Mplus VERSION 7.2
MUTHEN & MUTHEN
05/07/2014   2:35 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a Monte Carlo
  	simulation study for a growth mixture
  	model with two classes and a misspecified
  	model
  MONTECARLO:
  	NAMES ARE u y1-y4 x;
  	NOBSERVATIONS = 500;
  	NREPS = 10;
  	SEED = 53487;
  	GENERATE = u (1);
  	CATEGORICAL = u;
  	GENCLASSES = c (2);
  	CLASSES = c (1);
  MODEL POPULATION:
  	%OVERALL%
  	[x@0];
  	x@1;
  	i s | y1@0 y2@1 y3@2 y4@3;
  	i*.25 s*.04;
  	i WITH s*0;
  	y1*.4 y2*.35 y3*.3 y4*.25;
  	i ON x*.5;
  	s ON x*.1;
  	c#1 ON x*.2;
  	[c#1*0];
  	%c#1%
  	[u$1*1 i*3 s*.5];
  	%c#2%
  	[u$1*-1 i*1 s*0];
  ANALYSIS:	TYPE = MIXTURE;
  MODEL:
  	%OVERALL%	
  	i s | y1@0 y2@1 y3@2 y4@3;
  	i*.25 s*.04;
  	i WITH s*0;
  	y1*.4 y2*.35 y3*.3 y4*.25;
  	i ON x*.5;
  	s ON x*.1;
  !	c#1 ON x*.2;
  !	[c#1*0];
  	u ON x;
  	%c#1%
  	[u$1*1 i*3 s*.5];
  !	%c#2%
  !	[u$1*-1 i*1 s*0];
  OUTPUT:	TECH9;



INPUT READING TERMINATED NORMALLY



this is an example of a Monte Carlo
simulation study for a growth mixture
model with two classes and a misspecified
model

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

Number of replications
    Requested                                                   10
    Completed                                                   10
Value of seed                                                53487

Number of dependent variables                                    5
Number of independent variables                                  1
Number of continuous latent variables                            2
Number of categorical latent variables                           1

Observed dependent variables

  Continuous
   Y1          Y2          Y3          Y4

  Binary and ordered categorical (ordinal)
   U

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
Link                                                         LOGIT


SAMPLE STATISTICS FOR THE FIRST REPLICATION


     SAMPLE STATISTICS


           Means
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 1              1.945         2.184         2.388         2.596        -0.015


           Covariances
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 Y1             1.980
 Y2             1.851         2.627
 Y3             2.138         2.678         3.438
 Y4             2.437         3.084         3.704         4.594
 X              0.594         0.683         0.763         0.849         1.019


           Correlations
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 Y1             1.000
 Y2             0.812         1.000
 Y3             0.819         0.891         1.000
 Y4             0.808         0.888         0.932         1.000
 X              0.418         0.417         0.408         0.393         1.000




MODEL FIT INFORMATION

Number of Free Parameters                       13

Loglikelihood

    H0 Value

        Mean                             -3000.035
        Std Dev                             26.893
        Number of successful computations       10

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000        -3062.597      -3049.797
           0.980       1.000        -3055.266      -3049.797
           0.950       0.900        -3044.272      -3049.797
           0.900       0.900        -3034.502      -3049.797
           0.800       0.900        -3022.669      -3049.797
           0.700       0.700        -3014.138      -3018.056
           0.500       0.500        -3000.035      -3008.520
           0.300       0.200        -2985.932      -2989.738
           0.200       0.200        -2977.402      -2986.111
           0.100       0.100        -2965.569      -2975.105
           0.050       0.100        -2955.798      -2975.105
           0.020       0.000        -2944.804      -2975.105
           0.010       0.000        -2937.473      -2975.105

Information Criteria

    Akaike (AIC)

        Mean                              6026.070
        Std Dev                             53.787
        Number of successful computations       10

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000         5900.946       5916.357
           0.980       1.000         5915.609       5916.357
           0.950       0.900         5937.597       5916.357
           0.900       0.900         5957.137       5916.357
           0.800       0.800         5980.803       5916.357
           0.700       0.800         5997.865       5998.222
           0.500       0.500         6026.070       6025.402
           0.300       0.300         6054.276       6045.819
           0.200       0.100         6071.337       6062.111
           0.100       0.100         6095.003       6062.471
           0.050       0.100         6114.544       6062.471
           0.020       0.000         6136.532       6062.471
           0.010       0.000         6151.194       6062.471

