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 no 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); [f1-f2@0]; MODEL g2: f1-f2 BY y1-y10 (*1); [y1-y10]; OUTPUT: TECH1; INPUT READING TERMINATED NORMALLY this is an example of multiple-group EFA with continuous factor indicators with no 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 CORRELATION 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 63.815 Degrees of Freedom 52 P-Value 0.1261 Chi-Square Contributions From Each Group G1 33.275 G2 30.540 Chi-Square Test of Model Fit for the Baseline Model Value 2205.576 Degrees of Freedom 90 P-Value 0.0000 CFI/TLI CFI 0.994 TLI 0.990 Loglikelihood H0 Value -17300.588 H1 Value -17268.681 Information Criteria Number of Free Parameters 78 Akaike (AIC) 34757.177 Bayesian (BIC) 35139.982 Sample-Size Adjusted BIC 34892.249 (n* = (n + 2) / 24) RMSEA (Root Mean Square Error Of Approximation) Estimate 0.021 90 Percent C.I. 0.000 0.037 SRMR (Standardized Root Mean Square Residual) Value 0.019 MODEL RESULTS Two-Tailed Estimate S.E. Est./S.E. P-Value Group G1 F1 BY Y1 0.791 0.066 12.022 0.000 Y2 0.947 0.074 12.793 0.000 Y3 0.780 0.069 11.237 0.000 Y4 0.839 0.073 11.545 0.000 Y5 0.911 0.065 14.121 0.000 Y6 -0.032 0.072 -0.448 0.654 Y7 0.029 0.080 0.362 0.717 Y8 0.084 0.086 0.970 0.332 Y9 0.011 0.022 0.524 0.600 Y10 -0.085 0.078 -1.094 0.274 F2 BY Y1 0.004 0.051 0.077 0.938 Y2 -0.125 0.076 -1.654 0.098 Y3 0.049 0.072 0.677 0.499 Y4 0.017 0.071 0.235 0.814 Y5 -0.005 0.044 -0.106 0.915 Y6 0.798 0.074 10.736 0.000 Y7 0.731 0.081 8.992 0.000 Y8 0.728 0.085 8.608 0.000 Y9 0.776 0.064 12.053 0.000 Y10 0.722 0.078 9.250 0.000 F2 WITH F1 0.507 0.065 7.831 0.000 Means F1 0.000 0.000 999.000 999.000 F2 0.000 0.000 999.000 999.000 Intercepts Y1 0.907 0.057 15.906 0.000 Y2 1.113 0.057 19.406 0.000 Y3 1.040 0.055 18.776 0.000 Y4 0.949 0.059 16.085 0.000 Y5 1.041 0.059 17.678 0.000 Y6 0.959 0.055 17.432 0.000 Y7 1.032 0.058 17.872 0.000 Y8 1.091 0.060 18.112 0.000 Y9 0.987 0.056 17.544 0.000 Y10 1.008 0.056 17.914 0.000 Variances F1 1.000 0.000 999.000 999.000 F2 1.000 0.000 999.000 999.000 Residual Variances Y1 0.996 0.075 13.217 0.000 Y2 0.852 0.075 11.349 0.000 Y3 0.884 0.068 12.936 0.000 Y4 1.024 0.079 12.967 0.000 Y5 0.910 0.076 12.029 0.000 Y6 0.901 0.078 11.528 0.000 Y7 1.110 0.086 12.853 0.000 Y8 1.214 0.093 13.113 0.000 Y9 0.973 0.081 12.047 0.000 Y10 1.118 0.086 12.999 0.000 Group G2 F1 BY Y1 0.916 0.095 9.620 0.000 Y2 0.950 0.117 8.132 0.000 Y3 1.006 0.125 8.026 0.000 Y4 0.921 0.126 7.329 0.000 Y5 0.999 0.122 8.206 0.000 Y6 -0.041 0.117 -0.352 0.725 Y7 -0.056 0.117 -0.474 0.635 Y8 0.012 0.039 0.313 0.754 Y9 0.089 0.120 0.741 0.459 Y10 0.029 0.115 0.253 0.800 F2 BY Y1 0.014 0.034 0.420 0.674 Y2 0.034 0.114 0.298 0.765 Y3 -0.103 0.128 -0.806 0.420 Y4 0.094 0.130 0.720 0.472 Y5 -0.077 0.124 -0.620 0.535 Y6 1.354 0.114 11.840 0.000 Y7 1.123 0.113 9.959 0.000 Y8 1.301 0.092 14.113 0.000 Y9 1.012 0.112 9.061 0.000 Y10 1.227 0.114 10.750 0.000 F2 WITH F1 0.542 0.072 7.500 0.000 Means F1 0.000 0.000 999.000 999.000 F2 0.000 0.000 999.000 999.000 Intercepts Y1 1.263 0.077 16.391 0.000 Y2 1.319 0.075 17.594 0.000 Y3 1.303 0.079 16.529 0.000 Y4 1.349 0.079 17.178 0.000 Y5 1.333 0.077 17.213 0.000 Y6 1.672 0.086 19.524 0.000 Y7 1.603 0.083 19.383 0.000 Y8 1.624 0.086 18.960 0.000 Y9 1.528 0.080 19.043 0.000 Y10 1.602 0.086 18.738 0.000 Variances F1 1.000 0.000 999.000 999.000 F2 1.000 0.000 999.000 999.000 Residual Variances Y1 2.115 0.164 12.881 0.000 Y2 1.871 0.154 12.133 0.000 Y3 2.198 0.178 12.362 0.000 Y4 2.131 0.166 12.839 0.000 Y5 2.077 0.170 12.212 0.000 Y6 1.894 0.167 11.360 0.000 Y7 2.223 0.169 13.176 0.000 Y8 1.958 0.166 11.793 0.000 Y9 2.088 0.154 13.571 0.000 Y10 2.112 0.168 12.548 0.000 QUALITY OF NUMERICAL RESULTS Condition Number for the Information Matrix 0.161E-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 40 41 42 43 44 NU Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ 1 45 46 47 48 49 LAMBDA F1 F2 ________ ________ Y1 50 0 Y2 51 52 Y3 53 54 Y4 55 56 Y5 57 58 Y6 59 60 Y7 61 62 Y8 63 64 Y9 65 66 Y10 67 68 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 69 Y2 0 70 Y3 0 0 71 Y4 0 0 0 72 Y5 0 0 0 0 73 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 74 Y7 0 75 Y8 0 0 76 Y9 0 0 0 77 Y10 0 0 0 0 78 ALPHA F1 F2 ________ ________ 1 0 0 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 0.000 0.000 0.000 0.000 0.000 NU Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 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 42 43 44 45 46 NU Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ 1 47 48 49 50 51 LAMBDA F1 F2 ________ ________ Y1 52 53 Y2 54 55 Y3 56 57 Y4 58 59 Y5 60 61 Y6 62 63 Y7 64 65 Y8 66 67 Y9 68 69 Y10 70 71 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 72 Y2 0 73 Y3 0 0 74 Y4 0 0 0 75 Y5 0 0 0 0 76 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 77 Y7 0 78 Y8 0 0 79 Y9 0 0 0 80 Y10 0 0 0 0 81 ALPHA F1 F2 ________ ________ 1 0 0 BETA F1 F2 ________ ________ F1 0 0 F2 0 0 PSI F1 F2 ________ ________ F1 0 F2 82 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 0.000 0.000 0.000 0.000 0.000 NU Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 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: 17:08:29 Ending Time: 17:08:29 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