TESTS OF MODEL FIT Chi-Square Test of Model Fit Value 146.822 Degrees of Freedom 79 P-Value 0.0000 Chi-Square Contributions From Each Group G1 73.637 G2 73.185 Chi-Square Test of Model Fit for the Baseline Model Value 2205.576 Degrees of Freedom 90 P-Value 0.0000 CFI/TLI CFI 0.968 TLI 0.963 Loglikelihood H0 Value -17342.092 H1 Value -17268.681 Information Criteria Number of Free Parameters 51 Akaike (AIC) 34786.184 Bayesian (BIC) 35036.479 Sample-Size Adjusted BIC 34874.500 (n* = (n + 2) / 24) RMSEA (Root Mean Square Error Of Approximation) Estimate 0.041 90 Percent C.I. 0.031 0.052 SRMR (Standardized Root Mean Square Residual) Value 0.082 MODEL RESULTS Two-Tailed Estimate S.E. Est./S.E. P-Value Group G1 F1 BY Y1 0.834 0.065 12.927 0.000 Y2 0.955 0.064 14.974 0.000 Y3 0.855 0.050 17.000 0.000 Y4 0.874 0.066 13.267 0.000 Y5 0.948 0.060 15.787 0.000 Y6 -0.037 0.077 -0.478 0.632 Y7 0.007 0.010 0.756 0.450 Y8 0.066 0.080 0.825 0.409 Y9 0.046 0.076 0.607 0.544 Y10 -0.049 0.077 -0.636 0.525 F2 BY Y1 0.037 0.068 0.543 0.587 Y2 -0.070 0.068 -1.030 0.303 Y3 0.009 0.020 0.441 0.659 Y4 0.074 0.070 1.053 0.292 Y5 -0.020 0.059 -0.346 0.729 Y6 1.061 0.068 15.664 0.000 Y7 0.914 0.052 17.558 0.000 Y8 0.970 0.071 13.608 0.000 Y9 0.891 0.067 13.294 0.000 Y10 0.961 0.069 13.934 0.000 F1 WITH F2 0.524 0.104 5.020 0.000 Means F1 0.000 0.000 999.000 999.000 F2 0.000 0.000 999.000 999.000 Intercepts Y1 0.925 0.055 16.957 0.000 Y2 1.092 0.055 19.720 0.000 Y3 1.033 0.054 19.309 0.000 Y4 0.971 0.057 17.065 0.000 Y5 1.039 0.057 18.361 0.000 Y6 0.980 0.060 16.366 0.000 Y7 1.033 0.058 17.832 0.000 Y8 1.058 0.062 17.140 0.000 Y9 0.979 0.057 17.305 0.000 Y10 1.013 0.059 17.276 0.000 Variances F1 1.000 0.000 999.000 999.000 F2 1.000 0.000 999.000 999.000 Residual Variances Y1 0.992 0.074 13.353 0.000 Y2 0.868 0.073 11.921 0.000 Y3 0.871 0.068 12.886 0.000 Y4 1.021 0.078 13.140 0.000 Y5 0.914 0.074 12.277 0.000 Y6 0.866 0.074 11.648 0.000 Y7 1.095 0.082 13.333 0.000 Y8 1.200 0.090 13.344 0.000 Y9 0.994 0.076 13.130 0.000 Y10 1.099 0.084 13.157 0.000 Group G2 F1 BY Y1 0.834 0.065 12.927 0.000 Y2 0.955 0.064 14.974 0.000 Y3 0.855 0.050 17.000 0.000 Y4 0.874 0.066 13.267 0.000 Y5 0.948 0.060 15.787 0.000 Y6 -0.037 0.077 -0.478 0.632 Y7 0.007 0.010 0.756 0.450 Y8 0.066 0.080 0.825 0.409 Y9 0.046 0.076 0.607 0.544 Y10 -0.049 0.077 -0.636 0.525 F2 BY Y1 0.037 0.068 0.543 0.587 Y2 -0.070 0.068 -1.030 0.303 Y3 0.009 0.020 0.441 0.659 Y4 0.074 0.070 1.053 0.292 Y5 -0.020 0.059 -0.346 0.729 Y6 1.061 0.068 15.664 0.000 Y7 0.914 0.052 17.558 0.000 Y8 0.970 0.071 13.608 0.000 Y9 0.891 0.067 13.294 0.000 Y10 0.961 0.069 13.934 0.000 F1 WITH F2 0.524 0.104 5.020 0.000 Means F1 0.329 0.077 4.263 0.000 F2 0.620 0.076 8.177 0.000 Intercepts Y1 0.925 0.055 16.957 0.000 Y2 1.092 0.055 19.720 0.000 Y3 1.033 0.054 19.309 0.000 Y4 0.971 0.057 17.065 0.000 Y5 1.039 0.057 18.361 0.000 Y6 0.980 0.060 16.366 0.000 Y7 1.033 0.058 17.832 0.000 Y8 1.058 0.062 17.140 0.000 Y9 0.979 0.057 17.305 0.000 Y10 1.013 0.059 17.276 0.000 Variances F1 1.000 0.000 999.000 999.000 F2 1.000 0.000 999.000 999.000 Residual Variances Y1 2.137 0.155 13.796 0.000 Y2 1.863 0.145 12.892 0.000 Y3 2.268 0.164 13.820 0.000 Y4 2.131 0.157 13.569 0.000 Y5 2.078 0.157 13.208 0.000 Y6 2.003 0.163 12.316 0.000 Y7 2.256 0.166 13.608 0.000 Y8 2.090 0.162 12.875 0.000 Y9 2.079 0.153 13.619 0.000 Y10 2.231 0.169 13.203 0.000 QUALITY OF NUMERICAL RESULTS Condition