    Bayesian (BIC)

        Mean                              6080.860
        Std Dev                             53.787
        Number of successful computations       10

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000         5955.736       5971.146
           0.980       1.000         5970.399       5971.146
           0.950       0.900         5992.387       5971.146
           0.900       0.900         6011.927       5971.146
           0.800       0.800         6035.593       5971.146
           0.700       0.800         6052.655       6053.012
           0.500       0.500         6080.860       6080.192
           0.300       0.300         6109.066       6100.608
           0.200       0.100         6126.127       6116.901
           0.100       0.100         6149.793       6117.261
           0.050       0.100         6169.334       6117.261
           0.020       0.000         6191.322       6117.261
           0.010       0.000         6205.984       6117.261

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

        Mean                              6039.597
        Std Dev                             53.787
        Number of successful computations       10

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000         5914.474       5929.884
           0.980       1.000         5929.136       5929.884
           0.950       0.900         5951.124       5929.884
           0.900       0.900         5970.664       5929.884
           0.800       0.800         5994.331       5929.884
           0.700       0.800         6011.392       6011.749
           0.500       0.500         6039.597       6038.929
           0.300       0.300         6067.803       6059.346
           0.200       0.100         6084.864       6075.638
           0.100       0.100         6108.530       6075.998
           0.050       0.100         6128.071       6075.998
           0.020       0.000         6150.059       6075.998
           0.010       0.000         6164.721       6075.998



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

    Latent
   Classes

       1        500.00000          1.00000


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

    Latent
   Classes

       1        500.00000          1.00000


CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP

Class Counts and Proportions

    Latent
   Classes

       1              500          1.00000


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

           1

    1   1.000


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

           1

    1   1.000


Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)

              1

    1      0.000


MODEL RESULTS

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

 I        |
  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
  Y3                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y4                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

 S        |
  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
  Y3                  2.000     2.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y4                  3.000     3.0000     0.0000     0.0000     0.0000 1.000 0.000

 I          ON
  X                   0.500     0.6359     0.0441     0.0536     0.0202 0.300 1.000

 S          ON
  X                   0.100     0.1274     0.0245     0.0185     0.0013 0.700 1.000

 U          ON
  X                   0.000    -0.1568     0.1494     0.0907     0.0447 0.600 0.400

 I        WITH
  S                   0.000     0.2418     0.0185     0.0195     0.0588 0.000 1.000

 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
  Y3                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y4                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  I                   3.000     2.0350     0.0542     0.0550     0.9338 0.000 1.000
  S                   0.500     0.2445     0.0261     0.0181     0.0659 0.000 1.000

 Thresholds
  U$1                 1.000     0.0054     0.1075     0.0901     0.9997 0.000 0.000

 Residual Variances
  Y1                  0.400     0.4202     0.0443     0.0446     0.0022 1.000 1.000
  Y2                  0.350     0.3507     0.0252     0.0283     0.0006 1.000 1.000
  Y3                  0.300     0.3052     0.0406     0.0293     0.0015 0.900 1.000
  Y4                  0.250     0.2370     0.0483     0.0431     0.0023 0.900 1.000
  I                   0.250     1.2416     0.0722     0.0761     0.9881 0.000 1.000
  S                   0.040     0.1001     0.0148     0.0118     0.0038 0.000 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.343E-02
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR LATENT CLASS 1


           NU
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           LAMBDA
              I             S             X
              ________      ________      ________
 Y1                 0             0             0
 Y2                 0             0             0
 Y3                 0             0             0
 Y4                 0             0             0
 X                  0             0             0


           THETA
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 Y1                 1
 Y2                 0             2
 Y3                 0             0             3
 Y4                 0             0             0             4
 X                  0             0             0             0             0


           ALPHA
              I             S             X
              ________      ________      ________
 1                  5             6             0


           BETA
              I             S             X
              ________      ________      ________
 I                  0             0             7
 S                  0             0             8
 X                  0             0             0


           PSI
              I             S             X
              ________      ________      ________
 I                  9
 S                 10            11
 X                  0             0             0


     PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART


           TAU(U) FOR LATENT CLASS 1
              U$1
              ________
 1                 12


     PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1
              ________
 1                  0


