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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