Mplus VERSION 6.11 MUTHEN & MUTHEN 10/23/2011 2:47 PM INPUT INSTRUCTIONS title: Simulating x-m interaction effect on y using a random slope, saving the data for external Monte Carlo analysis: Binary Y, continuous M montecarlo: names = y m x; generate = y(1 p); categorical = y; nobs = 200; nreps = 500; repsave = all; save = n200xmrep*.dat; cutpoints = x(0); model population: x@1; [y$1*.5]; y on x*.3; beta1 | y on m; beta1 on x*.2; [beta1*.7]; beta1@0; [m*.5]; m on x*.5; m*.75; analysis: type = random; estimator = ml; link = probit; model: [y$1*.5] (beta0); y on x*.3 (beta2); beta1 | y on m; beta1 on x*.2 (beta3); [beta1*.7] (beta1); beta1@0; [m*.5] (gamma0); m on x*.5 (gamma1); m*.75; model constraint: new(ind*.45 dir*.4); ind=beta1*gamma1+beta3*gamma1; dir=beta3*gamma0+beta2; INPUT READING TERMINATED NORMALLY Simulating x-m interaction effect on y using a random slope, saving the data for external Monte Carlo analysis: Binary Y, continuous M SUMMARY OF ANALYSIS Number of groups 1 Number of observations 200 Number of replications Requested 500 Completed 500 Value of seed 0 Number of dependent variables 2 Number of independent variables 1 Number of continuous latent variables 1 Observed dependent variables Continuous M Binary and ordered categorical (ordinal) Y Observed independent variables X Continuous latent variables BETA1 Estimator ML Information matrix OBSERVED Optimization Specifications for the Quasi-Newton Algorithm for Continuous Outcomes Maximum number of iterations 100 Convergence criterion 0.100D-05 Optimization Specifications for the EM Algorithm Maximum number of iterations 500 Convergence criteria Loglikelihood change 0.100D-02 Relative loglikelihood change 0.100D-05 Derivative 0.100D-02 Optimization Specifications for the M step of the EM Algorithm for Categorical Latent variables Number of M step iterations 1 M step convergence criterion 0.100D-02 Basis for M step termination ITERATION Optimization Specifications for the M step of the EM Algorithm for Censored, Binary or Ordered Categorical (Ordinal), Unordered Categorical (Nominal) and Count Outcomes Number of M step iterations 1 M step convergence criterion 0.100D-02 Basis for M step termination ITERATION Maximum value for logit thresholds 10 Minimum value for logit thresholds -10 Minimum expected cell size for chi-square 0.100D-01 Optimization algorithm EMA Integration Specifications Type STANDARD Number of integration points 15 Dimensions of numerical integration 1 Adaptive quadrature ON Link PROBIT Cholesky ON SAMPLE STATISTICS FOR THE FIRST REPLICATION SAMPLE STATISTICS Means M X ________ ________ 1 0.757 0.445 Covariances M X ________ ________ M 0.907 X 0.144 0.248 Correlations M X ________ ________ M 1.000 X 0.304 1.000 MODEL FIT INFORMATION Number of Free Parameters 7 Loglikelihood H0 Value Mean -359.782 Std Dev 11.659 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 -386.904 -387.910 0.980 0.984 -383.726 -382.547 0.950 0.950 -378.960 -379.000 0.900 0.904 -374.724 -374.707 0.800 0.818 -369.594 -369.059 0.700 0.688 -365.896 -366.295 0.500 0.488 -359.782 -360.240 0.300 0.296 -353.668 -353.937 0.200 0.206 -349.970 -349.725 0.100 0.108 -344.840 -344.600 0.050 0.058 -340.604 -339.992 0.020 0.022 -335.838 -335.451 0.010 0.012 -332.660 -332.552 Information Criteria Akaike (AIC) Mean 733.564 Std Dev 23.318 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.988 679.319 677.590 0.980 0.978 685.676 683.355 0.950 0.942 695.208 693.859 0.900 0.892 703.679 703.036 0.800 0.794 713.939 713.346 0.700 0.704 721.336 721.842 0.500 0.512 733.564 734.319 0.300 0.312 745.792 746.514 0.200 0.182 753.188 752.064 0.100 0.096 763.448 762.380 0.050 0.050 771.919 771.482 0.020 0.016 781.452 778.831 0.010 0.010 787.808 785.620 Bayesian (BIC) Mean 756.652 Std Dev 23.318 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.988 702.407 700.678 0.980 0.978 708.764 706.443 0.950 0.942 718.296 716.948 