Number for the Information Matrix 0.355E-01 (ratio of smallest to largest eigenvalue) TECHNICAL 1 OUTPUT TECHNICAL 1 OUTPUT FOR THE UNROTATED SOLUTION PARAMETER SPECIFICATION FOR G1 NU Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ 1 1 2 3 4 5 NU Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ 1 6 7 8 9 10 LAMBDA F1 F2 ________ ________ Y1 11 0 Y2 12 13 Y3 14 15 Y4 16 17 Y5 18 19 Y6 20 21 Y7 22 23 Y8 24 25 Y9 26 27 Y10 28 29 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 30 Y2 0 31 Y3 0 0 32 Y4 0 0 0 33 Y5 0 0 0 0 34 Y6 0 0 0 0 0 Y7 0 0 0 0 0 Y8 0 0 0 0 0 Y9 0 0 0 0 0 Y10 0 0 0 0 0 THETA Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ Y6 35 Y7 0 36 Y8 0 0 37 Y9 0 0 0 38 Y10 0 0 0 0 39 ALPHA F1 F2 ________ ________ 1 0 0 BETA F1 F2 ________ ________ F1 0 0 F2 0 0 PSI F1 F2 ________ ________ F1 0 F2 0 0 PARAMETER SPECIFICATION FOR G2 NU Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ 1 1 2 3 4 5 NU Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ 1 6 7 8 9 10 LAMBDA F1 F2 ________ ________ Y1 11 0 Y2 12 13 Y3 14 15 Y4 16 17 Y5 18 19 Y6 20 21 Y7 22 23 Y8 24 25 Y9 26 27 Y10 28 29 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 40 Y2 0 41 Y3 0 0 42 Y4 0 0 0 43 Y5 0 0 0 0 44 Y6 0 0 0 0 0 Y7 0 0 0 0 0 Y8 0 0 0 0 0 Y9 0 0 0 0 0 Y10 0 0 0 0 0 THETA Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ Y6 45 Y7 0 46 Y8 0 0 47 Y9 0 0 0 48 Y10 0 0 0 0 49 ALPHA F1 F2 ________ ________ 1 50 51 BETA F1 F2 ________ ________ F1 0 0 F2 0 0 PSI F1 F2 ________ ________ F1 0 F2 0 0 STARTING VALUES FOR G1 NU Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ 1 0.907 1.113 1.040 0.949 1.041 NU Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ 1 0.959 1.032 1.091 0.987 1.008 LAMBDA F1 F2 ________ ________ Y1 1.000 0.000 Y2 1.000 1.000 Y3 1.000 1.000 Y4 1.000 1.000 Y5 1.000 1.000 Y6 1.000 1.000 Y7 1.000 1.000 Y8 1.000 1.000 Y9 1.000 1.000 Y10 1.000 1.000 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 0.814 Y2 0.000 0.824 Y3 0.000 0.000 0.768 Y4 0.000 0.000 0.000 0.872 Y5 0.000 0.000 0.000 0.000 0.869 Y6 0.000 0.000 0.000 0.000 0.000 Y7 0.000 0.000 0.000 0.000 0.000 Y8 0.000 0.000 0.000 0.000 0.000 Y9 0.000 0.000 0.000 0.000 0.000 Y10 0.000 0.000 0.000 0.000 0.000 THETA Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ Y6 0.758 Y7 0.000 0.835 Y8 0.000 0.000 0.908 Y9 0.000 0.000 0.000 0.794 Y10 0.000 0.000 0.000 0.000 0.794 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 1.000 F2 0.000 1.000 STARTING VALUES FOR G2 NU Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ 1 0.907 1.113 1.040 0.949 1.041 NU Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ 1 0.959 1.032 1.091 0.987 1.008 LAMBDA F1 F2 ________ ________ Y1 1.000 0.000 Y2 1.000 1.000 Y3 1.000 1.000 Y4 1.000 1.000 Y5 1.000 1.000 Y6 1.000 1.000 Y7 1.000 1.000 Y8 1.000 1.000 Y9 1.000 1.000 Y10 1.000 1.000 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 0.814 Y2 0.000 0.824 Y3 0.000 0.000 0.768 Y4 0.000 0.000 0.000 0.872 Y5 0.000 0.000 0.000 0.000 0.869 Y6 0.000 0.000 0.000 0.000 0.000 Y7 0.000 0.000 0.000 0.000 0.000 Y8 0.000 0.000 0.000 0.000 0.000 Y9 0.000 0.000 0.000 0.000 0.000 Y10 0.000 0.000 0.000 0.000 0.000 THETA Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ Y6 0.758 Y7 0.000 0.835 Y8 0.000 0.000 0.908 Y9 0.000 0.000 0.000 0.794 Y10 0.000 0.000 0.000 0.000 0.794 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 1.000 F2 0.000 1.000 TECHNICAL 1 OUTPUT FOR