Mplus DEVELOPMENT (Mpdev 6/1/2016)
MUTHEN & MUTHEN
06/03/2016   7:21 AM

INPUT INSTRUCTIONS

  title:
      Simulating binary X, cont latent M, binary Y
      Step 2

  data:
      file = n200Perc20replist.dat;
      type = montecarlo;

  variable:
      names = y m1-m3 x;
      usev = y x sum;
      categorical = y;

  define:
      sum = sum(m1-m3);

  analysis:
      estimator = ml;
      link = probit;

  model:
      y on x*-.2
      sum*-.25;
      [y$1*.75];
      sum on x*.7; !R-square 0.10

  model indirect:
      y IND sum x;





INPUT READING TERMINATED NORMALLY




Simulating binary X, cont latent M, binary Y
Step 2

SUMMARY OF ANALYSIS

Number of groups                                                 1
Average number of observations                                 200

Number of replications
    Requested                                                  500
    Completed                                                  500

Number of dependent variables                                    2
Number of independent variables                                  1
Number of continuous latent variables                            0

Observed dependent variables

  Continuous
   SUM

  Binary and ordered categorical (ordinal)
   Y

Observed independent variables
   X


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                            10
  Minimum value for logit thresholds                           -10
  Minimum expected cell size for chi-square              0.100D-01
Optimization algorithm                                         EMA
Integration Specifications
  Type                                                    STANDARD
  Number of integration points                                  15
  Dimensions of numerical integration                            0
  Adaptive quadrature                                           ON
Link                                                        PROBIT
Cholesky                                                        ON

Input data file(s)
  Multiple data files from
    n200Perc20replist.dat
Input data format  FREE


UNIVARIATE PROPORTIONS FOR CATEGORICAL VARIABLES FOR THE FIRST REPLICATION

    Y
      Category 1    0.780
      Category 2    0.220


SAMPLE STATISTICS

NOTE:  These are average results over 500 data sets.


     SAMPLE STATISTICS


           Means
              SUM           X
              ________      ________
 1              1.047         0.500


           Covariances
              SUM           X
              ________      ________
 SUM           12.119
 X              0.526         0.249


           Correlations
              SUM           X
              ________      ________
 SUM            1.000
 X              0.303         1.000




MODEL FIT INFORMATION

Number of Free Parameters                        6

Loglikelihood

    H0 Value

        Mean                              -575.745
        Std Dev                             12.210
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.994         -604.149       -602.979
           0.980       0.980         -600.820       -601.081
           0.950       0.956         -595.829       -595.352
           0.900       0.894         -591.393       -591.866
           0.800       0.786         -586.021       -586.719
           0.700       0.700         -582.148       -582.378
           0.500       0.500         -575.745       -575.795
           0.300       0.306         -569.343       -569.221
           0.200       0.194         -565.470       -565.782
           0.100       0.096         -560.098       -560.393
           0.050       0.050         -555.662       -555.758
           0.020       0.020         -550.671       -551.170
           0.010       0.014         -547.342       -546.022

Information Criteria

    Akaike (AIC)

        Mean                              1163.491
        Std Dev                             24.419
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.986         1106.685       1104.020
           0.980       0.980         1113.341       1113.039
           0.950       0.950         1123.324       1122.505
           0.900       0.904         1132.195       1132.415
           0.800       0.806         1142.940       1143.463
           0.700       0.694         1150.685       1150.429
           0.500       0.500         1163.491       1163.419
           0.300       0.300         1176.296       1176.245
           0.200       0.214         1184.042       1185.074
           0.100       0.106         1194.786       1195.357
           0.050       0.044         1203.658       1202.687
           0.020       0.020         1213.640       1212.179
           0.010       0.006         1220.297       1217.582

    Bayesian (BIC)

        Mean                              1183.281
        Std Dev                             24.419
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.986         1126.474       1123.810
           0.980       0.980         1133.131       1132.829
           0.950       0.950         1143.114       1142.295
           0.900       0.904         1151.985       1152.205
           0.800       0.806         1162.730       1163.253
           0.700       0.694         1170.475       1170.219
           0.500       0.500         1183.281       1183.209
           0.300       0.300         1196.086       1196.035
           0.200       0.214         1203.832       1204.864
           0.100       0.106         1214.576       1215.147
           0.050       0.044         1223.448       1222.477
           0.020       0.020         1233.430       1231.968
           0.010       0.006         1240.087       1237.372

    Sample-Size Adjusted BIC (n* = (n + 2) / 24)

