Mplus VERSION 7.4
MUTHEN & MUTHEN
10/17/2015   3:34 PM

INPUT INSTRUCTIONS

  title: Hayes PMI multiple mediators example

  data:
      file = pmi.txt;

  variable:
      names = cond pmi import reaction gender age;
      usev = reaction import pmi cond;

  analysis:
      estimator = Bayes;
      processors = 2;
      biter = (20000);

  model:
      reaction on import pmi cond;
      import on cond;
      pmi on cond;
      import with pmi;

  model indirect:
      reaction IND cond;

  output:
      tech1 tech8 cinterval;

  plot:
      type = plot3;



INPUT READING TERMINATED NORMALLY



Hayes PMI multiple mediators example

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         123

Number of dependent variables                                    3
Number of independent variables                                  1
Number of continuous latent variables                            0

Observed dependent variables

  Continuous
   REACTION    IMPORT      PMI

Observed independent variables
   COND


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)
  pmi.txt
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                              12

Bayesian Posterior Predictive Checking using Chi-Square

          95% Confidence Interval for the Difference Between
          the Observed and the Replicated Chi-Square Values

                                -13.196            14.524

          Posterior Predictive P-Value              0.478

Information Criteria

          Deviance (DIC)                         1315.474
          Estimated Number of Parameters (pD)      11.658
          Bayesian (BIC)                         1349.661



MODEL RESULTS

                                Posterior  One-Tailed         95% C.I.
                    Estimate       S.D.      P-Value   Lower 2.5%  Upper 2.5%  Significance

 REACTION   ON
    IMPORT             0.325       0.072      0.000       0.183       0.467      *
    PMI                0.397       0.094      0.000       0.210       0.582      *
    COND               0.102       0.242      0.334      -0.376       0.581

 IMPORT     ON
    COND               0.624       0.317      0.023       0.010       1.259      *

 PMI        ON
    COND               0.476       0.243      0.027      -0.006       0.954

 IMPORT   WITH
    PMI                0.597       0.227      0.002       0.190       1.081      *

 Intercepts
    REACTION          -0.157       0.535      0.382      -1.206       0.905
    IMPORT             3.907       0.218      0.000       3.480       4.333      *
    PMI                5.376       0.166      0.000       5.050       5.702      *

 Residual Variances
    REACTION           1.703       0.229      0.000       1.333       2.225      *
    IMPORT             3.065       0.409      0.000       2.400       3.988      *
    PMI                1.773       0.238      0.000       1.383       2.323      *


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 COND to REACTION

    Total              0.499       0.285      0.042      -0.066       1.055
    Total indirect     0.386       0.172      0.007       0.070       0.749      *

  Specific indirect

    REACTION
    IMPORT
    COND               0.194       0.115      0.023       0.003       0.458      *

    REACTION
    PMI
    COND               0.180       0.109      0.027      -0.002       0.429

  Direct
    REACTION
    COND               0.102       0.242      0.334      -0.376       0.581



CREDIBILITY INTERVALS OF MODEL RESULTS

                  Lower .5%  Lower 2.5%    Lower 5%    Estimate    Upper 5%  Upper 2.5%   Upper .5%

 REACTION ON
    IMPORT           0.140       0.183       0.206       0.325       0.445       0.467       0.510
    PMI              0.147       0.210       0.241       0.397       0.552       0.582       0.639
    COND            -0.518      -0.376      -0.294       0.102       0.501       0.581       0.748

 IMPORT   ON
    COND            -0.187       0.010       0.103       0.624       1.151       1.259       1.452

 PMI      ON
    COND            -0.153      -0.006       0.078       0.476       0.878       0.954       1.104

 IMPORT   WITH
    PMI              0.066       0.190       0.252       0.597       0.992       1.081       1.274

 Intercepts
    REACTION        -1.528      -1.206      -1.028      -0.157       0.730       0.905       1.247
    IMPORT           3.351       3.480       3.550       3.907       4.263       4.333       4.462
    PMI              4.952       5.050       5.104       5.376       5.653       5.702       5.802

 Residual Variances
    REACTION         1.234       1.333       1.385       1.703       2.128       2.225       2.439
    IMPORT           2.234       2.400       2.494       3.065       3.817       3.988       4.373
    PMI              1.289       1.383       1.437       1.773       2.218       2.323       2.502


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 COND to REACTION

  Total             -0.244      -0.066       0.025       0.499       0.967       1.055       1.230
  Total indirect    -0.023       0.070       0.122       0.386       0.686       0.749       0.880

