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;
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
________ ________ ________ ________ ________
1.945 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
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