THE ROTATED SOLUTION PARAMETER SPECIFICATION FOR G1 NU Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ 1 1 2 3 4 5 NU Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ 1 6 7 8 9 10 LAMBDA F1 F2 ________ ________ Y1 11 12 Y2 13 14 Y3 15 16 Y4 17 18 Y5 19 20 Y6 21 22 Y7 23 24 Y8 25 26 Y9 27 28 Y10 29 30 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 31 Y2 0 32 Y3 0 0 33 Y4 0 0 0 34 Y5 0 0 0 0 35 Y6 0 0 0 0 0 Y7 0 0 0 0 0 Y8 0 0 0 0 0 Y9 0 0 0 0 0 Y10 0 0 0 0 0 THETA Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ Y6 36 Y7 0 37 Y8 0 0 38 Y9 0 0 0 39 Y10 0 0 0 0 40 ALPHA F1 F2 ________ ________ 1 0 0 BETA F1 F2 ________ ________ F1 0 0 F2 0 0 PSI F1 F2 ________ ________ F1 0 F2 41 0 PARAMETER SPECIFICATION FOR G2 NU Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ 1 1 2 3 4 5 NU Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ 1 6 7 8 9 10 LAMBDA F1 F2 ________ ________ Y1 11 12 Y2 13 14 Y3 15 16 Y4 17 18 Y5 19 20 Y6 21 22 Y7 23 24 Y8 25 26 Y9 27 28 Y10 29 30 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 42 Y2 0 43 Y3 0 0 44 Y4 0 0 0 45 Y5 0 0 0 0 46 Y6 0 0 0 0 0 Y7 0 0 0 0 0 Y8 0 0 0 0 0 Y9 0 0 0 0 0 Y10 0 0 0 0 0 THETA Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ Y6 47 Y7 0 48 Y8 0 0 49 Y9 0 0 0 50 Y10 0 0 0 0 51 ALPHA F1 F2 ________ ________ 1 52 53 BETA F1 F2 ________ ________ F1 0 0 F2 0 0 PSI F1 F2 ________ ________ F1 0 F2 41 0 STARTING VALUES FOR G1 NU Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ 1 0.907 1.113 1.040 0.949 1.041 NU Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ 1 0.959 1.032 1.091 0.987 1.008 LAMBDA F1 F2 ________ ________ Y1 0.000 0.000 Y2 0.000 0.000 Y3 0.000 0.000 Y4 0.000 0.000 Y5 0.000 0.000 Y6 0.000 0.000 Y7 0.000 0.000 Y8 0.000 0.000 Y9 0.000 0.000 Y10 0.000 0.000 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 0.814 Y2 0.000 0.824 Y3 0.000 0.000 0.768 Y4 0.000 0.000 0.000 0.872 Y5 0.000 0.000 0.000 0.000 0.869 Y6 0.000 0.000 0.000 0.000 0.000 Y7 0.000 0.000 0.000 0.000 0.000 Y8 0.000 0.000 0.000 0.000 0.000 Y9 0.000 0.000 0.000 0.000 0.000 Y10 0.000 0.000 0.000 0.000 0.000 THETA Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ Y6 0.758 Y7 0.000 0.835 Y8 0.000 0.000 0.908 Y9 0.000 0.000 0.000 0.794 Y10 0.000 0.000 0.000 0.000 0.794 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 1.000 F2 0.000 1.000 STARTING VALUES FOR G2 NU Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ 1 0.907 1.113 1.040 0.949 1.041 NU Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ 1 0.959 1.032 1.091 0.987 1.008 LAMBDA F1 F2 ________ ________ Y1 0.000 0.000 Y2 0.000 0.000 Y3 0.000 0.000 Y4 0.000 0.000 Y5 0.000 0.000 Y6 0.000 0.000 Y7 0.000 0.000 Y8 0.000 0.000 Y9 0.000 0.000 Y10 0.000 0.000 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 0.814 Y2 0.000 0.824 Y3 0.000 0.000 0.768 Y4 0.000 0.000 0.000 0.872 Y5 0.000 0.000 0.000 0.000 0.869 Y6 0.000 0.000 0.000 0.000 0.000 Y7 0.000 0.000 0.000 0.000 0.000 Y8 0.000 0.000 0.000 0.000 0.000 Y9 0.000 0.000 0.000 0.000 0.000 Y10 0.000 0.000 0.000 0.000 0.000 THETA Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ Y6 0.758 Y7 0.000 0.835 Y8 0.000 0.000 0.908 Y9 0.000 0.000 0.000 0.794 Y10 0.000 0.000 0.000 0.000 0.794 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 1.000 F2 0.000 1.000 Beginning Time: 17:08:54 Ending Time: 17:08:55 Elapsed Time: 00:00:01 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) 1998-2008 Muthen & Muthen