```Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  11:06 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;

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

SAMPLE STATISTICS FOR THE FIRST REPLICATION

SAMPLE STATISTICS

Means
Y1            Y2            Y3            Y4            X
________      ________      ________      ________      ________
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 CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES

Latent
Classes

1        500.00000          1.00000

FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
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
________      ________      ________      ________      ________
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
________      ________      ________
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
________
12

PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART

ALPHA(C)
C#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
________
0

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

STARTING VALUES FOR LATENT CLASS 1

NU
Y1            Y2            Y3            Y4            X
________      ________      ________      ________      ________
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
________      ________      ________
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
________
1.000

STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART

ALPHA(C)
C#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
________
0.000

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

POPULATION VALUES FOR LATENT CLASS 1

NU
Y1            Y2            Y3            Y4            X
________      ________      ________      ________      ________
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
________      ________      ________
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
________      ________      ________      ________      ________
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
________      ________      ________
1.000         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
________
1.000

TAU(U) FOR LATENT CLASS 2
U\$1
________
-1.000

POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART

ALPHA(C)
C#1           C#2
________      ________
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:  23:06:31
Ending Time:  23:06:31
Elapsed Time:  00:00:00

MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA  90066

Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
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Copyright (c) 1998-2022 Muthen & Muthen
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