Mplus VERSION 7.4
MUTHEN & MUTHEN
06/01/2016 7:53 AM
INPUT INSTRUCTIONS
title:
Yuan and MacKinnon firefighters
mediation using Bayesian analysis
Elliot DL, Goldberg L, Kuehl KS, et al.
The PHLAME Study: process and outcomes
of 2 models of behavior change.
J Occup Environ Med. 2007;49(2):204-213.
data:
file = fire.dat;
variable:
names = y m x;
model:
y on m (b)
x;
m on x (a);
analysis:
estimator = bayes;
process = 2;
biter = (20000);
model priors:
a~N(0.35,0.04);
b~N(0.1,0.01);
Model Indirect:
y IND x;
output:
sampstat tech1 tech8 cinterval;
plot:
type = plot3;
*** WARNING in OUTPUT command
SAMPSTAT option is not available for ESTIMATOR=BAYES. Use TYPE=BASIC.
Request for SAMPSTAT is ignored.
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
Yuan and MacKinnon firefighters
mediation using Bayesian analysis
Elliot DL, Goldberg L, Kuehl KS, et al.
The PHLAME Study: process and outcomes
of 2 models of behavior change.
J Occup Environ Med. 2007;49(2):204-213.
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 354
Number of dependent variables 2
Number of independent variables 1
Number of continuous latent variables 0
Observed dependent variables
Continuous
Y M
Observed independent variables
X
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)
fire.dat
Input data format FREE
THE MODEL ESTIMATION TERMINATED NORMALLY
USE THE FBITERATIONS OPTION TO INCREASE THE NUMBER OF ITERATIONS BY A FACTOR
OF AT LEAST TWO TO CHECK CONVERGENCE AND THAT THE PSR VALUE DOES NOT INCREASE.
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
-11.902 10.232
Posterior Predictive P-Value 0.529
Information Criteria
Deviance (DIC) 2129.393
Estimated Number of Parameters (pD) 6.564
Bayesian (BIC) 2157.308
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
Y ON
M 0.133 0.046 0.002 0.044 0.223 *
X 0.111 0.117 0.167 -0.117 0.343
M ON
X 0.386 0.103 0.000 0.185 0.588 *
Intercepts
Y 0.418 0.057 0.000 0.306 0.529 *
M 0.000 0.059 0.498 -0.114 0.114
Residual Variances
Y 1.141 0.087 0.000 0.989 1.328 *
M 1.217 0.093 0.000 1.053 1.419 *
TOTAL, TOTAL INDIRECT, SPECIFIC INDIRECT, AND DIRECT EFFECTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
Effects from X to Y
Total 0.163 0.117 0.081 -0.066 0.392
Total indirect 0.049 0.023 0.003 0.013 0.103 *
Specific indirect
Y
M
X 0.049 0.023 0.003 0.013 0.103 *
Direct
Y
X 0.111 0.117 0.167 -0.117 0.343
CREDIBILITY INTERVALS OF MODEL RESULTS
Lower .5% Lower 2.5% Lower 5% Estimate Upper 5% Upper 2.5% Upper .5%
Y ON
M 0.016 0.044 0.059 0.133 0.209 0.223 0.252
X -0.187 -0.117 -0.082 0.111 0.307 0.343 0.411
M ON
X 0.123 0.185 0.216 0.386 0.555 0.588 0.650
Intercepts
Y 0.274 0.306 0.324 0.418 0.512 0.529 0.566
M -0.152 -0.114 -0.097 0.000 0.095 0.114 0.153
Residual Variances
Y 0.948 0.989 1.012 1.141 1.297 1.328 1.397
M 1.006 1.053 1.079 1.217 1.383 1.419 1.494
