Mplus VERSION 6.11 MUTHEN & MUTHEN 10/24/2011 9:30 AM INPUT INSTRUCTIONS title: Simulating x-m interaction effect on y using a random slope Count Y, continuous M Step 1: saving the data for external Monte Carlo analysis montecarlo: names = y m x; generate = y(p); count = y(p); nobs = 400; nreps = 500; repsave = all; save = xmrep*.dat; cutpoints = x(0); model population: x@1; [y*-.7]; ! this log rate gives a rate of about 0.5 y on x*.3; beta1 | y on m; beta1 on x*.2; [beta1*.4]; beta1@0; [m*.5]; m on x*.5; m*.75; analysis: type = random; estimator = ml; model: [y*-.7] (beta0); y on x*.3 (beta2); beta1 | y on m; beta1 on x*.2 (beta3); [beta1*.4] (beta1); beta1@0; [m*.5] (gamma0); m on x*.5 (gamma1); m*.75 (sig); model constraint: new(ind*.45 dir*.4 ey1 ey0 mum1 mum0 ay1 ay0 bym11 bym10 bym01 bym00 eym11 eym10 eym01 eym00 tie de total pie); ind=beta1*gamma1+beta3*gamma1; dir=beta3*gamma0+beta2; ey1=exp(beta0+beta2); ey0=exp(beta0); mum1=gamma0+gamma1; mum0=gamma0; ay1=2*sig*(beta1+beta3); ay0=2*sig*beta1; bym11=(ay1/mum1+2)/2; bym10=(ay1/mum0+2)/2; bym01=(ay0/mum1+2)/2; bym00=(ay0/mum0+2)/2; eym11=exp((bym11*bym11-1)*mum1*mum1/(2*sig)); eym10=exp((bym10*bym10-1)*mum0*mum0/(2*sig)); eym01=exp((bym01*bym01-1)*mum1*mum1/(2*sig)); eym00=exp((bym00*bym00-1)*mum0*mum0/(2*sig)); tie=ey1*eym11-ey1*eym10; de=ey1*eym10-ey0*eym00; total=ey1*eym11-ey0*eym00; pie=ey0*eym01-ey0*eym00; INPUT READING TERMINATED NORMALLY Simulating x-m interaction effect on y using a random slope Count Y, continuous M Step 1: saving the data for external Monte Carlo analysis SUMMARY OF ANALYSIS Number of groups 1 Number of observations 400 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 Count 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 15 Minimum value for logit thresholds -15 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 Cholesky OFF SAMPLE STATISTICS FOR THE FIRST REPLICATION SAMPLE STATISTICS Means M X ________ ________ 1 0.781 0.492 Covariances M X ________ ________ M 0.867 X 0.147 0.251 Correlations M X ________ ________ M 1.000 X 0.316 1.000 MODEL FIT INFORMATION Number of Free Parameters 7 Loglikelihood H0 Value Mean -997.729 Std Dev 20.270 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.994 -1044.883 -1044.151 0.980 0.984 -1039.358 -1038.466 0.950 0.966 -1031.071 -1029.109 0.900 0.912 -1023.707 -1022.830 0.800 0.788 -1014.788 -1015.856 0.700 0.694 -1008.359 -1008.766 0.500 0.476 -997.729 -998.805 0.300 0.276 -987.099 -989.052 0.200 0.206 -980.669 -980.521 0.100 0.116 -971.751 -970.009 0.050 0.064 -964.386 -961.781 0.020 0.032 -956.100 -951.473 0.010 0.016 -950.574 -948.559 Information Criteria Akaike (AIC) Mean 2009.458 Std Dev 40.540 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.984 1915.148 1908.426 0.980 0.968 1926.200 1916.826 0.950 0.936 1942.773 1934.241 0.900 0.884 1957.501 1952.662 0.800 0.794 1975.339 1974.375 0.700 0.724 1988.198 1992.064 0.500 0.524 2009.458 2011.513 0.300 0.306 2030.717 2031.311 0.200 0.212 2043.577 2045.110 0.100 0.088 2061.414 2058.246 0.050 0.034 2076.143 2071.466 0.020 0.016 2092.716 2089.627 0.010 0.006 2103.767 2097.906 Bayesian (BIC) Mean 2037.398 Std Dev 40.540 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.984 