        Mean                              1164.272
        Std Dev                             24.419
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.986         1107.466       1104.802
           0.980       0.980         1114.122       1113.820
           0.950       0.950         1124.105       1123.286
           0.900       0.904         1132.977       1133.196
           0.800       0.806         1143.721       1144.245
           0.700       0.694         1151.467       1151.210
           0.500       0.500         1164.272       1164.200
           0.300       0.300         1177.078       1177.026
           0.200       0.214         1184.823       1185.855
           0.100       0.106         1195.568       1196.138
           0.050       0.044         1204.439       1203.468
           0.020       0.020         1214.422       1212.960
           0.010       0.006         1221.078       1218.364



MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff
 Y          ON
  X                  -0.200    -0.9320     0.3218     0.3083     0.6393 0.328 0.892
  SUM                -0.250    -0.4858     0.0794     0.0751     0.0619 0.022 1.000

 SUM        ON
  X                   0.700     2.1155     0.4715     0.4684     2.2256 0.148 0.996

 Intercepts
  SUM                 1.247    -0.0102     0.3305     0.3311     1.6900 0.034 0.064

 Thresholds
  Y$1                 0.750     0.5279     0.1918     0.1791     0.0860 0.712 0.870

 Residual Variances
  SUM                 0.500    10.9482     1.1407     1.0947   110.4639 0.000 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.155E-01
       (ratio of smallest to largest eigenvalue)


TOTAL, TOTAL INDIRECT, SPECIFIC INDIRECT, AND DIRECT EFFECTS FOR LATENT RESPONSE VARIABLES


                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff

Effects from X to Y

  Indirect           -0.175    -1.0299     0.2937     0.2796     0.8170 0.066 0.996
  Direct effect      -0.200    -0.9320     0.3218     0.3083     0.6393 0.328 0.892


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


                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff

Effects from X to Y

  Tot natural IE     -0.028    -0.1254     0.0353     0.0347     0.0106 0.140 0.994
  Pure natural DE    -0.041    -0.1689     0.0550     0.0534     0.0194 0.338 0.898
  Total effect       -0.069    -0.2943     0.0548     0.0543     0.0536 0.024 0.998

 Odds ratios for binary Y

  Tot natural IE      0.711     0.3798     0.0886     0.0875     0.1177 0.098 1.000
  Pure natural DE     0.691     0.4556     0.1296     0.1250     0.0720 0.506 0.996
  Total effect        0.491     0.1739     0.0673     0.0641     0.1052 0.048 0.978

 Other effects

  Pure natural IE    -0.036    -0.1829     0.0419     0.0421     0.0233 0.056 0.996
  Tot natural DE     -0.033    -0.1114     0.0375     0.0363     0.0075 0.422 0.888
  Total effect       -0.069    -0.2943     0.0548     0.0543     0.0536 0.024 0.998

 Odds ratios for other effects for binary Y

  Pure natural IE     0.724     0.4147     0.0869     0.0861     0.1032 0.128 1.000
  Tot natural DE      0.678     0.4196     0.1334     0.1287     0.0848 0.436 0.992
  Total effect        0.491     0.1739     0.0673     0.0641     0.1052 0.048 0.978


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION


           TAU
              Y$1
              ________
 1                  6


           NU
              Y             SUM           X
              ________      ________      ________
 1                  0             0             0


           LAMBDA
              Y             SUM           X
              ________      ________      ________
 Y                  0             0             0
 SUM                0             0             0
 X                  0             0             0


           THETA
              Y             SUM           X
              ________      ________      ________
 Y                  0
 SUM                0             0
 X                  0             0             0


           ALPHA
              Y             SUM           X
              ________      ________      ________
 1                  0             1             0


           BETA
              Y             SUM           X
              ________      ________      ________
 Y                  0             2             3
 SUM                0             0             4
 X                  0             0             0


           PSI
              Y             SUM           X
              ________      ________      ________
 Y                  0
 SUM                0             5
 X                  0             0             0


     STARTING VALUES


           TAU
              Y$1
              ________
 1              0.750


           NU
              Y             SUM           X
              ________      ________      ________
 1              0.000         0.000         0.000


           LAMBDA
              Y             SUM           X
              ________      ________      ________
 Y              1.000         0.000         0.000
 SUM            0.000         1.000         0.000
 X              0.000         0.000         1.000


           THETA
              Y             SUM           X
              ________      ________      ________
 Y              0.000
 SUM            0.000         0.000
 X              0.000         0.000         0.000


           ALPHA
              Y             SUM           X
              ________      ________      ________
 1              0.000         1.247         0.000


           BETA
              Y             SUM           X
              ________      ________      ________
 Y              0.000        -0.250        -0.200
 SUM            0.000         0.000         0.700
 X              0.000         0.000         0.000


           PSI
              Y             SUM           X
              ________      ________      ________
 Y              1.000
 SUM            0.000         0.500
 X              0.000         0.000         0.500


     Beginning Time:  07:21:58
        Ending Time:  07:22:08
       Elapsed Time:  00:00:10



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