  Specific indirect

    REACTION
    IMPORT
    COND            -0.060       0.003       0.031       0.194       0.408       0.458       0.562

    REACTION
    PMI
    COND            -0.062      -0.002       0.028       0.180       0.382       0.429       0.520

  Direct
    REACTION
    COND            -0.518      -0.376      -0.294       0.102       0.501       0.581       0.748



TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION


           NU
              REACTION      IMPORT        PMI           COND
              ________      ________      ________      ________
 1                  0             0             0             0


           LAMBDA
              REACTION      IMPORT        PMI           COND
              ________      ________      ________      ________
 REACTION           0             0             0             0
 IMPORT             0             0             0             0
 PMI                0             0             0             0
 COND               0             0             0             0


           THETA
              REACTION      IMPORT        PMI           COND
              ________      ________      ________      ________
 REACTION           0
 IMPORT             0             0
 PMI                0             0             0
 COND               0             0             0             0


           ALPHA
              REACTION      IMPORT        PMI           COND
              ________      ________      ________      ________
 1                  1             2             3             0


           BETA
              REACTION      IMPORT        PMI           COND
              ________      ________      ________      ________
 REACTION           0             4             5             6
 IMPORT             0             0             0             7
 PMI                0             0             0             8
 COND               0             0             0             0


           PSI
              REACTION      IMPORT        PMI           COND
              ________      ________      ________      ________
 REACTION           9
 IMPORT             0            10
 PMI                0            11            12
 COND               0             0             0             0


     STARTING VALUES


           NU
              REACTION      IMPORT        PMI           COND
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           LAMBDA
              REACTION      IMPORT        PMI           COND
              ________      ________      ________      ________
 REACTION       1.000         0.000         0.000         0.000
 IMPORT         0.000         1.000         0.000         0.000
 PMI            0.000         0.000         1.000         0.000
 COND           0.000         0.000         0.000         1.000


           THETA
              REACTION      IMPORT        PMI           COND
              ________      ________      ________      ________
 REACTION       0.000
 IMPORT         0.000         0.000
 PMI            0.000         0.000         0.000
 COND           0.000         0.000         0.000         0.000


           ALPHA
              REACTION      IMPORT        PMI           COND
              ________      ________      ________      ________
 1              3.484         4.203         5.602         0.000


           BETA
              REACTION      IMPORT        PMI           COND
              ________      ________      ________      ________
 REACTION       0.000         0.000         0.000         0.000
 IMPORT         0.000         0.000         0.000         0.000
 PMI            0.000         0.000         0.000         0.000
 COND           0.000         0.000         0.000         0.000


           PSI
              REACTION      IMPORT        PMI           COND
              ________      ________      ________      ________
 REACTION       1.192
 IMPORT         0.000         1.496
 PMI            0.000         0.000         0.866
 COND           0.000         0.000         0.000         0.125



     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~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 7~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 8~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 9~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 10~IW(0.000,-3)             infinity            infinity            infinity
     Parameter 11~IW(0.000,-3)             infinity            infinity            infinity
     Parameter 12~IW(0.000,-3)             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 11    0.1400    0.2606
     Parameter 7    0.1300    0.3439
     Parameter 1    0.1300    0.3439
     Parameter 9    0.1200    0.4431
     Parameter 3    0.0900    0.7942
     Parameter 10    0.0800    0.8938
     Parameter 12    0.0800    0.8938
     Parameter 6    0.0700    0.9610
     Parameter 4    0.0700    0.9610
     Parameter 8    0.0700    0.9610
     Parameter 2    0.0600    0.9921
     Parameter 5    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 Improper Prior
     Parameter 4 Improper Prior
     Parameter 5 Improper Prior
     Parameter 6 Improper Prior
     Parameter 7 Improper Prior
     Parameter 8 Improper Prior
     Parameter 9 Improper Prior
     Parameter 10 Improper Prior
     Parameter 11 Improper Prior
     Parameter 12 Improper Prior