1943.089 1936.366 0.980 0.968 1954.140 1944.767 0.950 0.936 1970.713 1962.182 0.900 0.884 1985.441 1980.602 0.800 0.794 2003.279 2002.315 0.700 0.724 2016.139 2020.004 0.500 0.524 2037.398 2039.453 0.300 0.306 2058.657 2059.251 0.200 0.212 2071.517 2073.050 0.100 0.088 2089.355 2086.186 0.050 0.034 2104.083 2099.406 0.020 0.016 2120.656 2117.567 0.010 0.006 2131.707 2125.846 Sample-Size Adjusted BIC (n* = (n + 2) / 24) Mean 2015.186 Std Dev 40.540 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.984 1920.877 1914.155 0.980 0.968 1931.929 1922.555 0.950 0.936 1948.501 1939.970 0.900 0.884 1963.230 1958.391 0.800 0.794 1981.068 1980.104 0.700 0.724 1993.927 1997.793 0.500 0.524 2015.186 2017.242 0.300 0.306 2036.446 2037.039 0.200 0.212 2049.305 2050.839 0.100 0.088 2067.143 2063.975 0.050 0.034 2081.871 2077.195 0.020 0.016 2098.444 2095.356 0.010 0.006 2109.496 2103.634 MODEL RESULTS ESTIMATES S. E. M. S. E. 95% % Sig Population Average Std. Dev. Average Cover Coeff BETA1 ON X 0.200 0.2005 0.1257 0.1235 0.0158 0.950 0.400 Y ON X 0.300 0.3042 0.1742 0.1681 0.0303 0.934 0.434 M ON X 0.500 0.5016 0.0852 0.0863 0.0072 0.956 1.000 Intercepts M 0.500 0.4999 0.0612 0.0611 0.0037 0.948 1.000 BETA1 0.400 0.4049 0.1042 0.1019 0.0109 0.940 0.968 Y -0.700 -0.7122 0.1227 0.1204 0.0152 0.954 1.000 Residual Variances M 0.750 0.7431 0.0491 0.0525 0.0024 0.960 1.000 BETA1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 New/Additional Parameters IND 0.450 0.3035 0.0607 0.0630 0.0251 0.374 1.000 DIR 0.400 0.4048 0.1323 0.1304 0.0175 0.942 0.862 EY1 0.500 0.6693 0.0758 0.0779 0.0344 0.414 1.000 EY0 0.500 0.4942 0.0600 0.0591 0.0036 0.946 1.000 MUM1 0.500 1.0015 0.0639 0.0609 0.2555 0.000 1.000 MUM0 0.500 0.4999 0.0612 0.0611 0.0037 0.948 1.000 AY1 0.500 0.8993 0.1110 0.1210 0.1717 0.058 1.000 AY0 0.500 0.6008 0.1570 0.1574 0.0348 0.922 0.964 BYM11 0.500 1.4508 0.0627 0.0668 0.9080 0.000 1.000 BYM10 0.500 1.9128 0.1579 0.1691 2.0208 0.000 1.000 BYM01 0.500 1.3010 0.0807 0.0812 0.6481 0.000 1.000 BYM00 0.500 1.6110 0.1834 0.1789 1.2680 0.000 1.000 EYM11 0.500 2.1150 0.2191 0.2286 2.6561 0.000 1.000 EYM10 0.500 1.5574 0.1154 0.1193 1.1313 0.000 1.000 EYM01 0.500 1.6160 0.2251 0.2209 1.2961 0.000 1.000 EYM00 0.500 1.3106 0.1119 0.1131 0.6695 0.000 1.000 TIE 0.500 0.3667 0.0755 0.0772 0.0235 0.570 1.000 DE 0.500 0.3930 0.0945 0.0947 0.0204 0.798 0.988 TOTAL 0.500 0.7597 0.1166 0.1156 0.0810 0.396 1.000 PIE 0.500 0.1461 0.0508 0.0500 0.1278 0.000 0.942 QUALITY OF NUMERICAL RESULTS Average Condition Number for the Information Matrix 0.432E-03 (ratio of smallest to largest eigenvalue) TECHNICAL 1 OUTPUT PARAMETER SPECIFICATION NU Y#1 Y M X ________ ________ ________ ________ 1 0 0 0 0 LAMBDA BETA1 Y#1 Y M X ________ ________ ________ ________ ________ Y#1 0 0 0 0 0 Y 0 0 0 0 0 M 0 0 0 0 0 X 0 0 0 0 0 THETA Y#1 Y M X ________ ________ ________ ________ Y#1 0 Y 0 0 M 0 0 0 X 0 0 0 0 ALPHA BETA1 Y#1 Y M X ________ ________ ________ ________ ________ 1 1 0 2 3 0 BETA BETA1 Y#1 Y M X ________ ________ ________ ________ ________ BETA1 0 0 0 0 4 Y#1 0 0 0 0 0 Y 0 0 0 0 5 M 0 0 0 0 6 X 0 0 0 0 0 PSI BETA1 Y#1 Y M X ________ ________ ________ ________ ________ BETA1 0 Y#1 0 0 Y 0 0 0 M 0 0 0 7 X 0 0 0 0 0 PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS NEW/ADDITIONAL PARAMETERS IND DIR EY1 EY0 MUM1 ________ ________ ________ ________ ________ 1 8 9 10 11 12 NEW/ADDITIONAL PARAMETERS MUM0 AY1 AY0 BYM11 BYM10 ________ ________ ________ ________ ________ 1 13 14 15 16 17 NEW/ADDITIONAL PARAMETERS BYM01 BYM00 EYM11 EYM10 EYM01 ________ ________ ________ ________ ________ 1 18 19 20 21 22 NEW/ADDITIONAL PARAMETERS EYM00 TIE DE TOTAL PIE ________ ________ ________ ________ ________ 1 23 24 25 26 27 STARTING VALUES NU Y#1 Y M X ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 LAMBDA BETA1 Y#1 Y M X ________ ________ ________ ________ ________ Y#1 0.000 1.000 0.000 0.000 0.000 Y 0.000 0.000 1.000 0.000 0.000 M 0.000 0.000 0.000 1.000 0.000 X 0.000 0.000 0.000 0.000 1.000 THETA Y#1 Y M X ________ ________ ________ ________ Y#1 0.000 Y 0.000 0.000 M 0.000 0.000 0.000 X 0.000 0.000 0.000 0.000 ALPHA BETA1 Y#1 Y M X ________ ________ ________ ________ ________ 1 0.400 -20.000 -0.700 0.500 0.000 BETA BETA1 Y#1 Y M X ________ ________ ________ ________ ________ BETA1 0.000 0.000 0.000 0.000 0.200 Y#1 0.000 0.000 0.000 0.000 0.000 Y 0.000 0.000 0.000 0.000 0.300 M 0.000 0.000 0.000 0.000 0.500 X 0.000 0.000 0.000 0.000 0.000 PSI BETA1 Y#1 Y M X ________ ________ ________ ________ ________ BETA1 0.000 Y#1 0.000 0.000 Y 0.000 0.000 0.000 M 0.000 0.000 0.000 0.750 X 0.000 0.000 0.000 0.000 0.500 STARTING VALUES FOR THE ADDITIONAL PARAMETERS NEW/ADDITIONAL PARAMETERS IND DIR EY1 EY0 MUM1 ________ ________ ________ ________ ________ 1 0.450 0.400 0.500 0.500 0.500 NEW/ADDITIONAL PARAMETERS MUM0 AY1 AY0 BYM11 BYM10 ________ ________ ________ ________ ________ 1 0.500 0.500 0.500 0.500 0.500 NEW/ADDITIONAL PARAMETERS BYM01 BYM00 EYM11 EYM10 EYM01 ________ ________ ________ ________ ________ 1 0.500 0.500 0.500 0.500 0.500 NEW/ADDITIONAL PARAMETERS EYM00 TIE DE TOTAL PIE ________ ________ ________ ________ ________ 1 0.500 0.500 0.500 0.500 0.500 POPULATION VALUES NU Y#1 Y M X ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 LAMBDA BETA1 Y#1 Y M X ________ ________ ________ ________ ________ Y#1 0.000 1.000 0.000 0.000 0.000 Y 0.000 0.000 1.000 0.000 0.000 M 0.000 0.000 0.000 1.000 0.000 X 0.000 0.000 0.000 0.000 1.000 THETA Y#1 Y M X ________ ________ ________ ________ Y#1 0.000 Y 0.000 0.000 M 0.000 0.000 0.000 X 0.000 0.000 0.000 0.000 ALPHA BETA1 Y#1 Y M X ________ ________ ________ ________ ________ 1 0.400 -20.000 -0.700 0.500 0.000 BETA BETA1 Y#1 Y M X ________ ________ ________ ________ ________ BETA1 0.000 0.000 0.000 0.000 0.200 Y#1 0.000 0.000 0.000 0.000 0.000 Y 0.000 0.000 0.000 0.000 0.300 M 0.000 0.000 0.000 0.000 0.500 X 0.000 0.000 0.000 0.000 0.000 PSI BETA1 Y#1 Y M X ________ ________ ________ ________ ________ BETA1 0.000 Y#1 0.000 0.000 Y 0.000 0.000 0.000 M 0.000 0.000 0.000 0.750 X 0.000 0.000 0.000 0.000 1.000 SAVEDATA INFORMATION Order of variables Y M X Save file xmrep*.dat Save file format Free Save file record length 5000 Beginning Time: 09:30:26 Ending Time: 09:34:25 Elapsed Time: 00:03:59 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