Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
title:
this is an example of a SEM mixture model
montecarlo:
names are y1-y6;
genclasses = c(2);
classes = c(2);
nobs = 1000;
seed = 3454367;
nrep = 1;
save = ex7.20.dat;
analysis:
type = mixture;
model population:
%overall%
y1-y6*.25;
f1 by y1@1 y2-y3*.75;
f2 by y4@1 y5-y6*.85;
[f1-f2@0];
f1-f2*1;
f2 on f1*.5;
[c#1*0];
%c#1%
[f1*1 f2*-2];
f2 on f1*-.5;
model:
%overall%
y1-y6*.25;
f1 by y1@1 y2-y3*.75;
f2 by y4@1 y5-y6*.85;
[f1-f2@0];
f1-f2*1;
f2 on f1*.5;
[c#1*0];
%c#1%
[f1*1 f2*-2];
f2 on f1*-.5;
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a SEM mixture model
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 6
Number of independent variables 0
Number of continuous latent variables 2
Number of categorical latent variables 1
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5 Y6
Continuous latent variables
F1 F2
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 Y5
________ ________ ________ ________ ________
0.447 0.312 0.324 -1.302 -1.080
Means
Y6
________
-1.111
Covariances
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.552
Y2 0.945 0.931
Y3 0.958 0.690 0.969
Y4 -0.611 -0.401 -0.453 2.785
Y5 -0.520 -0.355 -0.370 2.202 2.147
Y6 -0.548 -0.376 -0.411 2.199 1.906
Covariances
Y6
________
Y6 2.140
Correlations
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.786 1.000
Y3 0.781 0.726 1.000
Y4 -0.294 -0.249 -0.276 1.000
Y5 -0.285 -0.251 -0.257 0.900 1.000
Y6 -0.301 -0.266 -0.286 0.900 0.889
Correlations
Y6
________
Y6 1.000
MODEL FIT INFORMATION
Number of Free Parameters 23
Loglikelihood
H0 Value
Mean -7076.192
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -7076.192 -7076.192
0.980 0.000 -7076.192 -7076.192
0.950 0.000 -7076.192 -7076.192
0.900 0.000 -7076.192 -7076.192
0.800 0.000 -7076.192 -7076.192
0.700 0.000 -7076.192 -7076.192
0.500 0.000 -7076.192 -7076.192
0.300 0.000 -7076.192 -7076.192
0.200 0.000 -7076.192 -7076.192
0.100 0.000 -7076.192 -7076.192
0.050 0.000 -7076.192 -7076.192
0.020 0.000 -7076.192 -7076.192
0.010 0.000 -7076.192 -7076.192
Information Criteria
Akaike (AIC)
Mean 14198.384
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 14198.384 14198.384
0.980 0.000 14198.384 14198.384
0.950 0.000 14198.384 14198.384
0.900 0.000 14198.384 14198.384
0.800 0.000 14198.384 14198.384
0.700 0.000 14198.384 14198.384
0.500 0.000 14198.384 14198.384
0.300 0.000 14198.384 14198.384
0.200 0.000 14198.384 14198.384
0.100 0.000 14198.384 14198.384
0.050 0.000 14198.384 14198.384
0.020 0.000 14198.384 14198.384
0.010 0.000 14198.384 14198.384
Bayesian (BIC)
Mean 14311.263
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 14311.263 14311.263
0.980 0.000 14311.263 14311.263
0.950 0.000 14311.263 14311.263
0.900 0.000 14311.263 14311.263
0.800 0.000 14311.263 14311.263
0.700 0.000 14311.263 14311.263
0.500 0.000 14311.263 14311.263
0.300 0.000 14311.263 14311.263
0.200 0.000 14311.263 14311.263
0.100 0.000 14311.263 14311.263
0.050 0.000 14311.263 14311.263
0.020 0.000 14311.263 14311.263
0.010 0.000 14311.263 14311.263
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 14238.213
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 14238.213 14238.213
0.980 0.000 14238.213 14238.213
0.950 0.000 14238.213 14238.213
0.900 0.000 14238.213 14238.213
0.800 0.000 14238.213 14238.213
0.700 0.000 14238.213 14238.213
0.500 0.000 14238.213 14238.213
0.300 0.000 14238.213 14238.213
0.200 0.000 14238.213 14238.213
0.100 0.000 14238.213 14238.213
0.050 0.000 14238.213 14238.213
0.020 0.000 14238.213 14238.213
0.010 0.000 14238.213 14238.213
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 516.55535 0.51656
2 483.44465 0.48344
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 516.55535 0.51656
2 483.44465 0.48344
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 493 0.49300
2 507 0.50700
CLASSIFICATION QUALITY
Entropy 0.587
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.899 0.101
2 0.144 0.856
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.858 0.142
2 0.103 0.897
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 1.801 0.000
2 -2.167 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Latent Class 1
