Mplus VERSION 7.4
MUTHEN & MUTHEN
06/02/2016   5:21 PM

INPUT INSTRUCTIONS

  title:
      Pearl (2011) artificial example for n=200

  data:
      file = n200expanded.txt;

  variable:
      names = y m x; !x: tx/ctrl, m: mediator, y: outcome
      categorical = y m;
      usev = y m x mx;

  define:
      mx=m*x;

  analysis:
      estimator = ml;
      bootstrap = 1000;


  model:
        y on m x mx;
        m on x;

  model indirect:
         y MOD m mx x;


  output:
      tech1 tech8 cinterval(bootstrap);

  plot:
      type = plot3;








INPUT READING TERMINATED NORMALLY




Pearl (2011) artificial example for n=200

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         200

Number of dependent variables                                    2
Number of independent variables                                  2
Number of continuous latent variables                            0

Observed dependent variables

  Binary and ordered categorical (ordinal)
   Y           M

Observed independent variables
   X           MX


Estimator                                                       ML
Information matrix                                        OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
  Maximum number of iterations                                 100
  Convergence criterion                                  0.100D-05
Optimization Specifications for the EM Algorithm
  Maximum number of iterations                                 500
  Convergence criteria
    Loglikelihood change                                 0.100D-02
    Relative loglikelihood change                        0.100D-05
    Derivative                                           0.100D-02
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
  Number of M step iterations                                    1
  M step convergence criterion                           0.100D-02
  Basis for M step termination                           ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
  Number of M step iterations                                    1
  M step convergence criterion                           0.100D-02
  Basis for M step termination                           ITERATION
  Maximum value for logit thresholds                            15
  Minimum value for logit thresholds                           -15
  Minimum expected cell size for chi-square              0.100D-01
Number of bootstrap draws
    Requested                                                 1000
    Completed                                                 1000
Optimization algorithm                                         EMA
Integration Specifications
  Type                                                    STANDARD
  Number of integration points                                  15
  Dimensions of numerical integration                            0
  Adaptive quadrature                                           ON
Link                                                         LOGIT
Cholesky                                                       OFF

Input data file(s)
  n200expanded.txt
Input data format  FREE


UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

    Y
      Category 1    0.500          100.000
      Category 2    0.500          100.000
    M
      Category 1    0.425           85.000
      Category 2    0.575          115.000



THE MODEL ESTIMATION TERMINATED NORMALLY



MODEL FIT INFORMATION

Number of Free Parameters                        6

Loglikelihood

          H0 Value                        -232.709

Information Criteria

          Akaike (AIC)                     477.418
          Bayesian (BIC)                   497.208
          Sample-Size Adjusted BIC         478.199
            (n* = (n + 2) / 24)



MODEL RESULTS

                                                    Two-Tailed
                    Estimate       S.E.  Est./S.E.    P-Value

 Y          ON
    M                  0.539      0.454      1.188      0.235
    X                  0.981      0.575      1.707      0.088
    MX                 1.253      0.753      1.664      0.096

 M          ON
    X                  1.568      0.309      5.066      0.000

 Thresholds
    Y$1                1.163      0.318      3.655      0.000
    M$1                0.382      0.200      1.908      0.056


LOGISTIC REGRESSION ODDS RATIO RESULTS

 Y          ON
    M                  1.714
    X                  2.667
    MX                 3.500

 M          ON
    X                  4.795



TOTAL, INDIRECT, AND DIRECT EFFECTS BASED ON COUNTERFACTUALS (CAUSALLY-DEFINED EFFECTS)


                                                    Two-Tailed
                    Estimate       S.E.  Est./S.E.    P-Value

Effects from X to Y

  Tot natural IE       0.136      0.050      2.716      0.007
  Pure natural DE      0.325      0.082      3.963      0.000
  Total effect         0.462      0.063      7.318      0.000

 Odds ratios for binary Y

  Tot natural IE       1.879      0.436      4.313      0.000
  Pure natural DE      3.933      1.784      2.205      0.027
  Total effect         7.389      2.782      2.656      0.008

 Other effects

  Pure natural IE      0.040      0.035      1.148      0.251
  Tot natural DE       0.422      0.072      5.843      0.000
  Total effect         0.462      0.063      7.318      0.000

 Odds ratios for other effects for binary Y

  Pure natural IE      1.208      0.199      6.074      0.000
  Tot natural DE       6.116      2.509      2.438      0.015
  Total effect         7.389      2.782      2.656      0.008


CONFIDENCE INTERVALS OF MODEL RESULTS

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

 Y        ON
    M               -0.584      -0.333      -0.202       0.539       1.300       1.459       1.749
    X               -0.470      -0.026       0.130       0.981       1.995       2.189       2.603
    MX              -0.843      -0.352      -0.045       1.253       2.454       2.702       3.134