           GAMMA(C)
              X
              ________
 C#1                0


     PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR GROWTH MODEL PART


           LAMBDA(F) FOR LATENT CLASS 1
              U
              ________
 U                  0


           ALPHA(F) FOR LATENT CLASS 1
              U
              ________
 1                  0


           GAMMA(F) FOR LATENT CLASS 1
              X
              ________
 U                 13


     STARTING VALUES FOR LATENT CLASS 1


           NU
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              I             S             X
              ________      ________      ________
 Y1             1.000         0.000         0.000
 Y2             1.000         1.000         0.000
 Y3             1.000         2.000         0.000
 Y4             1.000         3.000         0.000
 X              0.000         0.000         1.000


           THETA
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 Y1             0.400
 Y2             0.000         0.350
 Y3             0.000         0.000         0.300
 Y4             0.000         0.000         0.000         0.250
 X              0.000         0.000         0.000         0.000         0.000


           ALPHA
              I             S             X
              ________      ________      ________
 1              3.000         0.500         0.000


           BETA
              I             S             X
              ________      ________      ________
 I              0.000         0.000         0.500
 S              0.000         0.000         0.100
 X              0.000         0.000         0.000


           PSI
              I             S             X
              ________      ________      ________
 I              0.250
 S              0.000         0.040
 X              0.000         0.000         0.500


     STARTING VALUES FOR LATENT CLASS INDICATOR MODEL PART


           TAU(U) FOR LATENT CLASS 1
              U$1
              ________
 1              1.000


     STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1
              ________
 1              0.000


           GAMMA(C)
              X
              ________
 C#1            0.000


     STARTING VALUES FOR LATENT CLASS INDICATOR GROWTH MODEL PART


           LAMBDA(F) FOR CLASS LATENT CLASS 1
              U
              ________
 U              1.000


           ALPHA(F) FOR LATENT CLASS 1
              U
              ________
 1              0.000


           GAMMA(F) FOR LATENT CLASS 1
              X
              ________
 U              0.000


     POPULATION VALUES FOR LATENT CLASS 1


           NU
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              I             S             X
              ________      ________      ________
 Y1             1.000         0.000         0.000
 Y2             1.000         1.000         0.000
 Y3             1.000         2.000         0.000
 Y4             1.000         3.000         0.000
 X              0.000         0.000         1.000


           THETA
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 Y1             0.400
 Y2             0.000         0.350
 Y3             0.000         0.000         0.300
 Y4             0.000         0.000         0.000         0.250
 X              0.000         0.000         0.000         0.000         0.000


           ALPHA
              I             S             X
              ________      ________      ________
 1              3.000         0.500         0.000


           BETA
              I             S             X
              ________      ________      ________
 I              0.000         0.000         0.500
 S              0.000         0.000         0.100
 X              0.000         0.000         0.000


           PSI
              I             S             X
              ________      ________      ________
 I              0.250
 S              0.000         0.040
 X              0.000         0.000         1.000


     POPULATION VALUES FOR LATENT CLASS 2


           NU
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              I             S             X
              ________      ________      ________
 Y1             1.000         0.000         0.000
 Y2             1.000         1.000         0.000
 Y3             1.000         2.000         0.000
 Y4             1.000         3.000         0.000
 X              0.000         0.000         1.000


           THETA
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 Y1             0.400
 Y2             0.000         0.350
 Y3             0.000         0.000         0.300
 Y4             0.000         0.000         0.000         0.250
 X              0.000         0.000         0.000         0.000         0.000


           ALPHA
              I             S             X
              ________      ________      ________
 1              1.000         0.000         0.000


           BETA
              I             S             X
              ________      ________      ________
 I              0.000         0.000         0.500
 S              0.000         0.000         0.100
 X              0.000         0.000         0.000


           PSI
              I             S             X
              ________      ________      ________
 I              0.250
 S              0.000         0.040
 X              0.000         0.000         1.000


     POPULATION VALUES FOR LATENT CLASS INDICATOR MODEL PART


           TAU(U) FOR LATENT CLASS 1
              U$1
              ________
 1              1.000


           TAU(U) FOR LATENT CLASS 2
              U$1
              ________
 1             -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            0.200
 C#2            0.000


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



     Beginning Time:  14:35:46
        Ending Time:  14:35:46
       Elapsed Time:  00:00:00



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