Mplus DEVELOPMENT (Dev 10/23/2011) MUTHEN & MUTHEN 10/23/2011 2:50 PM INPUT INSTRUCTIONS title: Simulating x-m interaction effect on y using a random slope Step 2 Binary Y, continuous M data: file = n200xmreplist.dat; type = montecarlo; variable: names = y m x; usev = y m x xm; categorical = y; define: xm = x*m; analysis: estimator = ml; link = probit; model: [y\$1*.5] (mbeta0); y on x*.3 (beta2); y on m*.7 (beta1); y on xm*.2 (beta3); [m*.5] (gamma0); m on x*.5 (gamma1); m*.75 (sig2); model constraint: new(ind*.45 dir*.4 arg11*.7 arg10*.25 arg01*.2 arg00*-.15 v1*1.6075 v0*1.3675 probit11*.5521 probit10*.1972 probit01*.17103 probit00*-.1283 tie*.131 de*.129 pie*.119); dir=beta3*gamma0+beta2; ind=beta1*gamma1+beta3*gamma1; arg11=-mbeta0+beta2+(beta1+beta3)*(gamma0+gamma1); arg10=-mbeta0+beta2+(beta1+beta3)*gamma0; arg01=-mbeta0+beta1*(gamma0+gamma1); arg00=-mbeta0+beta1*gamma0; v1=(beta1+beta3)^2*sig2+1; v0=beta1^2*sig2+1; probit11=arg11/sqrt(v1); probit10=arg10/sqrt(v1); probit01=arg01/sqrt(v0); probit00=arg00/sqrt(v0); ! Phi function needed below: tie=phi(probit11)-phi(probit10); de=phi(probit10)-phi(probit00); pie=phi(probit01)-phi(probit00); INPUT READING TERMINATED NORMALLY Simulating x-m interaction effect on y using a random slope Step 2 Binary Y, continuous M SUMMARY OF ANALYSIS Number of groups 1 Average number of observations 200 Number of replications Requested 500 Completed 500 Number of dependent variables 2 Number of independent variables 2 Number of continuous latent variables 0 Observed dependent variables Continuous M Binary and ordered categorical (ordinal) Y Observed independent variables X XM 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 0 Adaptive quadrature ON Link PROBIT Cholesky ON Input data file(s) Multiple data files from n200xmreplist.dat Input data format FREE UNIVARIATE PROPORTIONS FOR CATEGORICAL VARIABLES NOTE: These are average results over 500 data sets. Y Category 1 0.425 Category 2 0.575 SAMPLE STATISTICS NOTE: These are average results over 500 data sets. SAMPLE STATISTICS Means M X XM ________ ________ ________ 1 0.747 0.497 0.493 Covariances M X XM ________ ________ ________ M 0.814 X 0.122 0.250 XM 0.499 0.248 0.624 Correlations M X XM ________ ________ ________ M 1.000 X 0.271 1.000 XM 0.700 0.629 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 -387.909 0.980 0.984 -383.726 -382.548 0.950 0.950 -378.960 -378.999 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 -360.239 0.300 0.296 -353.668 -353.937 0.200 0.206 -349.970 -349.725 0.100 0.108 -344.840 -344.599 0.050 0.058 -340.604 -339.993 0.020 0.022 -335.838 -335.451 0.010 0.012 -332.660 -332.551 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 0.942 695.208 693.858 0.900 0.892 703.679 703.035 0.800 0.794 713.939 713.345 0.700 0.704 721.336 721.841 0.500 0.512 733.564 734.318 0.300 0.312 745.791 746.516 0.200 0.182 753.188 752.065 0.100 0.096 763.448 762.380 0.050 0.050 771.919 771.481 0.020 0.016 781.452 778.832 0.010 0.010 787.808 785.619 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 0.942 718.296 716.946 0.900 0.892 726.768 726.123 0.800 0.794 737.027 736.433 0.700 0.704 744.424 744.929 0.500 0.512 756.652 757.407 0.300 0.312 768.880 769.604 0.200 0.182 776.276 775.153 0.100 0.096 786.536 785.468 0.050 0.050 795.007 794.569 0.020 0.016 804.540 801.920 0.010 0.010 810.896 808.707 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 0.988 680.231 678.501 0.980 0.978 686.587 684.267 0.950 0.942 696.119 694.770 0.900 0.892 704.591 703.946 0.800 0.794 714.851 714.256 0.700 0.704 722.247 722.753 0.500 0.512 734.475 735.230 0.300 0.312 746.703 747.427 0.200 0.182 754.099 752.976 0.100 0.096 764.359 