CREDIBILITY INTERVALS OF TOTAL, TOTAL INDIRECT, SPECIFIC INDIRECT, AND DIRECT EFFECTS
Lower .5% Lower 2.5% Lower 5% Estimate Upper 5% Upper 2.5% Upper .5%
Effects from X to Y
Total -0.132 -0.066 -0.028 0.163 0.357 0.392 0.465
Total indirect 0.004 0.013 0.018 0.049 0.093 0.103 0.123
Specific indirect
Y
M
X 0.004 0.013 0.018 0.049 0.093 0.103 0.123
Direct
Y
X -0.187 -0.117 -0.082 0.111 0.307 0.343 0.411
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
NU
Y M X
________ ________ ________
1 0 0 0
LAMBDA
Y M X
________ ________ ________
Y 0 0 0
M 0 0 0
X 0 0 0
THETA
Y M X
________ ________ ________
Y 0
M 0 0
X 0 0 0
ALPHA
Y M X
________ ________ ________
1 1 2 0
BETA
Y M X
________ ________ ________
Y 0 3 4
M 0 0 5
X 0 0 0
PSI
Y M X
________ ________ ________
Y 6
M 0 7
X 0 0 0
STARTING VALUES
NU
Y M X
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
Y M X
________ ________ ________
Y 1.000 0.000 0.000
M 0.000 1.000 0.000
X 0.000 0.000 1.000
THETA
Y M X
________ ________ ________
Y 0.000
M 0.000 0.000
X 0.000 0.000 0.000
ALPHA
Y M X
________ ________ ________
1 0.418 0.000 0.000
BETA
Y M X
________ ________ ________
Y 0.000 0.000 0.000
M 0.000 0.000 0.000
X 0.000 0.000 0.000
PSI
Y M X
________ ________ ________
Y 0.578
M 0.000 0.620
X 0.000 0.000 0.121
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(0.100,0.010) 0.1000 0.0100 0.1000
Parameter 4~N(0.000,infinity) 0.0000 infinity infinity
Parameter 5~N(0.350,0.040) 0.3500 0.0400 0.2000
Parameter 6~IG(-1.000,0.000) infinity infinity infinity
Parameter 7~IG(-1.000,0.000) infinity infinity infinity
TECHNICAL 8 OUTPUT
Kolmogorov-Smirnov comparing posterior distributions across chains 1 and 2 using 100 draws.
Parameter KS Statistic P-value
Parameter 3 0.1500 0.1930
Parameter 4 0.1400 0.2606
Parameter 2 0.0600 0.9921
Parameter 6 0.0600 0.9921
Parameter 1 0.0500 0.9995
Parameter 5 0.0500 0.9995
Parameter 7 0.0300 1.0000
Simulated prior distributions
Parameter Prior Mean Prior Variance Prior Std. Dev.
Parameter 1 Improper Prior
Parameter 2 Improper Prior
Parameter 3 0.1052 0.0099 0.0996
Parameter 4 Improper Prior
Parameter 5 0.3489 0.0422 0.2053
Parameter 6 Improper Prior
Parameter 7 Improper Prior
TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION
CHAIN BSEED
1 0
2 285380
POTENTIAL PARAMETER WITH
ITERATION SCALE REDUCTION HIGHEST PSR
100 1.031 4
200 1.012 1
300 1.001 4
400 1.008 3
500 1.004 3
600 1.002 6
700 1.000 3
800 1.003 1
900 1.002 1
1000 1.002 1
1100 1.002 2
1200 1.003 2
1300 1.003 2
1400 1.003 1
1500 1.002 2
1600 1.002 6
1700 1.001 2
1800 1.001 6
1900 1.002 6
2000 1.002 6
2100 1.003 6
2200 1.003 6
2300 1.002 6
2400 1.002 6
2500 1.001 6
2600 1.001 5
2700 1.001 5
2800 1.000 5
2900 1.000 1
3000 1.000 1
3100 1.001 1
3200 1.001 1
3300 1.002 1
3400 1.001 1
3500 1.000 1
