Mplus VERSION 5.1 MUTHEN & MUTHEN 05/01/2008 5:07 PM INPUT INSTRUCTIONS TITLE: this is an example of an EFA with covariates (MIMIC) with continuous factor indicators and direct effects DATA: FILE IS example1.dat; VARIABLE: NAMES ARE y1-y8 x1 x2; MODEL: f1-f2 BY y1-y8(*1); f1-f2 ON x1-x2; y1 ON x1; y8 ON x2; OUTPUT: TECH1; INPUT READING TERMINATED NORMALLY this is an example of an EFA with covariates (MIMIC) with continuous factor indicators and direct effects SUMMARY OF ANALYSIS Number of groups 1 Number of observations 500 Number of dependent variables 8 Number of independent variables 2 Number of continuous latent variables 2 Observed dependent variables Continuous Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Observed independent variables X1 X2 Continuous latent variables EFA factors *1: F1 F2 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) example1.dat Input data format FREE THE MODEL ESTIMATION TERMINATED NORMALLY TESTS OF MODEL FIT Chi-Square Test of Model Fit Value 30.268 Degrees of Freedom 23 P-Value 0.1419 Chi-Square Test of Model Fit for the Baseline Model Value 4254.549 Degrees of Freedom 44 P-Value 0.0000 CFI/TLI CFI 0.998 TLI 0.997 Loglikelihood H0 Value -6031.267 H1 Value -6016.132 Information Criteria Number of Free Parameters 37 Akaike (AIC) 12136.533 Bayesian (BIC) 12292.474 Sample-Size Adjusted BIC 12175.033 (n* = (n + 2) / 24) RMSEA (Root Mean Square Error Of Approximation) Estimate 0.025 90 Percent C.I. 0.000 0.047 Probability RMSEA <= .05 0.970 SRMR (Standardized Root Mean Square Residual) Value 0.010 MODEL RESULTS Two-Tailed Estimate S.E. Est./S.E. P-Value F1 BY Y1 0.754 0.040 18.904 0.000 Y2 0.861 0.049 17.435 0.000 Y3 0.820 0.043 19.184 0.000 Y4 0.855 0.049 17.573 0.000 Y5 0.773 0.049 15.654 0.000 Y6 -0.010 0.041 -0.248 0.804 Y7 0.003 0.022 0.126 0.900 Y8 0.009 0.040 0.226 0.821 F2 BY Y1 0.000 0.021 0.003 0.998 Y2 -0.054 0.039 -1.374 0.169 Y3 -0.004 0.025 -0.161 0.872 Y4 0.118 0.039 3.032 0.002 Y5 0.177 0.040 4.424 0.000 Y6 0.861 0.045 19.060 0.000 Y7 0.840 0.038 21.823 0.000 Y8 0.786 0.044 17.954 0.000 F1 ON X1 0.537 0.055 9.768 0.000 X2 0.271 0.050 5.389 0.000 F2 ON X1 0.946 0.061 15.571 0.000 X2 0.556 0.056 9.914 0.000 Y1 ON X1 0.387 0.039 9.856 0.000 Y8 ON X2 0.577 0.039 14.800 0.000 F2 WITH F1 0.593 0.039 15.215 0.000 Intercepts Y1 0.024 0.043 0.565 0.572 Y2 -0.029 0.046 -0.640 0.522 Y3 0.023 0.045 0.516 0.606 Y4 -0.020 0.049 -0.398 0.691 Y5 0.024 0.049 0.486 0.627 Y6 0.075 0.049 1.553 0.120 Y7 0.021 0.046 0.465 0.642 Y8 0.035 0.046 0.761 0.447 Residual Variances Y1 0.339 0.026 12.942 0.000 Y2 0.345 0.029 12.037 0.000 Y3 0.342 0.028 12.421 0.000 Y4 0.328 0.027 11.926 0.000 Y5 0.393 0.030 13.086 0.000 Y6 0.425 0.039 10.851 0.000 Y7 0.335 0.034 9.956 0.000 Y8 0.415 0.036 11.577 0.000 F1 1.000 0.000 999.000 999.000 F2 1.000 0.000 999.000 999.000 QUALITY OF NUMERICAL RESULTS Condition Number for the Information Matrix 0.263E-01 (ratio of smallest to largest eigenvalue) TECHNICAL 1 OUTPUT TECHNICAL 1 OUTPUT FOR THE UNROTATED SOLUTION PARAMETER SPECIFICATION