Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
TITLE:
this is an example of mixture modeling
with known classes (multiple group
analysis)
montecarlo:
names are y1-y4 g;
generate = g(1);
categorical = g;
genclasses = cg(2) c(2);
classes = cg(2) c(2);
nobs = 1000;
seed = 3454367;
nrep = 1;
save = ex7.21.dat;
ANALYSIS:
TYPE = MIXTURE;
MODEL POPULATION:
%OVERALL%
c#1 on cg#1*1;
MODEL POPULATION-c:
%c#1%
[y1-y4*-1];
%c#2%
[y1-y4*1];
MODEL POPULATION-cg:
%cg#1%
[g$1@15];
y1-y4*1;
%cg#2%
[g$1@-15];
y1-y4*.5;
MODEL:
%OVERALL%
c#1 on cg#1*1;
MODEL c:
%c#1%
[y1-y4*-1];
%c#2%
[y1-y4*1];
MODEL cg:
%cg#1%
[g$1@15];
y1-y4*1;
%cg#2%
[g$1@-15];
y1-y4*.5;
OUTPUT:
TECH8;
*** WARNING in MODEL command
All variables are uncorrelated with all other variables within class.
Check that this is what is intended.
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
this is an example of mixture modeling
with known classes (multiple group
analysis)
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of replications
Requested 1
Completed 1
Value of seed 3454367
Number of dependent variables 5
Number of independent variables 0
Number of continuous latent variables 0
Number of categorical latent variables 2
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4
Binary and ordered categorical (ordinal)
G
Categorical latent variables
CG 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
Parameterization LOGIT
Link LOGIT
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
Y1 Y2 Y3 Y4
________ ________ ________ ________
-0.239 -0.261 -0.262 -0.256
Covariances
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 1.628
Y2 0.821 1.542
Y3 0.869 0.868 1.689
Y4 0.851 0.901 0.933 1.704
Correlations
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 1.000
Y2 0.518 1.000
Y3 0.524 0.538 1.000
Y4 0.511 0.556 0.550 1.000
MODEL FIT INFORMATION
Number of Free Parameters 19
Loglikelihood
H0 Value
Mean -6273.830
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -6273.830 -6273.830
0.980 0.000 -6273.830 -6273.830
0.950 0.000 -6273.830 -6273.830
0.900 0.000 -6273.830 -6273.830
0.800 0.000 -6273.830 -6273.830
0.700 0.000 -6273.830 -6273.830
0.500 0.000 -6273.830 -6273.830
0.300 0.000 -6273.830 -6273.830
0.200 0.000 -6273.830 -6273.830
0.100 0.000 -6273.830 -6273.830
0.050 0.000 -6273.830 -6273.830
0.020 0.000 -6273.830 -6273.830
0.010 0.000 -6273.830 -6273.830
Information Criteria
Akaike (AIC)
Mean 12585.660
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 12585.660 12585.660
0.980 0.000 12585.660 12585.660
0.950 0.000 12585.660 12585.660
0.900 0.000 12585.660 12585.660
0.800 0.000 12585.660 12585.660
0.700 0.000 12585.660 12585.660
0.500 0.000 12585.660 12585.660
0.300 0.000 12585.660 12585.660
0.200 0.000 12585.660 12585.660
0.100 0.000 12585.660 12585.660
0.050 0.000 12585.660 12585.660
0.020 0.000 12585.660 12585.660
0.010 0.000 12585.660 12585.660
Bayesian (BIC)
Mean 12678.907
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 12678.907 12678.907
0.980 0.000 12678.907 12678.907
0.950 0.000 12678.907 12678.907
0.900 0.000 12678.907 12678.907
0.800 0.000 12678.907 12678.907
0.700 0.000 12678.907 12678.907
0.500 0.000 12678.907 12678.907
0.300 0.000 12678.907 12678.907
0.200 0.000 12678.907 12678.907
0.100 0.000 12678.907 12678.907
0.050 0.000 12678.907 12678.907
0.020 0.000 12678.907 12678.907
0.010 0.000 12678.907 12678.907
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 12618.562
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 12618.562 12618.562
0.980 0.000 12618.562 12618.562
0.950 0.000 12618.562 12618.562
0.900 0.000 12618.562 12618.562
0.800 0.000 12618.562 12618.562
0.700 0.000 12618.562 12618.562
0.500 0.000 12618.562 12618.562
0.300 0.000 12618.562 12618.562
0.200 0.000 12618.562 12618.562
0.100 0.000 12618.562 12618.562
0.050 0.000 12618.562 12618.562
0.020 0.000 12618.562 12618.562
0.010 0.000 12618.562 12618.562
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Mean 0.000
Std Dev 0.000
Degrees of freedom 0
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 0.000 0.000
0.980 0.000 0.000 0.000
0.950 0.000 0.000 0.000
0.900 0.000 0.000 0.000
