Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010  11:28 PM

INPUT INSTRUCTIONS

  title: jasac.inp

  montecarlo:
      names are y1 y2 x;
      nobs = 2000;
      nreps = 500;
      seed = 578243;
      classes = c(2);
      genclasses = c(2);
      cutpoints = x(0);

  analysis:
      type = mixture;

  model montecarlo:
      %overall%
      [x@0]; x@1;

      i by y1-y2@1;
      s by y1@0 y2@1;
      [y1-y2@0 i*0 s*1];
      i*6.25; ! SD = 2.5
      s*1;
      !total s variance is 1.25 (1/5 of i variance),  SD = 1.12
      i with s*.699; !this gives correlation 0.25
      y1*2.083 y2*0.417; !this gives y1 and y2 r-square 0.75
      ! y1 variance = 8.333, SD = 2.89
      ! y2 variance = 9.135, SD = 3.052
      ! within-group y2 variance = 9.135 - 0.25 = 9.065, SD = 3.01

      s on x*1;
      !this gives ES = 0.33 in y2 within-group SD terms (for low class)
      !r-squared for s is 20%

      [c#1*0];

      %c#1% ! high class
      [i*2.5 s*2.25];
      !high class grows at 3/4 SD per grade
      s on x*.25;
      ! high class has 1/4 effect of low class, ES = 0.08


      %c#2% !low class
      [i*0.0 s*.75];
      !low class grows at 1/4 SD per grade
      !low class is lower by 1 SD for intercept,
      !about 1.5 SD lower for slope



  model:
      %overall%

      i by y1-y2@1;
      s by y1@0 y2@1;
      [y1-y2@0 i*0 s*1];
      i*6.25; ! SD = 2.5
      s@0; !misspecified
      !total s variance is 1.25 (1/5 of i variance),  SD = 1.12
      i with s@0; !misspecified
      y1*2.083 y2*0.417; !this gives y1 and y2 r-square 0.75
      ! y1 variance = 8.333, SD = 2.89
      ! y2 variance = 9.135, SD = 3.052
      ! within-group y2 variance = 9.135 - 0.25 = 9.065, SD = 3.01

      s on x*1;
      !this gives ES = 0.33 in y2 within-group SD terms (for low class)
      !r-squared for s is 20%

      [c#1*0];

      %c#1% ! high class
      [i*2.5 s*2.25];
      !high class grows at 3/4 SD per grade
      s on x*.25;
      ! high class has 1/4 effect of low class, ES = 0.08


      %c#2% !low class
      [i*0.0 s*.75];
      !low class grows at 1/4 SD per grade
      !low class is lower by 1 SD for intercept,
      !about 1.5 SD lower for slope

  output:
      tech9;



INPUT READING TERMINATED NORMALLY



jasac.inp

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        2000

Number of replications
    Requested                                                  500
    Completed                                                  500
Value of seed                                               578243

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

Observed dependent variables

  Continuous
   Y1          Y2

Observed independent variables
   X

Continuous latent variables
   I           S

Categorical latent variables
   C


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-06
    Relative loglikelihood change                        0.100D-06
    Derivative                                           0.100D-05
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-05
  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-05
  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
Optimization algorithm                                         EMA


SAMPLE STATISTICS FOR THE FIRST REPLICATION


     SAMPLE STATISTICS


           Means
              Y1            Y2            X
              ________      ________      ________
 1              1.189         3.033         0.497


           Covariances
              Y1            Y2            X
              ________      ________      ________
 Y1            10.112
 Y2             9.460        12.845
 X             -0.032         0.111         0.250


           Correlations
              Y1            Y2            X
              ________      ________      ________
 Y1             1.000
 Y2             0.830         1.000
 X             -0.020         0.062         1.000




TESTS OF MODEL FIT

Number of Free Parameters                       10

Loglikelihood

    H0 Value

        Mean                             -9296.290
        Std Dev                             43.757
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.996        -9398.083      -9395.713
           0.980       0.974        -9386.155      -9390.063
           0.950       0.944        -9368.267      -9372.902
           0.900       0.900        -9352.370      -9353.321
           0.800       0.794        -9333.117      -9334.188
           0.700       0.694        -9319.237      -9320.084
           0.500       0.510        -9296.290      -9295.160
           0.300       0.300        -9273.344      -9273.498
           0.200       0.214        -9259.464      -9258.510
           0.100       0.096        -9240.211      -9240.559
           0.050       0.052        -9224.314      -9224.168
           0.020       0.016        -9206.426      -9209.654
           0.010       0.010        -9194.497      -9198.116

