Mplus VERSION 7.4
MUTHEN & MUTHEN
06/02/2016   6:18 AM

INPUT INSTRUCTIONS

  title:
      Selection modeling
      Muthen-Joreskog (1983), p. 146
      with data generated similar to Model 1, p. 158
      y missing if u=0

  montecarlo:
      names = y u x;
      nobs = 4000;
      nreps = 500;
      categorical = u; ! u = 1 if y observed
      generate = u(1 p);
      missing = y;

  model population:
      x@1;
      y on x*1;
      [y*0];
      y*1;

      f by y*-1 u@1;  ! gives residual corr = -0.5
      f@1;

      u on x*-1;

  analysis:
      estimator = mlr;
      link = probit;
      processors = 8;
      mconvergence = 0.00001;
      integration = 30;
  model:
      y on x*1;
      [y*0];
      y*1 (v);

      f by y*-1 (lam)
      u@1; ! gives -0.5 res. correlation
      f@1;

      u on x*-1 (slope);
      [u$1] (thresh);

  model missing:
      ! binary y = 1 denotes missing on continuous y
      ! logit regression for y with [y] denoting intercept
      [y@15]; ! probability one of missing on y if u = 0
      y on u@-30; ! probability zero of missing on y if u=1

  model constraint:
      new (rescorr*-.5 probint*0 probslop*-0.707107);
      rescorr = lam/(sqrt(lam*lam+v)*sqrt(1+1));
      probint = -thresh/sqrt(1+1);
      probslop = slope/sqrt(1+1);

  output:
       tech9;




INPUT READING TERMINATED NORMALLY




Selection modeling
Muthen-Joreskog (1983), p. 146
with data generated similar to Model 1, p. 158
y missing if u=0

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        4000

Number of replications
    Requested                                                  500
    Completed                                                  499
Value of seed                                                    0

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

Observed dependent variables

  Continuous
   Y

  Binary and ordered categorical (ordinal)
   U

Observed independent variables
   X

Continuous latent variables
   F


Estimator                                                      MLR
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-04
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
Maximum number of iterations for H1                           2000
Convergence criterion for H1                             0.100D-03
Optimization algorithm                                         EMA
Integration Specifications
  Type                                                    STANDARD
  Number of integration points                                  30
  Dimensions of numerical integration                            1
  Adaptive quadrature                                           ON
Link                                                        PROBIT
Cholesky                                                        ON


SUMMARY OF DATA FOR THE FIRST REPLICATION

     Number of missing data patterns             2
     Number of y missing data patterns           2
     Number of u missing data patterns           1


SUMMARY OF MISSING DATA PATTERNS FOR THE FIRST REPLICATION


     MISSING DATA PATTERNS FOR Y (x = not missing)

           1  2
 Y         x
 X         x  x


     MISSING DATA PATTERN FREQUENCIES FOR Y

    Pattern   Frequency     Pattern   Frequency
          1        1916           2        2084


COVARIANCE COVERAGE OF DATA FOR THE FIRST REPLICATION

Minimum covariance coverage value   0.100


     PROPORTION OF DATA PRESENT FOR Y


           Covariance Coverage
              Y             X
              ________      ________
 Y              0.479
 X              0.479         1.000


SAMPLE STATISTICS FOR THE FIRST REPLICATION


     ESTIMATED SAMPLE STATISTICS


           Means
              Y             X
              ________      ________
 1             -0.618         0.023


           Covariances
              Y             X
              ________      ________
 Y              2.313
 X              0.735         1.041


           Correlations
              Y             X
              ________      ________
 Y              1.000
 X              0.474         1.000


     MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -9035.653




MODEL FIT INFORMATION

Number of Free Parameters                        6

Loglikelihood

    H0 Value

        Mean                             -5678.191
        Std Dev                             65.682
        Number of successful computations      499

