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 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); OUTPUT: TECH1; INPUT READING TERMINATED NORMALLY this is an example of multiple-group EFA with continuous factor indicators with intercept and loading measurement 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 82.326 Degrees of Freedom 76 P-Value 0.2900 Chi-Square Contributions From Each Group G1 41.993 G2 40.333 Chi-Square Test of Model Fit for the Baseline Model Value 2205.576 Degrees of Freedom 90 P-Value 0.0000 CFI/TLI CFI 0.997 TLI 0.996 Loglikelihood H0 Value -17309.844 H1 Value -17268.681 Information Criteria Number of Free Parameters 54 Akaike (AIC) 34727.688 Bayesian (BIC) 34992.707 Sample-Size Adjusted BIC 34821.200 (n* = (n + 2) / 24) RMSEA (Root Mean Square Error Of Approximation) Estimate 0.013 90 Percent C.I. 0.000 0.029 SRMR (Standardized Root Mean Square Residual) Value 0.027 MODEL RESULTS Two-Tailed Estimate S.E. Est./S.E. P-Value Group G1 F1 BY Y1 0.786 0.062 12.697 0.000 Y2 0.891 0.063 14.233 0.000 Y3 0.815 0.053 15.518 0.000 Y4 0.823 0.063 13.006 0.000 Y5 0.900 0.060 14.897 0.000 Y6 -0.041 0.068 -0.598 0.550 Y7 0.011 0.016 0.718 0.473 Y8 0.059 0.074 0.799 0.425 Y9 0.053 0.070 0.763 0.446 Y10 -0.052 0.069 -0.747 0.455 F2 BY Y1 0.036 0.051 0.699 0.485 Y2 -0.037 0.051 -0.718 0.473 Y3 0.005 0.017 0.301 0.763 Y4 0.066 0.052 1.254 0.210 Y5 -0.014 0.043 -0.329 0.742 Y6 0.837 0.057 14.674 0.000 Y7 0.701 0.047 14.925 0.000 Y8 0.753 0.060 12.499 0.000 Y9 0.678 0.057 11.867 0.000 Y10 0.755 0.056 13.381 0.000 F2 WITH F1 0.483 0.068 7.106 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 0.053 17.447 0.000 Y2 1.091 0.054 20.217 0.000 Y3 1.034 0.052 19.828 0.000 Y4 0.971 0.055 17.630 0.000 Y5 1.040 0.055 18.866 0.000 Y6 0.978 0.052 18.632 0.000 Y7 1.035 0.052 19.963 0.000 Y8 1.058 0.055 19.286 0.000 Y9 0.981 0.050 19.459 0.000 Y10 1.011 0.052 19.290 0.000 Variances F1 1.000 0.000 999.000 999.000 F2 1.000 0.000 999.000 999.000 Residual Variances Y1 0.994 0.074 13.364 0.000 Y2 0.878 0.073 12.034 0.000 Y3 0.869 0.068 12.834 0.000 Y4 1.022 0.078 13.153 0.000 Y5 0.914 0.075 12.247 0.000 Y6 0.877 0.074 11.891 0.000 Y7 1.119 0.082 13.565 0.000 Y8 1.214 0.090 13.556 0.000 Y9 1.023 0.076 13.419 0.000 Y10 1.103 0.083 13.307 0.000 Group G2 F1 BY Y1 0.786 0.062 12.697 0.000 Y2 0.891 0.063 14.233 0.000 Y3 0.815 0.053 15.518 0.000 Y4 0.823 0.063 13.006 0.000 Y5 0.900 0.060 14.897 0.000 Y6 -0.041 0.068 -0.598 0.550 Y7 0.011 0.016 0.718 0.473 Y8 0.059 0.074 0.799 0.425 Y9 0.053 0.070 0.763 0.446 Y10 -0.052 0.069 -0.747 0.455 F2 BY Y1 0.036 0.051 0.699 0.485 Y2 -0.037 0.051 -0.718 0.473 Y3 0.005 0.017 0.301 0.763 Y4 0.066 0.052 1.254 0.210 Y5 -0.014 0.043 -0.329 0.742 Y6 0.837 0.057 14.674 0.000 Y7 0.701 0.047 14.925 0.000 Y8 0.753 0.060 12.499 0.000 Y9 0.678 0.057 11.867 0.000 Y10 0.755 0.056 13.381 0.000 F2 WITH F1 0.953 0.155 6.159 0.000 Means F1 0.342 0.082 4.162 0.000 F2 0.798 0.103 7.719 0.000 Intercepts Y1 0.925 0.053 17.447 0.000 Y2 1.091 0.054 20.217 0.000 Y3 1.034 0.052 19.828 0.000 Y4 0.971 0.055 17.630 0.000 Y5 1.040 0.055 18.866 0.000 Y6 0.978 0.052 18.632 0.000 Y7 1.035 0.052 19.963 0.000 Y8 1.058 0.055 19.286 0.000 Y9 0.981 0.050 19.459 0.000 Y10 1.011 0.052 19.290 0.000 Variances F1 1.246 0.155 8.030 0.000 F2 2.612 0.316 8.274 0.000 Residual Variances Y1 2.131 0.155 13.732 0.000 Y2 1.862 0.145 12.857 0.000 Y3 2.251 0.165 13.676 0.000 Y4 2.124 0.157 13.515 0.000 Y5 2.063 0.158 13.064 0.000 Y6 1.886 0.160 11.822 0.000 Y7 2.222 0.164 13.524 0.000 Y8 2.011 0.159 12.664 0.000 Y9 2.055 0.151 13.583 0.000 Y10 2.138 0.165 12.956 0.000 QUALITY OF NUMERICAL RESULTS Condition Number for the Information Matrix 0.986E-02 (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 52 F2 53 54 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 54 F2 55 56 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: 17:08:47 Ending Time: 17:08:47 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) 1998-2008 Muthen & Muthen