Mplus VERSION 6.1 MUTHEN & MUTHEN 10/15/2010 12:51 PM INPUT INSTRUCTIONS title: Mediation using Bayesian analysis ATLAS data from MacKinnon et al. (2004), MBR Step 1 data: file = mbr2004atlas.txt; variable: names = obs group severity nutrit; usev = group - nutrit; analysis: estimator = bayes; process = 2; model: severity on group (a); nutrit on severity (b) group; model constraint: new(indirect); indirect = a*b; output: tech1 tech8 standardized; plot: type = plot2; INPUT READING TERMINATED NORMALLY Mediation using Bayesian analysis ATLAS data from MacKinnon et al. (2004), MBR Step 1 SUMMARY OF ANALYSIS Number of groups 1 Number of observations 861 Number of dependent variables 2 Number of independent variables 1 Number of continuous latent variables 0 Observed dependent variables Continuous SEVERITY NUTRIT Observed independent variables GROUP 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) Convergence criterion 0.500D-01 Maximum number of iterations 50000 K-th iteration used for thinning 1 Input data file(s) mbr2004atlas.txt Input data format FREE THE MODEL ESTIMATION TERMINATED NORMALLY MODEL FIT INFORMATION Number of Free Parameters 7 Bayesian Posterior Predictive Checking using Chi-Square 95% Confidence Interval for the Difference Between the Observed and the Replicated Chi-Square Values -3.959 9.160 Posterior Predictive P-Value 0.333 Information Criterion Deviance (DIC) 5607.347 Estimated Number of Parameters (pD) 7.960 MODEL RESULTS Posterior One-Tailed 95% C.I. Estimate S.D. P-Value Lower 2.5% Upper 2.5% SEVERITY ON GROUP 0.282 0.106 0.010 0.095 0.486 NUTRIT ON SEVERITY 0.067 0.031 0.000 0.015 0.125 GROUP -0.011 0.089 0.440 -0.180 0.155 Intercepts SEVERITY 5.641 0.072 0.000 5.513 5.779 NUTRIT 3.698 0.191 0.000 3.309 4.018 Residual Variances SEVERITY 1.722 0.072 0.000 1.614 1.868 NUTRIT 1.331 0.070 0.000 1.198 1.468 New/Additional Parameters INDIRECT 0.016 0.013 0.010 0.002 0.052 STANDARDIZED MODEL RESULTS STDYX Standardization Posterior One-Tailed 95% C.I. Estimate S.D. P-Value Lower 2.5% Upper 2.5% SEVERITY ON GROUP 0.107 0.040 0.010 0.036 0.178 NUTRIT ON SEVERITY 0.077 0.035 0.000 0.018 0.143 GROUP -0.005 0.038 0.440 -0.078 0.066 Intercepts SEVERITY 4.259 0.105 0.000 4.094 4.485 NUTRIT 3.190 0.194 0.000 2.798 3.513 Residual Variances SEVERITY 0.989 0.008 0.000 0.968 0.999 NUTRIT 0.993 0.006 0.000 0.977 0.999 STDY Standardization Posterior One-Tailed 95% C.I. Estimate S.D. P-Value Lower 2.5% Upper 2.5% SEVERITY ON GROUP 0.107 0.040 0.010 0.036 0.178 NUTRIT ON SEVERITY 0.077 0.035 0.000 0.018 0.143 GROUP -0.005 0.038 0.440 -0.078 0.066 Intercepts SEVERITY 4.259 0.105 0.000 4.094 4.485 NUTRIT 3.190 0.194 0.000 2.798 3.513 Residual Variances SEVERITY 0.989 0.008 0.000 0.968 0.999 NUTRIT 0.993 0.006 0.000 0.977 0.999 STD Standardization Posterior One-Tailed 95% C.I. Estimate S.D. P-Value Lower 