0.800 0.000 0.000 0.000
0.700 0.000 0.000 0.000
0.500 0.000 0.000 0.000
0.300 0.000 0.000 0.000
0.200 0.000 0.000 0.000
0.100 0.000 0.000 0.000
0.050 0.000 0.000 0.000
0.020 0.000 0.000 0.000
0.010 0.000 0.000 0.000
Likelihood Ratio Chi-Square
Mean 0.000
Std Dev 0.000
Degrees of freedom 0
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 0.000 0.000
0.980 0.000 0.000 0.000
0.950 0.000 0.000 0.000
0.900 0.000 0.000 0.000
0.800 0.000 0.000 0.000
0.700 0.000 0.000 0.000
0.500 0.000 0.000 0.000
0.300 0.000 0.000 0.000
0.200 0.000 0.000 0.000
0.100 0.000 0.000 0.000
0.050 0.000 0.000 0.000
0.020 0.000 0.000 0.000
0.010 0.000 0.000 0.000
MODEL RESULTS USE THE LATENT CLASS VARIABLE ORDER
CG C
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON THE ESTIMATED MODEL
Latent Class
Pattern
1 1 386.99769 0.38700
1 2 126.00232 0.12600
2 1 235.02303 0.23502
2 2 251.97696 0.25198
FINAL CLASS COUNTS AND PROPORTIONS FOR EACH LATENT CLASS VARIABLE
BASED ON THE ESTIMATED MODEL
Latent Class
Variable Class
CG 1 513.00000 0.51300
2 487.00000 0.48700
C 1 622.02069 0.62202
2 377.97928 0.37798
LATENT TRANSITION PROBABILITIES BASED ON THE ESTIMATED MODEL
CG Classes (Rows) by C Classes (Columns)
1 2
1 0.754 0.246
2 0.483 0.517
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent Class
Pattern
1 1 386.99763 0.38700
1 2 126.00238 0.12600
2 1 235.02304 0.23502
2 2 251.97695 0.25198
FINAL CLASS COUNTS AND PROPORTIONS FOR EACH LATENT CLASS VARIABLE
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent Class
Variable Class
CG 1 513.00000 0.51300
2 487.00000 0.48700
C 1 622.02063 0.62202
2 377.97931 0.37798
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON THEIR MOST LIKELY LATENT CLASS PATTERN
Class Counts and Proportions
Latent Class
Pattern
1 1 387 0.38700
1 2 126 0.12600
2 1 235 0.23500
2 2 252 0.25200
FINAL CLASS COUNTS AND PROPORTIONS FOR EACH LATENT CLASS VARIABLE
BASED ON THEIR MOST LIKELY LATENT CLASS PATTERN
Latent Class
Variable Class
CG 1 513 0.51300
2 487 0.48700
C 1 622 0.62200
2 378 0.37800
CLASSIFICATION QUALITY
Entropy 0.980
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Parameters for Class-specific Model Parts of CG
Latent Class CG#1
Thresholds
G$1 15.000 15.0000 0.0000 0.0000 0.0000 1.000 0.000
Variances
Y1 1.000 1.0205 0.0000 0.0660 0.0004 1.000 1.000
Y2 1.000 0.9857 0.0000 0.0647 0.0002 1.000 1.000
Y3 1.000 0.9902 0.0000 0.0626 0.0001 1.000 1.000
Y4 1.000 1.0008 0.0000 0.0603 0.0000 1.000 1.000
Latent Class CG#2
Thresholds
G$1 -15.000 -15.0000 0.0000 0.0000 0.0000 1.000 0.000
Variances
Y1 0.500 0.5513 0.0000 0.0352 0.0026 1.000 1.000
Y2 0.500 0.4468 0.0000 0.0270 0.0028 0.000 1.000
Y3 0.500 0.5139 0.0000 0.0315 0.0002 1.000 1.000
Y4 0.500 0.4646 0.0000 0.0301 0.0013 1.000 1.000
Parameters for Class-specific Model Parts of C
Latent Class C#1
Means
Y1 -1.000 -0.9596 0.0000 0.0359 0.0016 1.000 1.000
Y2 -1.000 -0.9574 0.0000 0.0333 0.0018 1.000 1.000
Y3 -1.000 -1.0097 0.0000 0.0343 0.0001 1.000 1.000
Y4 -1.000 -1.0405 0.0000 0.0336 0.0016 1.000 1.000
Latent Class C#2
Means
Y1 1.000 0.9381 0.0000 0.0415 0.0038 1.000 1.000
Y2 1.000 0.9049 0.0000 0.0386 0.0090 0.000 1.000
Y3 1.000 0.9704 0.0000 0.0414 0.0009 1.000 1.000
Y4 1.000 1.0084 0.0000 0.0399 0.0001 1.000 1.000
Categorical Latent Variables
C#1 ON
CG#1 1.000 1.1918 0.0000 0.1402 0.0368 1.000 1.000
Means
CG#1 0.000 0.0520 0.0000 0.0633 0.0027 1.000 0.000
C#1 0.000 -0.0697 0.0000 0.0910 0.0049 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.345E-01
(ratio of smallest to largest eigenvalue)
C-SPECIFIC CLASSIFICATION RESULTS
Classification Quality for CG
Entropy 1.000
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 1.000 0.000
2 0.000 1.000
Classification Quality for C
Entropy 0.961
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.993 0.007
2 0.011 0.989
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS PATTERN 1 1
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
1 2 3 4
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 5
Y2 0 6
Y3 0 0 7
Y4 0 0 0 8
PARAMETER SPECIFICATION FOR LATENT CLASS PATTERN 1 2
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
9 10 11 12
