Mplus DEVELOPMENT (Dev 10/23/2011) MUTHEN & MUTHEN 10/23/2011 2:51 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 data: file = n200xmreplist.dat; type = montecarlo; variable: names = y m x; usev = y m x xm; categorical = y; define: xm = x*m; analysis: estimator = bayes; fbiter = 10000; 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 ortie*1.7788 orde*1.6808 orpie*1.614); 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); ortie=(phi(probit11)/(1-phi(probit11)))/ (phi(probit10)/(1-phi(probit10))); orde=(phi(probit10)/(1-phi(probit10)))/ (phi(probit00)/(1-phi(probit00))); orpie=(phi(probit01)/(1-phi(probit01)))/ (phi(probit00)/(1-phi(probit00))); 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 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 BAYES Specifications for Bayesian Estimation Point estimate MEDIAN Number of Markov chain Monte Carlo (MCMC) chains 2 Random seed for the first chain 0 Starting value information UNPERTURBED Treatment of categorical mediator LATENT Algorithm used for Markov chain Monte Carlo GIBBS(PX1) Fixed number of iterations 10000 K-th iteration used for thinning 1 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 MODEL FIT INFORMATION Number of Free Parameters 7 Bayesian Posterior Predictive Checking using Chi-Square Posterior Predictive P-Value Number of successful computations 500 Proportions Expected Observed 0.990 1.000 0.980 1.000 0.950 1.000 0.900 1.000 0.800 1.000 0.700 1.000 0.500 1.000 0.300 1.000 0.200 1.000 0.100 1.000 0.050 1.000 0.020 1.000 0.010 1.000 MODEL RESULTS ESTIMATES S. E. M. S. E. 95% % Sig Population Average Std. Dev. Average Cover Coeff Y ON X 0.300 0.2677 0.2760 0.2762 0.0771 0.954 0.188 M 0.700 0.7126 0.1830 0.1812 0.0336 0.950 0.990 XM 0.200 0.2513 0.2841 0.2869 0.0832 0.958 0.128 M ON X 0.500 0.4897 0.1207 0.1240 0.0147 0.946 0.968 Intercepts M 0.500 0.5044 0.0863 0.0875 0.0075 0.972 1.000 Thresholds Y$1 0.500 0.5062 0.1655 0.1656 0.0274 0.950 0.886 Residual Variances M 0.750 0.7650 0.0828 0.0777 0.0071 0.926 1.000 New/Additional Parameters IND 0.450 0.4616 0.1629 0.1664 0.0266 0.956 0.966 DIR 0.400 0.3961 0.2133 0.2134 0.0454 0.956 0.452 ARG11 0.700 0.7204 0.1879 0.1851 0.0357 0.946 0.992 ARG10 0.250 0.2510 0.1851 0.1818 0.0342 0.944 0.296 ARG01 0.200 0.2012 0.1785 0.1714 0.0318 0.940 0.234 ARG00 -0.150 -0.1460 0.1544 0.1500 0.0238 0.946 0.194 V1 1.607 1.7456 0.3648 0.3644 0.1519 0.940 1.000 V0 1.367 1.4134 0.2252 0.2157 0.0527 0.954 1.000 PROBIT11 0.552 0.5465 0.1305 0.1312 0.0170 0.952 0.992 PROBIT10 0.197 0.1949 0.1451 0.1421 0.0210 0.946 0.296 PROBIT01 0.171 0.1645 0.1427 0.1376 0.0204 0.940 0.234 PROBIT00 -0.128 -0.1234 0.1305 0.1250 0.0170 0.946 0.194 TIE 0.131 0.1266 0.0385 0.0387 0.0015 0.950 0.966 DE 0.129 0.1245 0.0673 0.0665 0.0045 0.954 0.468 PIE 0.119 0.1106 0.0352 0.0363 0.0013 0.956 0.960 ORTIE 1.779 1.7858 0.3050 0.3211 0.0929 0.944 1.000 ORDE 1.681 1.7321 0.4935 0.5272 0.2457 0.956 1.000 ORPIE 1.614 1.5914 0.2379 0.2553 0.0570 0.958 1.000 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 NEW/ADDITIONAL PARAMETERS ORTIE ORDE ORPIE ________ ________ ________ 1 23 24 25 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 NEW/ADDITIONAL PARAMETERS ORTIE ORDE ORPIE ________ ________ ________ 1 1.779 1.681 1.614 PRIORS FOR ALL PARAMETERS PRIOR MEAN PRIOR VARIANCE PRIOR STD. DEV. Parameter 1~N(0.000,infinity) 0.0000 infinity infinity Parameter 2~N(0.000,5.000) 0.0000 5.0000 2.2361 Parameter 3~N(0.000,5.000) 0.0000 5.0000 2.2361 Parameter 4~N(0.000,5.000) 0.0000 5.0000 2.2361 Parameter 5~N(0.000,infinity) 0.0000 infinity infinity Parameter 6~IG(-1.000,0.000) infinity infinity infinity Parameter 7~N(0.000,5.000) 0.0000 5.0000 2.2361 Beginning Time: 14:51:21 Ending Time: 15:13:19 Elapsed Time: 00:21:58 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