Information Criteria

    Akaike (AIC)

        Mean                             18612.581
        Std Dev                             87.515
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.990        18408.995      18397.719
           0.980       0.984        18432.851      18437.372
           0.950       0.948        18468.627      18465.954
           0.900       0.904        18500.422      18500.769
           0.800       0.786        18538.928      18533.514
           0.700       0.700        18566.688      18566.375
           0.500       0.490        18612.581      18609.790
           0.300       0.306        18658.473      18658.822
           0.200       0.206        18686.233      18687.212
           0.100       0.100        18724.740      18723.781
           0.050       0.056        18756.534      18764.992
           0.020       0.026        18792.310      18795.835
           0.010       0.004        18816.166      18809.595

    Bayesian (BIC)

        Mean                             18668.590
        Std Dev                             87.515
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.990        18465.004      18453.728
           0.980       0.984        18488.860      18493.381
           0.950       0.948        18524.636      18521.963
           0.900       0.904        18556.431      18556.778
           0.800       0.786        18594.937      18589.523
           0.700       0.700        18622.697      18622.384
           0.500       0.490        18668.590      18665.799
           0.300       0.306        18714.482      18714.831
           0.200       0.206        18742.242      18743.221
           0.100       0.100        18780.749      18779.790
           0.050       0.056        18812.543      18821.001
           0.020       0.026        18848.319      18851.844
           0.010       0.004        18872.176      18865.604

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

        Mean                             18636.819
        Std Dev                             87.515
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.990        18433.233      18421.958
           0.980       0.984        18457.090      18461.611
           0.950       0.948        18492.866      18490.193
           0.900       0.904        18524.660      18525.008
           0.800       0.786        18563.167      18557.752
           0.700       0.700        18590.926      18590.614
           0.500       0.490        18636.819      18634.028
           0.300       0.306        18682.712      18683.060
           0.200       0.206        18710.472      18711.451
           0.100       0.100        18748.978      18748.019
           0.050       0.056        18780.772      18789.230
           0.020       0.026        18816.548      18820.073
           0.010       0.004        18840.405      18833.834



FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL

    Latent
   Classes

       1        996.02167          0.49801
       2       1003.97833          0.50199


FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES

    Latent
   Classes

       1        996.02166          0.49801
       2       1003.97834          0.50199


CLASSIFICATION QUALITY

     Entropy                         0.287


CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP

Class Counts and Proportions

    Latent
   Classes

       1              990          0.49511
       2             1010          0.50489


Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)

           1        2

    1   0.745    0.255
    2   0.255    0.745


MODEL RESULTS

                           ESTIMATES              S. E.     M. S. E.  95%  % Sig
              Population   Average   Std. Dev.   Average             Cover Coeff
Latent Class 1

 I        BY
  Y1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

 S        BY
  Y1               0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

 S          ON
  X                0.250     0.1598     0.4394     0.2816     0.2008 0.914 0.312

 I        WITH
  S                0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

 Means
  I                2.500     2.4208     0.5286     0.4725     0.2852 0.824 0.942

 Intercepts
  Y1               0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2               0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  S                2.250     2.3008     0.3900     0.3123     0.1544 0.878 0.984

 Variances
  I                6.250     7.1659     1.0393     0.9698     1.9170 0.788 0.988

 Residual Variances
  Y1               2.083     1.2453     0.3479     0.3401     0.8226 0.256 0.874
  Y2               0.417     2.1656     0.4721     0.4891     3.2799 0.094 0.952
  S                0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

Latent Class 2

 I        BY
  Y1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

 S        BY
  Y1               0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

 S          ON
  X                1.000     1.0897     0.4316     0.2961     0.1940 0.928 0.950

 I        WITH
  S                0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

 Means
  I                0.000     0.1082     0.5541     0.4819     0.3182 0.830 0.170

 Intercepts
  Y1               0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2               0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  S                0.750     0.7024     0.3462     0.3197     0.1219 0.892 0.696