2.5% Upper 2.5% SEVERITY ON GROUP 0.282 0.106 0.010 0.095 0.486 NUTRIT ON SEVERITY 0.067 0.031 0.000 0.015 0.125 GROUP -0.011 0.089 0.440 -0.180 0.155 Intercepts SEVERITY 5.641 0.072 0.000 5.513 5.779 NUTRIT 3.698 0.191 0.000 3.309 4.018 Residual Variances SEVERITY 1.722 0.072 0.000 1.614 1.868 NUTRIT 1.331 0.070 0.000 1.198 1.468 R-SQUARE Posterior One-Tailed 95% C.I. Variable Estimate S.D. P-Value Lower 2.5% Upper 2.5% SEVERITY 0.011 0.008 0.000 0.001 0.032 NUTRIT 0.007 0.006 0.000 0.001 0.023 TECHNICAL 1 OUTPUT PARAMETER SPECIFICATION NU SEVERITY NUTRIT GROUP ________ ________ ________ 1 0 0 0 LAMBDA SEVERITY NUTRIT GROUP ________ ________ ________ SEVERITY 0 0 0 NUTRIT 0 0 0 GROUP 0 0 0 THETA SEVERITY NUTRIT GROUP ________ ________ ________ SEVERITY 0 NUTRIT 0 0 GROUP 0 0 0 ALPHA SEVERITY NUTRIT GROUP ________ ________ ________ 1 1 2 0 BETA SEVERITY NUTRIT GROUP ________ ________ ________ SEVERITY 0 0 3 NUTRIT 4 0 5 GROUP 0 0 0 PSI SEVERITY NUTRIT GROUP ________ ________ ________ SEVERITY 6 NUTRIT 0 7 GROUP 0 0 0 PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS NEW/ADDITIONAL PARAMETERS INDIRECT ________ 1 8 STARTING VALUES NU SEVERITY NUTRIT GROUP ________ ________ ________ 1 0.000 0.000 0.000 LAMBDA SEVERITY NUTRIT GROUP ________ ________ ________ SEVERITY 1.000 0.000 0.000 NUTRIT 0.000 1.000 0.000 GROUP 0.000 0.000 1.000 THETA SEVERITY NUTRIT GROUP ________ ________ ________ SEVERITY 0.000 NUTRIT 0.000 0.000 GROUP 0.000 0.000 0.000 ALPHA SEVERITY NUTRIT GROUP ________ ________ ________ 1 5.776 4.083 0.000 BETA SEVERITY NUTRIT GROUP ________ ________ ________ SEVERITY 0.000 0.000 0.000 NUTRIT 0.000 0.000 0.000 GROUP 0.000 0.000 0.000 PSI SEVERITY NUTRIT GROUP ________ ________ ________ SEVERITY 0.866 NUTRIT 0.000 0.668 GROUP 0.000 0.000 0.125 STARTING VALUES FOR THE ADDITIONAL PARAMETERS NEW/ADDITIONAL PARAMETERS INDIRECT ________ 1 0.500 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,infinity) 0.0000 infinity infinity Parameter 3~N(0.000,infinity) 0.0000 infinity infinity Parameter 4~N(0.000,infinity) 0.0000 infinity infinity Parameter 5~N(0.000,infinity) 0.0000 infinity infinity Parameter 6~IG(-1.000,0.000) infinity infinity infinity Parameter 7~IG(-1.000,0.000) infinity infinity infinity TECHNICAL 8 OUTPUT TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION CHAIN BSEED 1 0 2 285380 POTENTIAL PARAMETER WITH ITERATION SCALE REDUCTION HIGHEST PSR 100 1.037 2 PLOT INFORMATION The following plots are available: Bayesian posterior parameter distributions Bayesian posterior parameter trace plots Bayesian autocorrelation plots Bayesian posterior predictive checking scatterplots Bayesian posterior predictive checking distribution plots Beginning Time: 12:51:46 Ending Time: 12:51:46 Elapsed Time: 00:00:00 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) 1998-2010 Muthen & Muthen