Mplus DEVELOPMENT (Dev 10/23/2011) MUTHEN & MUTHEN 10/23/2011 8:46 PM INPUT INSTRUCTIONS title: Pearl (2011) artificial example, Prevention Science data: file = binbinprobreplist.dat; type = montecarlo; variable: names = y m x; !x: tx/ctrl, m: mediator, y: outcome categorical = y m; usev = y m x xm; define: xm=x*m; analysis: estimator = bayes; fbiter = 10000; mediator = observed; model: [m\$1*.254] (fm0); ! Negative intercept. P(m=1 | x=0)=0.40 m on x*.929 (fm1); ! P(m=1 | x=1)=0.75 [y\$1*.84] (fy00); ! Negative intercept. P(y=1 | x=0,m=0)=0.20 y on x*.586 (fy10); ! direct effect of x on y. P(y=1 |x=1,m=0)=0.40 y on m*.315 (fy01); ! main effect of m on y. P(y=1 | x=0,m=1)=0.30 y on xm*.779 (fy11); ! interaction between x and m in their influence on y !P(y=1 | x=1,m=1)=0.80 model constraint: new(de*.32 tie*.14 pie*.035 te*.46 tiete*.304 piete*.07 dete*.696 compdete*.304 orde*4.0303 ortie*1.8333 pfm0 pfm1 pfy00 pfy10 pfy01 pfy11 numde dende numtie dentie); pfm0=phi(-fm0); pfm1=phi(-fm0+fm1); pfy00=phi(-fy00); pfy10=phi(-fy00+fy10); pfy01=phi(-fy00+fy01); pfy11=phi(-fy00+fy10+fy01+fy11); de=(pfy10-pfy00)*(1-pfm0)+(pfy11-pfy01)*pfm0; tie=(pfy11-pfy10)*(pfm1-pfm0); pie=(pfy01-pfy00)*(pfm1-pfm0); te=pfy11*pfm1+pfy10*(1-pfm1) -(pfy01*pfm0+pfy00*(1-pfm0)); tiete=tie/te; piete=pie/te; dete=de/te; compdete=1-de/te; numde=pfy10*(1-pfm0)+pfy11*pfm0; dende=pfy00*(1-pfm0)+pfy01*pfm0; orde=(numde/(1-numde))/(dende/(1-dende)); numtie=pfy10*(1-pfm1)+pfy11*pfm1; dentie=pfy10*(1-pfm0)+pfy11*pfm0; ortie=(numtie/(1-numtie))/(dentie/(1-dentie)); INPUT READING TERMINATED NORMALLY Pearl (2011) artificial example, Prevention Science SUMMARY OF ANALYSIS Number of groups 1 Average number of observations 400 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 Binary and ordered categorical (ordinal) Y M 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 OBSERVED 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 binbinprobreplist.dat Input data format FREE UNIVARIATE PROPORTIONS FOR CATEGORICAL VARIABLES NOTE: These are average results over 500 data sets. Y Category 1 0.520 Category 2 0.480 M Category 1 0.375 Category 2 0.625 MODEL FIT INFORMATION Number of Free Parameters 6 MODEL RESULTS ESTIMATES S. E. M. S. E. 95% % Sig Population Average Std. Dev. Average Cover Coeff M ON X 0.929 0.9334 0.1318 0.1310 0.0174 0.958 1.000 Y ON X 0.586 0.5963 0.2204 0.2241 0.0486 0.958 0.772 M 0.315 0.3110 0.1976 0.1993 0.0390 0.954 0.330 XM 0.779 0.7916 0.2792 0.2919 0.0780 0.970 0.808 Thresholds Y\$1 0.840 0.8481 0.1320 0.1308 0.0175 0.952 1.000 M\$1 0.254 0.2581 0.0881 0.0894 0.0078 0.946 0.824 New/Additional Parameters DE 0.320 0.3208 0.0536 0.0537 0.0029 0.956 1.000 TIE 0.140 0.1371 0.0323 0.0324 0.0011 0.946 1.000 PIE 0.035 0.0334 0.0221 0.0227 0.0005 0.958 0.330 TE 0.460 0.4598 0.0431 0.0441 0.0019 0.958 1.000 TIETE 0.304 0.3027 