 Variances
  I                6.250     7.1659     1.0393     0.9698     1.9170 0.788 0.988

 Residual Variances
  Y1               2.083     1.2453     0.3479     0.3401     0.8226 0.256 0.874
  Y2               0.417     2.1656     0.4721     0.4891     3.2799 0.094 0.952
  S                0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

Categorical Latent Variables

 Means
  C#1              0.000    -0.0079     0.6143     0.4992     0.3767 0.946 0.054


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.483E-02
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR LATENT CLASS 1


           NU
              Y1            Y2            X
              ________      ________      ________
 1                  0             0             0


           LAMBDA
              I             S             X
              ________      ________      ________
 Y1                 0             0             0
 Y2                 0             0             0
 X                  0             0             0


           THETA
              Y1            Y2            X
              ________      ________      ________
 Y1                 1
 Y2                 0             2
 X                  0             0             0


           ALPHA
              I             S             X
              ________      ________      ________
 1                  3             4             0


           BETA
              I             S             X
              ________      ________      ________
 I                  0             0             0
 S                  0             0             5
 X                  0             0             0


           PSI
              I             S             X
              ________      ________      ________
 I                  6
 S                  0             0
 X                  0             0             0


     PARAMETER SPECIFICATION FOR LATENT CLASS 2


           NU
              Y1            Y2            X
              ________      ________      ________
 1                  0             0             0


           LAMBDA
              I             S             X
              ________      ________      ________
 Y1                 0             0             0
 Y2                 0             0             0
 X                  0             0             0


           THETA
              Y1            Y2            X
              ________      ________      ________
 Y1                 1
 Y2                 0             2
 X                  0             0             0


           ALPHA
              I             S             X
              ________      ________      ________
 1                  7             8             0


           BETA
              I             S             X
              ________      ________      ________
 I                  0             0             0
 S                  0             0             9
 X                  0             0             0


           PSI
              I             S             X
              ________      ________      ________
 I                  6
 S                  0             0
 X                  0             0             0


     PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1           C#2
              ________      ________
 1                 10             0


           GAMMA(C)
              X
              ________
 C#1                0
 C#2                0


     STARTING VALUES FOR LATENT CLASS 1


           NU
              Y1            Y2            X
              ________      ________      ________
 1              0.000         0.000         0.000


           LAMBDA
              I             S             X
              ________      ________      ________
 Y1             1.000         0.000         0.000
 Y2             1.000         1.000         0.000
 X              0.000         0.000         1.000


           THETA
              Y1            Y2            X
              ________      ________      ________
 Y1             2.083
 Y2             0.000         0.417
 X              0.000         0.000         0.000


           ALPHA
              I             S             X
              ________      ________      ________
 1              2.500         2.250         0.000


           BETA
              I             S             X
              ________      ________      ________
 I              0.000         0.000         0.000
 S              0.000         0.000         0.250
 X              0.000         0.000         0.000


           PSI
              I             S             X
              ________      ________      ________
 I              6.250
 S              0.000         0.000
 X              0.000         0.000         0.500


     STARTING VALUES FOR LATENT CLASS 2


           NU
              Y1            Y2            X
              ________      ________      ________
 1              0.000         0.000         0.000


           LAMBDA
              I             S             X
              ________      ________      ________
 Y1             1.000         0.000         0.000
 Y2             1.000         1.000         0.000
 X              0.000         0.000         1.000


           THETA
              Y1            Y2            X
              ________      ________      ________
 Y1             2.083
 Y2             0.000         0.417
 X              0.000         0.000         0.000


           ALPHA
              I             S             X
              ________      ________      ________
 1              0.000         0.750         0.000


           BETA
              I             S             X
              ________      ________      ________
 I              0.000         0.000         0.000
 S              0.000         0.000         1.000
 X              0.000         0.000         0.000


           PSI
              I             S             X
              ________      ________      ________
 I              6.250
 S              0.000         0.000
 X              0.000         0.000         0.500


     STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1           C#2
              ________      ________
 1              0.000         0.000


           GAMMA(C)
              X
              ________
 C#1            0.000
 C#2            0.000


     POPULATION VALUES FOR LATENT CLASS 1


           NU
              Y1            Y2            X
              ________      ________      ________
 1              0.000         0.000         0.000