763.291 0.050 0.050 772.831 772.392 0.020 0.016 782.363 779.744 0.010 0.010 788.720 786.530 MODEL RESULTS ESTIMATES S. E. M. S. E. 95% % Sig Population Average Std. Dev. Average Cover Coeff Y ON X 0.300 0.2740 0.2796 0.2770 0.0787 0.952 0.194 M 0.700 0.7138 0.1848 0.1799 0.0343 0.956 0.990 XM 0.200 0.2370 0.2865 0.2842 0.0833 0.954 0.110 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 Thresholds Y\$1 0.500 0.5058 0.1670 0.1672 0.0279 0.952 0.880 Residual Variances M 0.750 0.7465 0.0808 0.0746 0.0065 0.920 1.000 New/Additional Parameters IND 0.450 0.4661 0.1621 0.1600 0.0265 0.948 0.950 DIR 0.400 0.3935 0.2140 0.2122 0.0458 0.952 0.462 ARG11 0.700 0.7134 0.1858 0.1819 0.0346 0.962 0.992 ARG10 0.250 0.2473 0.1846 0.1807 0.0340 0.950 0.304 ARG01 0.200 0.2037 0.1788 0.1699 0.0319 0.942 0.218 ARG00 -0.150 -0.1462 0.1546 0.1489 0.0239 0.948 0.188 V1 1.607 1.7107 0.3486 0.3263 0.1319 0.948 1.000 V0 1.367 1.4057 0.2238 0.1998 0.0515 0.942 1.000 PROBIT11 0.552 0.5484 0.1317 0.1327 0.0173 0.952 0.992 PROBIT10 0.197 0.1948 0.1468 0.1442 0.0215 0.946 0.260 PROBIT01 0.171 0.1678 0.1437 0.1383 0.0206 0.942 0.240 PROBIT00 -0.128 -0.1244 0.1315 0.1256 0.0173 0.952 0.190 TIE 0.131 0.1303 0.0391 0.0388 0.0015 0.946 0.958 DE 0.129 0.1255 0.0689 0.0676 0.0047 0.952 0.450 PIE 0.119 0.1151 0.0358 0.0362 0.0013 0.936 0.950 QUALITY OF NUMERICAL RESULTS Average Condition Number for the Information Matrix 0.150E-02 (ratio of smallest to largest eigenvalue) TECHNICAL 1 OUTPUT PARAMETER SPECIFICATION TAU Y\$1 ________ 1 7 NU Y M X XM ________ ________ ________ ________ 1 0 0 0 0 LAMBDA Y M X XM ________ ________ ________ ________ Y 0 0 0 0 M 0 0 0 0 X 0 0 0 0 XM 0 0 0 0 THETA Y M X XM ________ ________ ________ ________ Y 0 M 0 0 X 0 0 0 XM 0 0 0 0 ALPHA Y M X XM ________ ________ ________ ________ 1 0 1 0 0 BETA Y M X XM ________ ________ ________ ________ Y 0 2 3 4 M 0 0 5 0 X 0 0 0 0 XM 0 0 0 0 PSI Y M X XM ________ ________ ________ ________ Y 0 M 0 6 X 0 0 0 XM 0 0 0 0 PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS NEW/ADDITIONAL PARAMETERS IND DIR ARG11 ARG10 ARG01 ________ ________ ________ ________ ________ 1 8 9 10 11 12 NEW/ADDITIONAL PARAMETERS ARG00 V1 V0 PROBIT11 PROBIT10 ________ ________ ________ ________ ________ 1 13 14 15 16 17 NEW/ADDITIONAL PARAMETERS PROBIT01 PROBIT00 TIE DE PIE ________ ________ ________ ________ ________ 1 18 19 20 21 22 STARTING VALUES TAU Y\$1 ________ 1 0.500 NU Y M X XM ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 LAMBDA Y M X XM ________ ________ ________ ________ Y 1.000 0.000 0.000 0.000 M 0.000 1.000 0.000 0.000 X 0.000 0.000 1.000 0.000 XM 0.000 0.000 0.000 1.000 THETA Y M X XM ________ ________ ________ ________ Y 0.000 M 0.000 0.000 X 0.000 0.000 0.000 XM 0.000 0.000 0.000 0.000 ALPHA Y M X XM ________ ________ ________ ________ 1 0.000 0.500 0.000 0.000 BETA Y M X XM ________ ________ ________ ________ Y 0.000 0.700 0.300 0.200 M 0.000 0.000 0.500 0.000 X 0.000 0.000 0.000 0.000 XM 0.000 0.000 0.000 0.000 PSI Y M X XM ________ ________ ________ ________ Y 1.000 M 0.000 0.750 X 0.000 0.000 0.500 XM 0.000 0.000 0.000 0.500 STARTING VALUES FOR THE ADDITIONAL PARAMETERS NEW/ADDITIONAL PARAMETERS IND DIR ARG11 ARG10 ARG01 ________ ________ ________ ________ ________ 1 0.450 0.400 0.700 0.250 0.200 NEW/ADDITIONAL PARAMETERS ARG00 V1 V0 PROBIT11 PROBIT10 ________ ________ ________ ________ ________ 1 -0.150 1.607 1.367 0.552 0.197 NEW/ADDITIONAL PARAMETERS PROBIT01 PROBIT00 TIE DE PIE ________ ________ ________ ________ ________ 1 0.171 -0.128 0.131 0.129 0.119 Beginning Time: 14:50:11 Ending Time: 14:50:21 Elapsed Time: 00:00:10 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