Mplus DEVELOPMENT (Dev 10/23/2011) MUTHEN & MUTHEN 10/24/2011 9:24 AM INPUT INSTRUCTIONS title: Pearl (2011) artificial example for n=200 Probit. data: file = n200.dat; variable: names = y m x w; !x: tx/ctrl, m: mediator, y: outcome freqweight = w; 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 pfm0*.4 pfm1*.75 pfy00*.2 pfy10*.4 pfy01*.3 pfy11*.8 numde*.56 dende*.24 orde*4.0303 numind*.7 denind*.56 orind*1.8333); 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)); numind=pfy10*(1-pfm1)+pfy11*pfm1; denind=pfy10*(1-pfm0)+pfy11*pfm0; orind=(numind/(1-numind))/(denind/(1-denind)); output: tech1 tech8; plot: type = plot3; INPUT READING TERMINATED NORMALLY Pearl (2011) artificial example for n=200 Probit. SUMMARY OF ANALYSIS Number of groups 1 Number of observations 200 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) n200.dat Input data format FREE UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES Y Category 1 0.500 100.000 Category 2 0.500 100.000 M Category 1 0.425 85.000 Category 2 0.575 115.000 THE MODEL ESTIMATION TERMINATED NORMALLY MODEL FIT INFORMATION Number of Free Parameters 6 MODEL RESULTS Posterior One-Tailed 95% C.I. Estimate S.D. P-Value Lower 2.5% Upper 2.5% M ON X 0.960 0.187 0.000 0.598 1.325 Y ON X 0.596 0.314 0.031 -0.030 1.212 M 0.328 0.259 0.103 -0.179 0.843 XM 0.757 0.406 0.031 -0.030 1.553 Thresholds Y\$1 0.709 0.170 0.000 0.378 1.051 M\$1 0.232 0.122 0.028 -0.005 0.469 New/Additional Parameters DE 0.322 0.077 0.000 0.168 0.470 TIE 0.131 0.046 0.000 0.051 0.231 PIE 0.038 0.033 0.103 -0.021 0.111 TE 0.456 0.061 0.000 0.332 0.569 TIETE 0.288 0.113 0.000 0.109 0.547 PIETE 0.084 0.076 0.103 -0.047 0.258 DETE 0.712 0.113 0.000 0.453 0.891 COMPDETE 0.288 0.113 0.000 0.109 0.547 PFM0 0.408 0.047 0.000 0.319 0.502 PFM1 0.767 0.043 0.000 0.674 0.844 PFY00 0.239 0.052 0.000 0.147 0.353 PFY10 0.455 0.102 0.000 0.259 0.658 PFY01 0.351 0.071 0.000 0.221 0.497 PFY11 0.834 0.044 0.000 0.735 0.906 NUMDE 0.609 0.066 0.000 0.477 0.736 DENDE 0.285 0.043 0.000 0.208 0.376 ORDE 3.908 1.508 0.000 2.024 7.852 NUMIND 0.744 0.045 0.000 0.649 0.825 DENIND 0.609 0.066 0.000 0.477 0.736 ORIND 1.841 0.398 0.000 1.290 2.831 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 PFM0 PFM1 ________ ________ ________ ________ ________ 1 12 13 14 15 16 NEW/ADDITIONAL PARAMETERS PFY00 PFY10 PFY01 PFY11 NUMDE ________ ________ ________ ________ ________ 1 17 18 19 20 21 NEW/ADDITIONAL PARAMETERS DENDE ORDE NUMIND DENIND ORIND ________ ________ ________ ________ ________ 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 0.125 XM 0.000 0.000 0.000 0.116 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 PFM0 PFM1 ________ ________ ________ ________ ________ 1 0.070 0.696 0.304 0.400 0.750 NEW/ADDITIONAL PARAMETERS PFY00 PFY10 PFY01 PFY11 NUMDE ________ ________ ________ ________ ________ 1 0.200 0.400 0.300 0.800 0.560 NEW/ADDITIONAL PARAMETERS DENDE ORDE NUMIND DENIND ORIND ________ ________ ________ ________ ________ 1 0.240 4.030 0.700 0.560 1.833 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 TECHNICAL 8 OUTPUT TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION CHAIN BSEED 1 0 2 285380 POTENTIAL PARAMETER WITH ITERATION SCALE REDUCTION HIGHEST PSR 100 1.009 2 200 1.009 1 300 1.000 3 400 1.014 3 500 1.014 5 600 1.003 5 700 1.001 5 800 1.008 5 900 1.006 5 1000 1.006 5 1100 1.006 5 1200 1.012 5 1300 1.013 5 1400 1.009 5 1500 1.004 5 1600 1.002 4 1700 1.001 5 1800 1.001 5 1900 1.000 5 2000 1.000 6 2100 1.000 2 2200 1.000 2 2300 1.000 5 2400 1.001 2 2500 1.001 5 2600 1.001 5 2700 1.000 3 2800 1.000 4 2900 1.001 3 3000 1.003 4 3100 1.001 4 3200 1.002 4 3300 1.002 4 3400 1.001 4 3500 1.000 3 3600 1.000 3 3700 1.001 3 3800 1.001 3 3900 1.002 3 4000 1.001 3 4100 1.001 2 4200 1.002 2 4300 1.003 2 4400 1.003 2 4500 1.002 2 4600 1.002 2 4700 1.002 2 4800 1.002 2 4900 1.001 2 5000 1.002 2 5100 1.001 2 5200 1.001 2 5300 1.000 2 5400 1.001 1 5500 1.001 1 5600 1.001 1 5700 1.001 1 5800 1.001 1 5900 1.001 1 6000 1.002 1 6100 1.002 1 6200 1.002 1 6300 1.002 1 6400 1.002 1 6500 1.003 1 6600 1.002 1 6700 1.002 1 6800 1.002 1 6900 1.001 1 7000 1.002 1 7100 1.001 1 7200 1.001 1 7300 1.001 1 7400 1.001 1 7500 1.001 1 7600 1.001 1 7700 1.001 1 7800 1.001 1 7900 1.001 1 8000 1.001 1 8100 1.001 1 8200 1.001 1 8300 1.001 1 8400 1.001 1 8500 1.001 1 8600 1.001 1 8700 1.001 1 8800 1.001 1 8900 1.001 1 9000 1.001 1 9100 1.001 1 9200 1.000 1 9300 1.000 1 9400 1.000 1 9500 1.000 1 9600 1.000 1 9700 1.001 1 9800 1.001 1 9900 1.000 1 10000 1.000 1 PLOT INFORMATION The following plots are available: Histograms (sample values) Scatterplots (sample values) Bayesian posterior parameter distributions Bayesian posterior parameter trace plots Bayesian autocorrelation plots Bayesian posterior predictive checking scatterplots Bayesian posterior predictive checking distribution plots Sample proportions and estimated probabilities Beginning Time: 09:24:16 Ending Time: 09:24:20 Elapsed Time: 00:00:04 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