NU Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ 1 0 1 2 3 4 NU Y6 Y7 Y8 X1 X2 ________ ________ ________ ________ ________ 1 5 6 0 0 0 LAMBDA F1 F2 Y1 Y8 X1 ________ ________ ________ ________ ________ Y1 0 0 0 0 0 Y2 7 8 0 0 0 Y3 9 10 0 0 0 Y4 11 12 0 0 0 Y5 13 14 0 0 0 Y6 15 16 0 0 0 Y7 17 18 0 0 0 Y8 0 0 0 0 0 X1 0 0 0 0 0 X2 0 0 0 0 0 LAMBDA X2 ________ Y1 0 Y2 0 Y3 0 Y4 0 Y5 0 Y6 0 Y7 0 Y8 0 X1 0 X2 0 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 0 Y2 0 19 Y3 0 0 20 Y4 0 0 0 21 Y5 0 0 0 0 22 Y6 0 0 0 0 0 Y7 0 0 0 0 0 Y8 0 0 0 0 0 X1 0 0 0 0 0 X2 0 0 0 0 0 THETA Y6 Y7 Y8 X1 X2 ________ ________ ________ ________ ________ Y6 23 Y7 0 24 Y8 0 0 0 X1 0 0 0 0 X2 0 0 0 0 0 ALPHA F1 F2 Y1 Y8 X1 ________ ________ ________ ________ ________ 1 0 0 25 26 0 ALPHA X2 ________ 1 0 BETA F1 F2 Y1 Y8 X1 ________ ________ ________ ________ ________ F1 0 0 0 0 27 F2 0 0 0 0 29 Y1 31 0 0 0 32 Y8 33 34 0 0 0 X1 0 0 0 0 0 X2 0 0 0 0 0 BETA X2 ________ F1 28 F2 30 Y1 0 Y8 35 X1 0 X2 0 PSI F1 F2 Y1 Y8 X1 ________ ________ ________ ________ ________ F1 0 F2 0 0 Y1 0 0 36 Y8 0 0 0 37 X1 0 0 0 0 0 X2 0 0 0 0 0 PSI X2 ________ X2 0 STARTING VALUES NU Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ 1 0.000 -0.034 0.019 -0.024 0.020 NU Y6 Y7 Y8 X1 X2 ________ ________ ________ ________ ________ 1 0.077 0.023 0.000 0.000 0.000 LAMBDA F1 F2 Y1 Y8 X1 ________ ________ ________ ________ ________ Y1 0.000 0.000 1.000 0.000 0.000 Y2 1.000 1.000 0.000 0.000 0.000 Y3 1.000 1.000 0.000 0.000 0.000 Y4 1.000 1.000 0.000 0.000 0.000 Y5 1.000 1.000 0.000 0.000 0.000 Y6 1.000 1.000 0.000 0.000 0.000 Y7 1.000 1.000 0.000 0.000 0.000 Y8 0.000 0.000 0.000 1.000 0.000 X1 0.000 0.000 0.000 0.000 1.000 X2 0.000 0.000 0.000 0.000 0.000 LAMBDA X2 ________ Y1 0.000 Y2 0.000 Y3 0.000 Y4 0.000 Y5 0.000 Y6 0.000 Y7 0.000 Y8 0.000 X1 0.000 X2 1.000 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 0.000 Y2 0.000 0.628 Y3 0.000 0.000 0.630 Y4 0.000 0.000 0.000 0.813 Y5 0.000 0.000 0.000 0.000 0.819 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 X1 0.000 0.000 0.000 0.000 0.000 X2 0.000 0.000 0.000 0.000 0.000 THETA Y6 Y7 Y8 X1 X2 ________ ________ ________ ________ ________ Y6 1.038 Y7 0.000 0.966 Y8 0.000 0.000 0.000 X1 0.000 0.000 0.000 0.000 X2 0.000 0.000 0.000 0.000 0.000 ALPHA F1 F2 Y1 Y8 X1 ________ ________ ________ ________ ________ 1 0.000 0.000 -0.008 0.109 -0.073 ALPHA X2 ________ 1 0.127 BETA F1 F2 Y1 Y8 X1 ________ ________ ________ ________ ________ F1 0.000 0.000 0.000 0.000 0.000 F2 0.000 0.000 0.000 0.000 0.000 Y1 1.000 0.000 0.000 0.000 0.000 Y8 1.000 1.000 0.000 0.000 0.000 X1 0.000 0.000 0.000 0.000 0.000 X2 0.000 0.000 0.000 0.000 0.000 BETA X2 ________ F1 0.000 F2 0.000 Y1 0.000 Y8 0.000 X1 0.000 X2 0.000 PSI F1 F2 Y1 Y8 X1 ________ ________ ________ ________ ________ F1 1.000 F2 0.000 1.000 Y1 0.000 0.000 0.798 Y8 0.000 0.000 0.000 1.341 X1 0.000 0.000 0.000 0.000 0.990 X2 0.000 0.000 0.000 0.000 0.070 PSI X2 ________ X2 0.945 TECHNICAL 1 OUTPUT FOR THE ROTATED SOLUTION PARAMETER SPECIFICATION