 M        ON
    X                0.698       0.992       1.075       1.568       2.096       2.187       2.369

 Thresholds
    Y$1              0.433       0.610       0.693       1.163       1.705       1.833       2.065
    M$1             -0.103       0.000       0.056       0.382       0.722       0.783       0.924



CONFIDENCE INTERVALS OF TOTAL, INDIRECT, AND DIRECT EFFECTS BASED ON COUNTERFACTUALS (CAUSALLY-DEFINED EFFECTS)


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

Effects from X to Y

  Tot natural IE     0.023       0.046       0.061       0.136       0.216       0.241       0.285
  Pure natural DE    0.112       0.166       0.192       0.325       0.462       0.488       0.543
  Total effect       0.293       0.334       0.355       0.462       0.566       0.584       0.616

 Odds ratios for binary Y

  Tot natural IE     1.117       1.265       1.351       1.879       2.655       2.929       3.406
  Pure natural DE    1.589       1.966       2.213       3.933       7.593       8.735      11.504
  Total effect       3.382       4.048       4.457       7.389      13.272      14.885      18.378

 Other effects

  Pure natural IE   -0.049      -0.024      -0.014       0.040       0.097       0.112       0.146
  Tot natural DE     0.222       0.272       0.300       0.422       0.533       0.559       0.606
  Total effect       0.293       0.334       0.355       0.462       0.566       0.584       0.616

 Odds ratios for other effects for binary Y

  Pure natural IE    0.777       0.888       0.933       1.208       1.568       1.662       1.909
  Tot natural DE     2.476       3.129       3.549       6.116      11.117      13.050      16.806
  Total effect       3.382       4.048       4.457       7.389      13.272      14.885      18.378


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION


           TAU
              Y$1           M$1
              ________      ________
 1                  5             6


           NU
              Y             M             X             MX
              ________      ________      ________      ________
 1                  0             0             0             0


           LAMBDA
              Y             M             X             MX
              ________      ________      ________      ________
 Y                  0             0             0             0
 M                  0             0             0             0
 X                  0             0             0             0
 MX                 0             0             0             0


           THETA
              Y             M             X             MX
              ________      ________      ________      ________
 Y                  0
 M                  0             0
 X                  0             0             0
 MX                 0             0             0             0


           ALPHA
              Y             M             X             MX
              ________      ________      ________      ________
 1                  0             0             0             0


           BETA
              Y             M             X             MX
              ________      ________      ________      ________
 Y                  0             1             2             3
 M                  0             0             4             0
 X                  0             0             0             0
 MX                 0             0             0             0


           PSI
              Y             M             X             MX
              ________      ________      ________      ________
 Y                  0
 M                  0             0
 X                  0             0             0
 MX                 0             0             0             0


     STARTING VALUES


           TAU
              Y$1           M$1
              ________      ________
 1              0.000        -0.302


           NU
              Y             M             X             MX
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           LAMBDA
              Y             M             X             MX
              ________      ________      ________      ________
 Y              1.000         0.000         0.000         0.000
 M              0.000         1.000         0.000         0.000
 X              0.000         0.000         1.000         0.000
 MX             0.000         0.000         0.000         1.000


           THETA
              Y             M             X             MX
              ________      ________      ________      ________
 Y              0.000
 M              0.000         0.000
 X              0.000         0.000         0.000
 MX             0.000         0.000         0.000         0.000


           ALPHA
              Y             M             X             MX
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           BETA
              Y             M             X             MX
              ________      ________      ________      ________
 Y              0.000         0.000         0.000         0.000
 M              0.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         0.000
 MX             0.000         0.000         0.000         0.000


           PSI
              Y             M             X             MX
              ________      ________      ________      ________
 Y              1.000
 M              0.000         1.000
 X              0.000         0.000         0.125
 MX             0.000         0.000         0.000         0.115


TECHNICAL 8 OUTPUT


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.27500036D+03    0.0000000    0.0000000  EM
              2 -0.23328374D+03   41.7166201    0.1516966  EM
              3 -0.23271165D+03    0.5720894    0.0024523  EM
              4 -0.23270909D+03    0.0025598    0.0000110  EM
              5 -0.23270909D+03    0.0000001    0.0000000  EM


PLOT INFORMATION

The following plots are available:

  Histograms (sample values)
  Scatterplots (sample values)
  Sample proportions
  Bootstrap distributions

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\chapter8\ex8.31.dgm

     Beginning Time:  17:21:44
        Ending Time:  17:21:45
       Elapsed Time:  00:00:01



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