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.986        -5830.988      -5879.058
           0.980       0.978        -5813.083      -5819.083
           0.950       0.950        -5786.232      -5787.180
           0.900       0.908        -5762.370      -5761.261
           0.800       0.796        -5733.469      -5735.578
           0.700       0.703        -5712.635      -5712.537
           0.500       0.509        -5678.191      -5677.147
           0.300       0.303        -5643.748      -5643.563
           0.200       0.188        -5622.913      -5626.643
           0.100       0.092        -5594.013      -5598.251
           0.050       0.048        -5570.151      -5571.426
           0.020       0.016        -5543.300      -5549.972
           0.010       0.010        -5525.395      -5529.955

Information Criteria

    Akaike (AIC)

        Mean                             11368.383
        Std Dev                            131.364
        Number of successful computations      499

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.990        11062.791      11057.027
           0.980       0.984        11098.600      11103.231
           0.950       0.952        11152.302      11141.701
           0.900       0.908        11200.027      11205.712
           0.800       0.812        11257.827      11261.583
           0.700       0.697        11299.496      11295.978
           0.500       0.491        11368.383      11365.334
           0.300       0.297        11437.270      11434.447
           0.200       0.204        11478.939      11480.230
           0.100       0.092        11536.739      11531.103
           0.050       0.050        11584.464      11583.108
           0.020       0.022        11638.165      11642.066
           0.010       0.014        11673.975      11743.840

    Bayesian (BIC)

        Mean                             11406.147
        Std Dev                            131.364
        Number of successful computations      499

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.990        11100.555      11094.792
           0.980       0.984        11136.365      11140.995
           0.950       0.952        11190.066      11179.465
           0.900       0.908        11237.791      11243.476
           0.800       0.812        11295.591      11299.347
           0.700       0.697        11337.260      11333.742
           0.500       0.491        11406.147      11403.098
           0.300       0.297        11475.034      11472.211
           0.200       0.204        11516.703      11517.994
           0.100       0.092        11574.503      11568.868
           0.050       0.050        11622.228      11620.872
           0.020       0.022        11675.930      11679.830
           0.010       0.014        11711.739      11781.605

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

        Mean                             11387.082
        Std Dev                            131.364
        Number of successful computations      499

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.990        11081.490      11075.726
           0.980       0.984        11117.299      11121.930
           0.950       0.952        11171.001      11160.400
           0.900       0.908        11218.726      11224.411
           0.800       0.812        11276.526      11280.282
           0.700       0.697        11318.194      11314.677
           0.500       0.491        11387.082      11384.033
           0.300       0.297        11455.969      11453.146
           0.200       0.204        11497.638      11498.929
           0.100       0.092        11555.438      11549.802
           0.050       0.050        11603.163      11601.807
           0.020       0.022        11656.864      11660.765
           0.010       0.014        11692.674      11762.539



MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff
 F        BY
  Y                  -1.000    -0.9723     0.3049     0.2869     0.0935 0.908 0.858
  U                   1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

 Y          ON
  X                   1.000     0.9917     0.0894     0.0863     0.0081 0.924 0.992

 U          ON
  X                  -1.000    -1.0004     0.0355     0.0356     0.0013 0.942 1.000

 Intercepts
  Y                   0.000    -0.0150     0.1818     0.1724     0.0332 0.914 0.086

 Thresholds
  U$1                 0.000     0.0000     0.0296     0.0303     0.0009 0.952 0.048

 Variances
  F                   1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

 Residual Variances
  Y                   1.000     0.9738     0.3612     0.3670     0.1309 0.886 0.691

New/Additional Parameters
  RESCORR            -0.500    -0.4809     0.1406     0.1277     0.0201 0.906 0.874
  PROBINT             0.000     0.0000     0.0210     0.0215     0.0004 0.952 0.048
  PROBSLOP           -0.707    -0.7074     0.0251     0.0251     0.0006 0.942 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.257E-03
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION


           TAU
              U$1
              ________
 1                  6


           NU
              U             Y             X
              ________      ________      ________
 1                  0             0             0


           LAMBDA
              F             U             Y             X
              ________      ________      ________      ________
 U                  0             0             0             0
 Y                  0             0             0             0
 X                  0             0             0             0