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.010               8
     200              1.014               7
     300              1.008               10
     400              1.006               4
     500              1.009               4
     600              1.004               1
     700              1.002               1
     800              1.000               1
     900              1.000               1
     1000             1.002               12
     1100             1.002               12
     1200             1.003               12
     1300             1.001               12
     1400             1.002               12
     1500             1.001               12
     1600             1.002               6
     1700             1.001               2
     1800             1.001               2
     1900             1.000               7
     2000             1.000               7
     2100             1.001               9
     2200             1.002               9
     2300             1.002               9
     2400             1.001               5
     2500             1.002               9
     2600             1.001               9
     2700             1.001               9
     2800             1.001               9
     2900             1.001               9
     3000             1.001               9
     3100             1.000               9
     3200             1.001               9
     3300             1.001               9
     3400             1.002               9
     3500             1.001               9
     3600             1.001               9
     3700             1.000               6
     3800             1.000               12
     3900             1.000               12
     4000             1.000               12
     4100             1.000               12
     4200             1.000               1
     4300             1.000               1
     4400             1.000               2
     4500             1.000               2
     4600             1.000               2
     4700             1.000               7
     4800             1.000               4
     4900             1.000               4
     5000             1.000               7
     5100             1.000               7
     5200             1.000               8
     5300             1.000               8
     5400             1.001               4
     5500             1.000               4
     5600             1.000               8
     5700             1.001               8
     5800             1.001               8
     5900             1.001               8
     6000             1.001               8
     6100             1.001               8
     6200             1.001               8
     6300             1.001               8
     6400             1.001               4
     6500             1.000               4
     6600             1.001               4
     6700             1.000               4
     6800             1.001               4
     6900             1.000               4
     7000             1.001               4
     7100             1.001               4
     7200             1.001               4
     7300             1.001               4
     7400             1.001               4
     7500             1.001               4
     7600             1.000               4
     7700             1.000               4
     7800             1.000               4
     7900             1.000               4
     8000             1.000               4
     8100             1.000               2
     8200             1.000               4
     8300             1.000               4
     8400             1.000               4
     8500             1.000               4
     8600             1.000               4
     8700             1.000               4
     8800             1.000               4
     8900             1.000               4
     9000             1.000               4
     9100             1.000               4
     9200             1.000               4
     9300             1.000               4
     9400             1.000               10
     9500             1.000               10
     9600             1.000               10
     9700             1.000               10
     9800             1.000               9
     9900             1.000               10
     10000            1.000               10
     10100            1.000               10
     10200            1.000               10
     10300            1.000               10
     10400            1.000               10
     10500            1.000               10
     10600            1.000               10
     10700            1.000               10
     10800            1.000               4
     10900            1.000               4
     11000            1.000               4
     11100            1.000               4
     11200            1.000               4
     11300            1.001               4
     11400            1.000               4
     11500            1.000               4
     11600            1.000               10
     11700            1.000               4
     11800            1.000               10
     11900            1.000               10
     12000            1.000               10
     12100            1.000               10
     12200            1.000               4
     12300            1.000               4
     12400            1.000               8
     12500            1.000               10
     12600            1.000               10
     12700            1.000               10
     12800            1.000               10
     12900            1.000               10
     13000            1.000               4
     13100            1.000               10
     13200            1.000               10
     13300            1.000               10
     13400            1.000               10
     13500            1.000               10
     13600            1.000               10
     13700            1.000               10
     13800            1.000               8
     13900            1.000               10
     14000            1.000               8
     14100            1.000               8
     14200            1.000               8
     14300            1.000               8
     14400            1.000               8
     14500            1.000               8
     14600            1.000               8
     14700            1.000               4
     14800            1.000               4
     14900            1.000               7
     15000            1.000               5
     15100            1.000               7
     15200            1.000               7
     15300            1.000               2
     15400            1.000               5
     15500            1.000               5
     15600            1.000               5
     15700            1.000               5
     15800            1.000               5
     15900            1.000               5
     16000            1.000               5
     16100            1.000               5
     16200            1.000               5
     16300            1.000               5
     16400            1.000               5
     16500            1.000               5
     16600            1.000               5
     16700            1.000               5
     16800            1.000               9
     16900            1.000               8
     17000            1.000               10
     17100            1.000               8
     17200            1.000               8
     17300            1.000               8
     17400            1.000               6
     17500            1.000               6
     17600            1.000               6
     17700            1.000               6
     17800            1.000               6
     17900            1.000               6
     18000            1.000               6
     18100            1.000               6
     18200            1.000               6
     18300            1.000               6
     18400            1.000               6
     18500            1.000               6
     18600            1.000               6
     18700            1.000               10
     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               3
     19500            1.000               3
     19600            1.000               3
     19700            1.000               3
     19800            1.000               3
     19900            1.000               3
     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 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\bengt 2013\documents\bengt\mplus runs\a book - topic 1 mplus runs\path analysis\hayes p

     Beginning Time:  15:34:06
        Ending Time:  15:34:06
       Elapsed Time:  00:00:00



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