Mplus VERSION 6.1 MUTHEN & MUTHEN 10/15/2010 12:54 PM INPUT INSTRUCTIONS title: Mediation using Bayesian analysis ATLAS data from MacKinnon et al. (2004), MBR Step 2: 10K data: file = mbr2004atlas.txt; variable: names = obs group severity nutrit; usev = group - nutrit; analysis: estimator = bayes; process = 2; fbiter = 10000; 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 2: 10K 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) Fixed number of iterations 10000 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 -10.941 10.274 Posterior Predictive P-Value 0.485 Information Criterion Deviance (DIC) 5605.395 Estimated Number of Parameters (pD) 7.035 MODEL RESULTS Posterior One-Tailed 95% C.I. Estimate S.D. P-Value Lower 2.5% Upper 2.5% SEVERITY ON GROUP 0.272 0.089 0.001 0.098 0.448 NUTRIT ON SEVERITY 0.074 0.030 0.008 0.014 0.133 GROUP -0.018 0.080 0.408 -0.177 0.140 Intercepts SEVERITY 5.648 0.062 0.000 5.525 5.768 NUTRIT 3.663 0.177 0.000 3.313 4.014 Residual Variances SEVERITY 1.719 0.083 0.000 1.566 1.895 NUTRIT 1.333 0.065 0.000 1.215 1.467 New/Additional Parameters INDIRECT 0.019 0.011 0.009 0.003 0.045 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 0.103 0.033 0.001 0.037 0.168 NUTRIT ON SEVERITY 0.084 0.034 0.008 0.016 0.151 GROUP -0.008 0.034 0.408 -0.075 0.061 Intercepts SEVERITY 4.282 0.118 0.000 4.049 4.510 NUTRIT 3.160 0.177 0.000 2.802 3.503 Residual Variances SEVERITY 0.989 0.007 0.000 0.972 0.999 NUTRIT 0.992 0.006 0.000 0.976 0.999 STDY Standardization Posterior One-Tailed 95% C.I. Estimate S.D. P-Value Lower 2.5% Upper 2.5% SEVERITY ON GROUP 0.103 0.033 0.001 0.037 0.168 NUTRIT ON SEVERITY 0.084 0.034 0.008 0.016 0.151 GROUP -0.008 0.034 0.408 -0.075 0.061 Intercepts SEVERITY 4.282 0.118 0.000 4.049 4.510 NUTRIT 3.160 0.177 0.000 2.802 3.503 Residual Variances SEVERITY 0.989 0.007 0.000 0.972 0.999 NUTRIT 0.992 0.006 0.000 0.976 0.999 STD Standardization Posterior One-Tailed 95% C.I. Estimate S.D. P-Value Lower 2.5% Upper 2.5% SEVERITY ON GROUP 0.272 0.089 0.001 0.098 0.448 NUTRIT ON SEVERITY 0.074 0.030 0.008 0.014 0.133 GROUP -0.018 0.080 0.408 -0.177 0.140 Intercepts SEVERITY 5.648 0.062 0.000 5.525 5.768 NUTRIT 3.663 0.177 0.000 3.313 4.014 Residual Variances SEVERITY 1.719 0.083 0.000 1.566 1.895 NUTRIT 1.333 0.065 0.000 1.215 1.467 R-SQUARE Posterior One-Tailed 95% C.I. Variable Estimate S.D. P-Value Lower 2.5% Upper 2.5% SEVERITY 0.011 0.007 0.000 0.001 0.028 NUTRIT 0.008 0.006 0.000 0.001 0.024 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 2 200 1.014 4 300 1.002 2 400 1.003 3 500 1.002 7 600 1.002 6 700 1.000 6 800 1.003 1 900 1.002 1 1000 1.002 1 1100 1.003 5 1200 1.004 5 1300 1.004 5 1400 1.004 1 1500 1.002 5 1600 1.000 5 1700 1.001 5 1800 1.000 6 1900 1.000 6 2000 1.000 3 2100 1.001 6 2200 1.002 6 2300 1.001 6 2400 1.002 6 2500 1.001 1 2600 1.000 6 2700 1.000 6 2800 1.000 6 2900 1.000 1 3000 1.000 1 3100 1.000 6 3200 1.001 1 3300 1.001 1 3400 1.001 1 3500 1.001 6 3600 1.001 1 3700 1.001 1 3800 1.001 6 3900 1.001 6 4000 1.001 6 4100 1.000 6 4200 1.000 6 4300 1.000 6 4400 1.000 6 4500 1.000 6 4600 1.001 6 4700 1.000 6 4800 1.000 6 4900 1.000 6 5000 1.001 6 5100 1.001 6 5200 1.000 1 5300 1.000 2 5400 1.000 2 5500 1.000 2 5600 1.000 2 5700 1.001 2 5800 1.001 2 5900 1.000 2 6000 1.000 2 6100 1.000 2 6200 1.000 5 6300 1.000 5 6400 1.000 5 6500 1.000 2 6600 1.000 2 6700 1.000 1 6800 1.000 1 6900 1.000 1 7000 1.000 2 7100 1.000 2 7200 1.000 1 7300 1.000 1 7400 1.000 1 7500 1.000 1 7600 1.000 1 7700 1.001 1 7800 1.001 1 7900 1.000 1 8000 1.000 1 8100 1.000 3 8200 1.000 3 8300 1.000 3 8400 1.000 3 8500 1.000 1 8600 1.000 1 8700 1.000 1 8800 1.000 1 8900 1.000 1 9000 1.000 1 9100 1.000 1 9200 1.000 7 9300 1.000 7 9400 1.000 7 9500 1.000 7 9600 1.000 7 9700 1.000 7 9800 1.000 7 9900 1.000 7 10000 1.000 7 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: 12:54:10 Ending Time: 12:54:11 Elapsed Time: 00:00:01 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