3600 1.001 1
3700 1.001 1
3800 1.000 1
3900 1.000 1
4000 1.000 1
4100 1.000 1
4200 1.000 1
4300 1.000 1
4400 1.000 1
4500 1.000 1
4600 1.000 1
4700 1.000 1
4800 1.001 2
4900 1.001 2
5000 1.001 4
5100 1.001 4
5200 1.001 1
5300 1.001 1
5400 1.001 4
5500 1.001 4
5600 1.001 4
5700 1.001 4
5800 1.001 4
5900 1.001 4
6000 1.001 4
6100 1.000 2
6200 1.000 1
6300 1.000 1
6400 1.000 1
6500 1.001 1
6600 1.000 1
6700 1.000 1
6800 1.000 1
6900 1.000 1
7000 1.000 1
7100 1.000 1
7200 1.000 1
7300 1.000 1
7400 1.000 1
7500 1.000 1
7600 1.000 1
7700 1.000 1
7800 1.000 1
7900 1.000 4
8000 1.000 4
8100 1.000 4
8200 1.000 4
8300 1.000 4
8400 1.000 2
8500 1.000 1
8600 1.000 2
8700 1.000 1
8800 1.000 1
8900 1.000 1
9000 1.000 1
9100 1.000 1
9200 1.000 1
9300 1.000 1
9400 1.000 1
9500 1.000 1
9600 1.000 1
9700 1.000 1
9800 1.000 1
9900 1.000 1
10000 1.000 1
10100 1.000 1
10200 1.000 1
10300 1.000 1
10400 1.000 7
10500 1.000 7
10600 1.000 7
10700 1.000 7
10800 1.000 7
10900 1.000 7
11000 1.000 7
11100 1.000 7
11200 1.000 7
11300 1.000 7
11400 1.000 7
11500 1.000 1
11600 1.000 3
11700 1.000 3
11800 1.000 7
11900 1.000 7
12000 1.000 3
12100 1.000 3
12200 1.000 7
12300 1.000 7
12400 1.000 7
12500 1.000 7
12600 1.000 3
12700 1.000 3
12800 1.000 3
12900 1.000 3
13000 1.000 3
13100 1.000 3
13200 1.000 1
13300 1.000 1
13400 1.000 3
13500 1.000 3
13600 1.000 3
13700 1.000 3
13800 1.000 3
13900 1.000 3
14000 1.000 3
14100 1.000 3
14200 1.000 3
14300 1.000 3
14400 1.000 3
14500 1.000 3
14600 1.000 3
14700 1.000 3
14800 1.000 3
14900 1.000 3
15000 1.000 3
15100 1.000 3
15200 1.000 3
15300 1.000 3
15400 1.000 3
15500 1.000 3
15600 1.000 3
15700 1.000 3
15800 1.000 3
15900 1.000 3
16000 1.000 3
16100 1.000 3
16200 1.000 3
16300 1.000 3
16400 1.000 3
16500 1.000 3
16600 1.000 3
16700 1.000 3
16800 1.000 3
16900 1.000 3
17000 1.000 3
17100 1.000 3
17200 1.000 3
17300 1.000 3
17400 1.000 3
17500 1.000 3
17600 1.000 3
17700 1.000 3
17800 1.000 3
17900 1.000 3
18000 1.000 3
18100 1.000 3
18200 1.000 3
18300 1.000 3
18400 1.000 3
18500 1.000 3
18600 1.000 3
18700 1.000 3
18800 1.000 3
18900 1.000 3
19000 1.000 3
19100 1.000 3
19200 1.000 3
19300 1.000 3
19400 1.000 7
19500 1.000 7
19600 1.000 3
19700 1.000 7
19800 1.000 7
19900 1.000 7
20000 1.000 3
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 prior parameter distributions
Bayesian posterior predictive checking scatterplots
Bayesian posterior predictive checking distribution plots
DIAGRAM INFORMATION
Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram.
If running Mplus from the Mplus Diagrammer, the diagram opens automatically.
Diagram output
c:\users\gryphon\desktop\chapter 9 bayes\9-11 7-9-15 fire bayes priors.dgm
Beginning Time: 07:53:52
Ending Time: 07:53:53
Elapsed Time: 00:00:01
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