0.0773 0.0770 0.0060 0.946 1.000 PIETE 0.070 0.0735 0.0488 0.0518 0.0024 0.956 0.330 DETE 0.696 0.6973 0.0773 0.0770 0.0060 0.946 1.000 COMPDETE 0.304 0.3027 0.0773 0.0770 0.0060 0.946 1.000 ORDE 4.030 4.2200 1.0343 1.1117 1.1036 0.950 1.000 ORTIE 1.833 1.8375 0.2559 0.2614 0.0654 0.954 1.000 PFM0 0.500 0.3986 0.0338 0.0342 0.0114 0.176 1.000 PFM1 0.500 0.7492 0.0319 0.0303 0.0631 0.000 1.000 PFY00 0.500 0.2002 0.0360 0.0361 0.0912 0.000 1.000 PFY10 0.500 0.4021 0.0688 0.0681 0.0143 0.712 1.000 PFY01 0.500 0.2974 0.0485 0.0507 0.0434 0.034 1.000 PFY11 0.500 0.8008 0.0312 0.0319 0.0915 0.000 1.000 NUMDE 0.500 0.5614 0.0461 0.0453 0.0059 0.730 1.000 DENDE 0.500 0.2400 0.0288 0.0299 0.0684 0.000 1.000 NUMTIE 0.500 0.7008 0.0319 0.0320 0.0413 0.000 1.000 DENTIE 0.500 0.5614 0.0461 0.0453 0.0059 0.730 1.000 TECHNICAL 1 OUTPUT PARAMETER SPECIFICATION TAU Y\$1 M\$1 ________ ________ 1 5 6 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 0 0 0 BETA Y M X XM ________ ________ ________ ________ Y 0 1 2 3 M 0 0 4 0 X 0 0 0 0 XM 0 0 0 0 PSI Y M X XM ________ ________ ________ ________ Y 0 M 0 0 X 0 0 0 XM 0 0 0 0 PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS NEW/ADDITIONAL PARAMETERS DE TIE PIE TE TIETE ________ ________ ________ ________ ________ 1 7 8 9 10 11 NEW/ADDITIONAL PARAMETERS PIETE DETE COMPDETE ORDE ORTIE ________ ________ ________ ________ ________ 1 12 13 14 15 16 NEW/ADDITIONAL PARAMETERS PFM0 PFM1 PFY00 PFY10 PFY01 ________ ________ ________ ________ ________ 1 17 18 19 20 21 NEW/ADDITIONAL PARAMETERS PFY11 NUMDE DENDE NUMTIE DENTIE ________ ________ ________ ________ ________ 1 22 23 24 25 26 STARTING VALUES TAU Y\$1 M\$1 ________ ________ 1 0.840 0.254 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 0.000 0.000 0.000 BETA Y M X XM ________ ________ ________ ________ Y 0.000 0.315 0.586 0.779 M 0.000 0.000 0.929 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 1.000 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 DE TIE PIE TE TIETE ________ ________ ________ ________ ________ 1 0.320 0.140 0.035 0.460 0.304 NEW/ADDITIONAL PARAMETERS PIETE DETE COMPDETE ORDE ORTIE ________ ________ ________ ________ ________ 1 0.070 0.696 0.304 4.030 1.833 NEW/ADDITIONAL PARAMETERS PFM0 PFM1 PFY00 PFY10 PFY01 ________ ________ ________ ________ ________ 1 0.500 0.500 0.500 0.500 0.500 NEW/ADDITIONAL PARAMETERS PFY11 NUMDE DENDE NUMTIE DENTIE ________ ________ ________ ________ ________ 1 0.500 0.500 0.500 0.500 0.500 PRIORS FOR ALL PARAMETERS PRIOR MEAN PRIOR VARIANCE PRIOR STD. DEV. Parameter 1~N(0.000,5.000) 0.0000 5.0000 2.2361 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(0.000,5.000) 0.0000 5.0000 2.2361 Parameter 6~N(0.000,5.000) 0.0000 5.0000 2.2361 Beginning Time: 20:46:29 Ending Time: 21:38:02 Elapsed Time: 00:51:33 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