NU Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ 1 0 1 2 3 4 NU Y6 Y7 Y8 X1 X2 ________ ________ ________ ________ ________ 1 5 6 0 0 0 LAMBDA F1 F2 Y1 Y8 X1 ________ ________ ________ ________ ________ Y1 0 0 0 0 0 Y2 7 8 0 0 0 Y3 9 10 0 0 0 Y4 11 12 0 0 0 Y5 13 14 0 0 0 Y6 15 16 0 0 0 Y7 17 18 0 0 0 Y8 0 0 0 0 0 X1 0 0 0 0 0 X2 0 0 0 0 0 LAMBDA X2 ________ Y1 0 Y2 0 Y3 0 Y4 0 Y5 0 Y6 0 Y7 0 Y8 0 X1 0 X2 0 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 0 Y2 0 19 Y3 0 0 20 Y4 0 0 0 21 Y5 0 0 0 0 22 Y6 0 0 0 0 0 Y7 0 0 0 0 0 Y8 0 0 0 0 0 X1 0 0 0 0 0 X2 0 0 0 0 0 THETA Y6 Y7 Y8 X1 X2 ________ ________ ________ ________ ________ Y6 23 Y7 0 24 Y8 0 0 0 X1 0 0 0 0 X2 0 0 0 0 0 ALPHA F1 F2 Y1 Y8 X1 ________ ________ ________ ________ ________ 1 0 0 25 26 0 ALPHA X2 ________ 1 0 BETA F1 F2 Y1 Y8 X1 ________ ________ ________ ________ ________ F1 0 0 0 0 27 F2 0 0 0 0 29 Y1 31 32 0 0 33 Y8 34 35 0 0 0 X1 0 0 0 0 0 X2 0 0 0 0 0 BETA X2 ________ F1 28 F2 30 Y1 0 Y8 36 X1 0 X2 0 PSI F1 F2 Y1 Y8 X1 ________ ________ ________ ________ ________ F1 0 F2 37 0 Y1 0 0 38 Y8 0 0 0 39 X1 0 0 0 0 0 X2 0 0 0 0 0 PSI X2 ________ X2 0 STARTING VALUES NU Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ 1 0.000 -0.034 0.019 -0.024 0.020 NU Y6 Y7 Y8 X1 X2 ________ ________ ________ ________ ________ 1 0.077 0.023 0.000 0.000 0.000 LAMBDA F1 F2 Y1 Y8 X1 ________ ________ ________ ________ ________ Y1 0.000 0.000 1.000 0.000 0.000 Y2 0.000 0.000 0.000 0.000 0.000 Y3 0.000 0.000 0.000 0.000 0.000 Y4 0.000 0.000 0.000 0.000 0.000 Y5 0.000 0.000 0.000 0.000 0.000 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 1.000 0.000 X1 0.000 0.000 0.000 0.000 1.000 X2 0.000 0.000 0.000 0.000 0.000 LAMBDA X2 ________ Y1 0.000 Y2 0.000 Y3 0.000 Y4 0.000 Y5 0.000 Y6 0.000 Y7 0.000 Y8 0.000 X1 0.000 X2 1.000 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 0.000 Y2 0.000 0.628 Y3 0.000 0.000 0.630 Y4 0.000 0.000 0.000 0.813 Y5 0.000 0.000 0.000 0.000 0.819 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 X1 0.000 0.000 0.000 0.000 0.000 X2 0.000 0.000 0.000 0.000 0.000 THETA Y6 Y7 Y8 X1 X2 ________ ________ ________ ________ ________ Y6 1.038 Y7 0.000 0.966 Y8 0.000 0.000 0.000 X1 0.000 0.000 0.000 0.000 X2 0.000 0.000 0.000 0.000 0.000 ALPHA F1 F2 Y1 Y8 X1 ________ ________ ________ ________ ________ 1 0.000 0.000 -0.008 0.109 -0.073 ALPHA X2 ________ 1 0.127 BETA F1 F2 Y1 Y8 X1 ________ ________ ________ ________ ________ F1 0.000 0.000 0.000 0.000 0.000 F2 0.000 0.000 0.000 0.000 0.000 Y1 0.000 0.000 0.000 0.000 0.000 Y8 0.000 0.000 0.000 0.000 0.000 X1 0.000 0.000 0.000 0.000 0.000 X2 0.000 0.000 0.000 0.000 0.000 BETA X2 ________ F1 0.000 F2 0.000 Y1 0.000 Y8 0.000 X1 0.000 X2 0.000 PSI F1 F2 Y1 Y8 X1 ________ ________ ________ ________ ________ F1 1.000 F2 0.000 1.000 Y1 0.000 0.000 0.798 Y8 0.000 0.000 0.000 1.341 X1 0.000 0.000 0.000 0.000 0.990 X2 0.000 0.000 0.000 0.000 0.070 PSI X2 ________ X2 0.945 Beginning Time: 17:07:24 Ending Time: 17:07:24 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