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 5
Y2 0 6
Y3 0 0 7
Y4 0 0 0 8
PARAMETER SPECIFICATION FOR LATENT CLASS PATTERN 2 1
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
1 2 3 4
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 13
Y2 0 14
Y3 0 0 15
Y4 0 0 0 16
PARAMETER SPECIFICATION FOR LATENT CLASS PATTERN 2 2
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
9 10 11 12
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 13
Y2 0 14
Y3 0 0 15
Y4 0 0 0 16
PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS PATTERN 1 1
G$1
________
0
TAU(U) FOR LATENT CLASS PATTERN 1 2
G$1
________
0
TAU(U) FOR LATENT CLASS PATTERN 2 1
G$1
________
0
TAU(U) FOR LATENT CLASS PATTERN 2 2
G$1
________
0
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
CG#1 CG#2 C#1 C#2
________ ________ ________ ________
17 0 18 0
BETA(C)
CG#1 CG#2
________ ________
C#1 19 0
C#2 0 0
STARTING VALUES FOR LATENT CLASS PATTERN 1 1
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
-1.000 -1.000 -1.000 -1.000
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 1.000
Y2 0.000 1.000
Y3 0.000 0.000 1.000
Y4 0.000 0.000 0.000 1.000
STARTING VALUES FOR LATENT CLASS PATTERN 1 2
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
1.000 1.000 1.000 1.000
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 1.000
Y2 0.000 1.000
Y3 0.000 0.000 1.000
Y4 0.000 0.000 0.000 1.000
STARTING VALUES FOR LATENT CLASS PATTERN 2 1
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
-1.000 -1.000 -1.000 -1.000
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
STARTING VALUES FOR LATENT CLASS PATTERN 2 2
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
1.000 1.000 1.000 1.000
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
STARTING VALUES FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS PATTERN 1 1
G$1
________
15.000
TAU(U) FOR LATENT CLASS PATTERN 1 2
G$1
________
15.000
TAU(U) FOR LATENT CLASS PATTERN 2 1
G$1
________
-15.000
TAU(U) FOR LATENT CLASS PATTERN 2 2
G$1
________
-15.000
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
CG#1 CG#2 C#1 C#2
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA(C)
CG#1 CG#2
________ ________
C#1 1.000 0.000
C#2 0.000 0.000
POPULATION VALUES FOR LATENT CLASS PATTERN 1 1
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
-1.000 -1.000 -1.000 -1.000
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 1.000
Y2 0.000 1.000
Y3 0.000 0.000 1.000
Y4 0.000 0.000 0.000 1.000
POPULATION VALUES FOR LATENT CLASS PATTERN 1 2
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
1.000 1.000 1.000 1.000
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 1.000
Y2 0.000 1.000
Y3 0.000 0.000 1.000
Y4 0.000 0.000 0.000 1.000
POPULATION VALUES FOR LATENT CLASS PATTERN 2 1
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
-1.000 -1.000 -1.000 -1.000
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
POPULATION VALUES FOR LATENT CLASS PATTERN 2 2
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
1.000 1.000 1.000 1.000
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
POPULATION VALUES FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS PATTERN 1 1
G$1
________
15.000
TAU(U) FOR LATENT CLASS PATTERN 1 2
G$1
________
15.000
TAU(U) FOR LATENT CLASS PATTERN 2 1
G$1
________
-15.000
TAU(U) FOR LATENT CLASS PATTERN 2 2
G$1
________
-15.000
POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
CG#1 CG#2 C#1 C#2
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA(C)
CG#1 CG#2
________ ________
C#1 1.000 0.000
C#2 0.000 0.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.62849684D+04 0.0000000 0.0000000 EM
2 -0.62738425D+04 11.1259400 0.0017702 EM
3 -0.62738300D+04 0.0124337 0.0000020 EM
4 -0.62738299D+04 0.0001678 0.0000000 EM
5 -0.62738299D+04 0.0000028 0.0000000 EM
6 -0.62738299D+04 0.0000001 0.0000000 EM
SAVEDATA INFORMATION
Order of variables
G
Y1
Y2
Y3
Y4
CG
C
Save file
ex7.21.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:33
Ending Time: 22:24:33
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
Support: Support@StatModel.com
Copyright (c) 1998-2022 Muthen & Muthen
Back to examples