           LAMBDA
              I             S             X
              ________      ________      ________
 Y1             1.000         0.000         0.000
 Y2             1.000         1.000         0.000
 X              0.000         0.000         1.000


           THETA
              Y1            Y2            X
              ________      ________      ________
 Y1             2.083
 Y2             0.000         0.417
 X              0.000         0.000         0.000


           ALPHA
              I             S             X
              ________      ________      ________
 1              2.500         2.250         0.000


           BETA
              I             S             X
              ________      ________      ________
 I              0.000         0.000         0.000
 S              0.000         0.000         0.250
 X              0.000         0.000         0.000


           PSI
              I             S             X
              ________      ________      ________
 I              6.250
 S              0.699         1.000
 X              0.000         0.000         1.000


     POPULATION VALUES FOR LATENT CLASS 2


           NU
              Y1            Y2            X
              ________      ________      ________
 1              0.000         0.000         0.000


           LAMBDA
              I             S             X
              ________      ________      ________
 Y1             1.000         0.000         0.000
 Y2             1.000         1.000         0.000
 X              0.000         0.000         1.000


           THETA
              Y1            Y2            X
              ________      ________      ________
 Y1             2.083
 Y2             0.000         0.417
 X              0.000         0.000         0.000


           ALPHA
              I             S             X
              ________      ________      ________
 1              0.000         0.750         0.000


           BETA
              I             S             X
              ________      ________      ________
 I              0.000         0.000         0.000
 S              0.000         0.000         1.000
 X              0.000         0.000         0.000


           PSI
              I             S             X
              ________      ________      ________
 I              6.250
 S              0.699         1.000
 X              0.000         0.000         1.000


     POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1           C#2
              ________      ________
 1              0.000         0.000


           GAMMA(C)
              X
              ________
 C#1            0.000
 C#2            0.000


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)


     REPLICATION 154:
     WARNING:  THE RESIDUAL COVARIANCE MATRIX (THETA)  IN CLASS 1 IS NOT
     POSITIVE DEFINITE.  THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
     VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
     BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
     OBSERVED VARIABLES.  CHECK THE RESULTS SECTION FOR MORE INFORMATION.
     PROBLEM INVOLVING VARIABLE Y1.


     REPLICATION 154:
     WARNING:  THE RESIDUAL COVARIANCE MATRIX (THETA)  IN CLASS 2 IS NOT
     POSITIVE DEFINITE.  THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
     VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
     BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
     OBSERVED VARIABLES.  CHECK THE RESULTS SECTION FOR MORE INFORMATION.
     PROBLEM INVOLVING VARIABLE Y1.


     REPLICATION 350:
     WARNING:  THE RESIDUAL COVARIANCE MATRIX (THETA)  IN CLASS 1 IS NOT
     POSITIVE DEFINITE.  THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
     VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
     BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
     OBSERVED VARIABLES.  CHECK THE RESULTS SECTION FOR MORE INFORMATION.
     PROBLEM INVOLVING VARIABLE Y1.


     REPLICATION 350:
     WARNING:  THE RESIDUAL COVARIANCE MATRIX (THETA)  IN CLASS 2 IS NOT
     POSITIVE DEFINITE.  THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
     VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
     BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
     OBSERVED VARIABLES.  CHECK THE RESULTS SECTION FOR MORE INFORMATION.
     PROBLEM INVOLVING VARIABLE Y1.


     REPLICATION 490:
     WARNING:  THE RESIDUAL COVARIANCE MATRIX (THETA)  IN CLASS 1 IS NOT
     POSITIVE DEFINITE.  THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
     VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
     BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
     OBSERVED VARIABLES.  CHECK THE RESULTS SECTION FOR MORE INFORMATION.
     PROBLEM INVOLVING VARIABLE Y1.


     REPLICATION 490:
     WARNING:  THE RESIDUAL COVARIANCE MATRIX (THETA)  IN CLASS 2 IS NOT
     POSITIVE DEFINITE.  THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
     VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
     BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
     OBSERVED VARIABLES.  CHECK THE RESULTS SECTION FOR MORE INFORMATION.
     PROBLEM INVOLVING VARIABLE Y1.



     Beginning Time:  23:28:16
        Ending Time:  23:29:34
       Elapsed Time:  00:01:18



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