0.900 0.892 726.768 726.124 0.800 0.794 737.028 736.434 0.700 0.704 744.424 744.931 0.500 0.512 756.652 757.408 0.300 0.312 768.880 769.603 0.200 0.182 776.276 775.153 0.100 0.096 786.536 785.468 0.050 0.050 795.008 794.570 0.020 0.016 804.540 801.919 0.010 0.010 810.897 808.708 Sample-Size Adjusted BIC (n* = (n + 2) / 24) Mean 734.475 Std Dev 23.318 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.988 680.231 678.502 0.980 0.978 686.587 684.266 0.950 0.942 696.119 694.771 0.900 0.892 704.591 703.947 0.800 0.794 714.851 714.257 0.700 0.704 722.247 722.754 0.500 0.512 734.475 735.231 0.300 0.312 746.703 747.426 0.200 0.182 754.100 752.976 0.100 0.096 764.360 763.291 0.050 0.050 772.831 772.393 0.020 0.016 782.363 779.742 0.010 0.010 788.720 786.531 MODEL RESULTS ESTIMATES S. E. M. S. E. 95% % Sig Population Average Std. Dev. Average Cover Coeff BETA1 ON X 0.200 0.2369 0.2865 0.2753 0.0833 0.948 0.126 Y ON X 0.300 0.2740 0.2796 0.2729 0.0787 0.948 0.204 M ON X 0.500 0.4894 0.1207 0.1223 0.0146 0.942 0.972 Intercepts M 0.500 0.5044 0.0863 0.0861 0.0074 0.970 1.000 BETA1 0.700 0.7139 0.1849 0.1755 0.0343 0.948 0.990 Thresholds Y$1 0.500 0.5059 0.1671 0.1658 0.0279 0.952 0.882 Residual Variances M 0.750 0.7465 0.0808 0.0746 0.0065 0.920 1.000 BETA1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 New/Additional Parameters IND 0.450 0.4661 0.1621 0.1574 0.0265 0.946 0.952 DIR 0.400 0.3935 0.2141 0.2117 0.0458 0.952 0.464 QUALITY OF NUMERICAL RESULTS Average Condition Number for the Information Matrix 0.168E-02 (ratio of smallest to largest eigenvalue) TECHNICAL 1 OUTPUT PARAMETER SPECIFICATION TAU Y$1 ________ 1 7 NU Y M X ________ ________ ________ 1 0 0 0 LAMBDA BETA1 Y M X ________ ________ ________ ________ Y 0 0 0 0 M 0 0 0 0 X 0 0 0 0 THETA Y M X ________ ________ ________ Y 0 M 0 0 X 0 0 0 ALPHA BETA1 Y M X ________ ________ ________ ________ 1 1 0 2 0 BETA BETA1 Y M X ________ ________ ________ ________ BETA1 0 0 0 3 Y 0 0 0 4 M 0 0 0 5 X 0 0 0 0 PSI BETA1 Y M X ________ ________ ________ ________ BETA1 0 Y 0 0 M 0 0 6 X 0 0 0 0 PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS NEW/ADDITIONAL PARAMETERS IND DIR ________ ________ 1 8 9 STARTING VALUES TAU Y$1 ________ 1 0.500 NU Y M X ________ ________ ________ 1 0.000 0.000 0.000 LAMBDA BETA1 Y M X ________ ________ ________ ________ Y 0.000 1.000 0.000 0.000 M 0.000 0.000 1.000 0.000 X 0.000 0.000 0.000 1.000 THETA Y M X ________ ________ ________ Y 0.000 M 0.000 0.000 X 0.000 0.000 0.000 ALPHA BETA1 Y M X ________ ________ ________ ________ 1 0.700 0.000 0.500 0.000 BETA BETA1 Y M X ________ ________ ________ ________ BETA1 0.000 0.000 0.000 0.200 Y 0.000 0.000 0.000 0.300 M 0.000 0.000 0.000 0.500 X 0.000 0.000 0.000 0.000 PSI BETA1 Y M X ________ ________ ________ ________ BETA1 0.000 Y 0.000 1.000 M 0.000 0.000 0.750 X 0.000 0.000 0.000 0.500 STARTING VALUES FOR THE ADDITIONAL PARAMETERS NEW/ADDITIONAL PARAMETERS IND DIR ________ ________ 1 0.450 0.400 POPULATION VALUES TAU Y$1 ________ 1 0.500 NU Y M X ________ ________ ________ 1 0.000 0.000 0.000 LAMBDA BETA1 Y M X ________ ________ ________ ________ Y 0.000 1.000 0.000 0.000 M 0.000 0.000 1.000 0.000 X 0.000 0.000 0.000 1.000 THETA Y M X ________ ________ ________ Y 0.000 M 0.000 0.000 X 0.000 0.000 0.000 ALPHA BETA1 Y M X ________ ________ ________ ________ 1 0.700 0.000 0.500 0.000 BETA BETA1 Y M X ________ ________ ________ ________ BETA1 0.000 0.000 0.000 0.200 Y 0.000 0.000 0.000 0.300 M 0.000 0.000 0.000 0.500 X 0.000 0.000 0.000 0.000 PSI BETA1 Y M X ________ ________ ________ ________ BETA1 0.000 Y 0.000 0.000 M 0.000 0.000 0.750 X 0.000 0.000 0.000 1.000 SAVEDATA INFORMATION Order of variables Y M X Save file n200xmrep*.dat Save file format Free Save file record length 5000 Beginning Time: 14:47:21 Ending Time: 14:47:53 Elapsed Time: 00:00:32 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) 1998-2011 Muthen & Muthen