           THETA
              U             Y             X
              ________      ________      ________
 U                  0
 Y                  0             0
 X                  0             0             0


           ALPHA
              F             U             Y             X
              ________      ________      ________      ________
 1                  0             0             1             0


           BETA
              F             U             Y             X
              ________      ________      ________      ________
 F                  0             0             0             0
 U                  0             0             0             2
 Y                  3             0             0             4
 X                  0             0             0             0


           PSI
              F             U             Y             X
              ________      ________      ________      ________
 F                  0
 U                  0             0
 Y                  0             0             5
 X                  0             0             0             0


     PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS


           NEW/ADDITIONAL PARAMETERS
              RESCORR       PROBINT       PROBSLOP
              ________      ________      ________
 1                  7             8             9


     STARTING VALUES


           TAU
              U$1
              ________
 1              0.000


           NU
              U             Y             X
              ________      ________      ________
 1              0.000         0.000         0.000


           LAMBDA
              F             U             Y             X
              ________      ________      ________      ________
 U              0.000         1.000         0.000         0.000
 Y              0.000         0.000         1.000         0.000
 X              0.000         0.000         0.000         1.000


           THETA
              U             Y             X
              ________      ________      ________
 U              0.000
 Y              0.000         0.000
 X              0.000         0.000         0.000


           ALPHA
              F             U             Y             X
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           BETA
              F             U             Y             X
              ________      ________      ________      ________
 F              0.000         0.000         0.000         0.000
 U              1.000         0.000         0.000        -1.000
 Y             -1.000         0.000         0.000         1.000
 X              0.000         0.000         0.000         0.000


           PSI
              F             U             Y             X
              ________      ________      ________      ________
 F              1.000
 U              0.000         1.000
 Y              0.000         0.000         1.000
 X              0.000         0.000         0.000         0.500


     STARTING VALUES FOR THE ADDITIONAL PARAMETERS


           NEW/ADDITIONAL PARAMETERS
              RESCORR       PROBINT       PROBSLOP
              ________      ________      ________
 1             -0.500         0.000        -0.707


     POPULATION VALUES


           TAU
              U$1
              ________
 1              0.000


           NU
              U             Y             X
              ________      ________      ________
 1              0.000         0.000         0.000


           LAMBDA
              F             U             Y             X
              ________      ________      ________      ________
 U              0.000         1.000         0.000         0.000
 Y              0.000         0.000         1.000         0.000
 X              0.000         0.000         0.000         1.000


           THETA
              U             Y             X
              ________      ________      ________
 U              0.000
 Y              0.000         0.000
 X              0.000         0.000         0.000


           ALPHA
              F             U             Y             X
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           BETA
              F             U             Y             X
              ________      ________      ________      ________
 F              0.000         0.000         0.000         0.000
 U              1.000         0.000         0.000        -1.000
 Y             -1.000         0.000         0.000         1.000
 X              0.000         0.000         0.000         0.000


           PSI
              F             U             Y             X
              ________      ________      ________      ________
 F              1.000
 U              0.000         0.000
 Y              0.000         0.000         1.000
 X              0.000         0.000         0.000         1.000


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)

     REPLICATION 334:
     THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO A NON-ZERO
     DERIVATIVE OF THE OBSERVED-DATA LOGLIKELIHOOD.

     THE MCONVERGENCE CRITERION OF THE EM ALGORITHM IS NOT FULFILLED.
     CHECK YOUR STARTING VALUES OR INCREASE THE NUMBER OF MITERATIONS.
     ESTIMATES CANNOT BE TRUSTED.  THE LOGLIKELIHOOD DERIVATIVE
     FOR THE FOLLOWING PARAMETER IS -0.24252797D-03:
     Parameter 5, Y (equality/label)



DIAGRAM INFORMATION

  Mplus diagrams are currently not available for Monte Carlo analysis.
  No diagram output was produced.


     Beginning Time:  06:18:12
        Ending Time:  06:29:12
       Elapsed Time:  00:11:00



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