F1 BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 0.750 0.7194 0.0000 0.0198 0.0009 1.000 1.000
Y3 0.750 0.7291 0.0000 0.0206 0.0004 1.000 1.000
F2 BY
Y4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y5 0.850 0.8657 0.0000 0.0143 0.0002 1.000 1.000
Y6 0.850 0.8654 0.0000 0.0129 0.0002 1.000 1.000
F2 ON
F1 -0.500 -0.4841 0.0000 0.0672 0.0003 1.000 1.000
Means
F1 1.000 0.9435 0.0000 0.1164 0.0032 1.000 1.000
Intercepts
Y1 0.000 -0.0405 0.0000 0.0623 0.0016 1.000 0.000
Y2 0.000 -0.0390 0.0000 0.0463 0.0015 1.000 0.000
Y3 0.000 -0.0312 0.0000 0.0473 0.0010 1.000 0.000
Y4 0.000 -0.0919 0.0000 0.0775 0.0084 1.000 0.000
Y5 0.000 -0.0324 0.0000 0.0677 0.0011 1.000 0.000
Y6 0.000 -0.0637 0.0000 0.0679 0.0041 1.000 0.000
F2 -2.000 -1.8857 0.0000 0.1250 0.0131 1.000 1.000
Variances
F1 1.000 1.0918 0.0000 0.0709 0.0084 1.000 1.000
Residual Variances
Y1 0.250 0.2375 0.0000 0.0227 0.0002 1.000 1.000
Y2 0.250 0.2512 0.0000 0.0155 0.0000 1.000 1.000
Y3 0.250 0.2705 0.0000 0.0177 0.0004 1.000 1.000
Y4 0.250 0.2429 0.0000 0.0186 0.0001 1.000 1.000
Y5 0.250 0.2418 0.0000 0.0159 0.0001 1.000 1.000
Y6 0.250 0.2364 0.0000 0.0155 0.0002 1.000 1.000
F2 1.000 0.9589 0.0000 0.0648 0.0017 1.000 1.000
Latent Class 2
F1 BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 0.750 0.7194 0.0000 0.0198 0.0009 1.000 1.000
Y3 0.750 0.7291 0.0000 0.0206 0.0004 1.000 1.000
F2 BY
Y4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y5 0.850 0.8657 0.0000 0.0143 0.0002 1.000 1.000
Y6 0.850 0.8654 0.0000 0.0129 0.0002 1.000 1.000
F2 ON
F1 0.500 0.3941 0.0000 0.0545 0.0112 1.000 1.000
Means
F1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Intercepts
Y1 0.000 -0.0405 0.0000 0.0623 0.0016 1.000 0.000
Y2 0.000 -0.0390 0.0000 0.0463 0.0015 1.000 0.000
Y3 0.000 -0.0312 0.0000 0.0473 0.0010 1.000 0.000
Y4 0.000 -0.0919 0.0000 0.0775 0.0084 1.000 0.000
Y5 0.000 -0.0324 0.0000 0.0677 0.0011 1.000 0.000
Y6 0.000 -0.0637 0.0000 0.0679 0.0041 1.000 0.000
F2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Variances
F1 1.000 1.0918 0.0000 0.0709 0.0084 1.000 1.000
Residual Variances
Y1 0.250 0.2375 0.0000 0.0227 0.0002 1.000 1.000
Y2 0.250 0.2512 0.0000 0.0155 0.0000 1.000 1.000
Y3 0.250 0.2705 0.0000 0.0177 0.0004 1.000 1.000
Y4 0.250 0.2429 0.0000 0.0186 0.0001 1.000 1.000
Y5 0.250 0.2418 0.0000 0.0159 0.0001 1.000 1.000
Y6 0.250 0.2364 0.0000 0.0155 0.0002 1.000 1.000
F2 1.000 0.9589 0.0000 0.0648 0.0017 1.000 1.000
Categorical Latent Variables
Means
C#1 0.000 0.0662 0.0000 0.1236 0.0044 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.118E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
NU
Y6
________
6
LAMBDA
F1 F2
________ ________
Y1 0 0
Y2 7 0
Y3 8 0
Y4 0 0
Y5 0 9
Y6 0 10
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 11
Y2 0 12
Y3 0 0 13
Y4 0 0 0 14
Y5 0 0 0 0 15
Y6 0 0 0 0 0
THETA
Y6
________
Y6 16
ALPHA
F1 F2
________ ________
17 18
BETA
F1 F2
________ ________
F1 0 0
F2 19 0
PSI
F1 F2
________ ________
F1 20
F2 0 21
PARAMETER SPECIFICATION FOR LATENT CLASS 2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
NU
Y6
________
6
LAMBDA
F1 F2
________ ________
Y1 0 0
Y2 7 0
Y3 8 0
Y4 0 0
Y5 0 9
Y6 0 10
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 11
Y2 0 12
Y3 0 0 13
Y4 0 0 0 14
Y5 0 0 0 0 15
Y6 0 0 0 0 0
THETA
Y6
________
Y6 16
ALPHA
F1 F2
________ ________
0 0
BETA
F1 F2
________ ________
F1 0 0
F2 22 0
PSI
F1 F2
________ ________
F1 20
F2 0 21
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
23 0
STARTING VALUES FOR LATENT CLASS 1
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y6
________
0.000
LAMBDA
F1 F2
________ ________
Y1 1.000 0.000
Y2 0.750 0.000
Y3 0.750 0.000
Y4 0.000 1.000
Y5 0.000 0.850
Y6 0.000 0.850
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.250
Y2 0.000 0.250
Y3 0.000 0.000 0.250
Y4 0.000 0.000 0.000 0.250
Y5 0.000 0.000 0.000 0.000 0.250
Y6 0.000 0.000 0.000 0.000 0.000
THETA
Y6
________
Y6 0.250
ALPHA
F1 F2
________ ________
1.000 -2.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 -0.500 0.000
PSI
F1 F2
________ ________
F1 1.000
F2 0.000 1.000
STARTING VALUES FOR LATENT CLASS 2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y6
________
0.000
LAMBDA
F1 F2
________ ________
Y1 1.000 0.000
Y2 0.750 0.000
Y3 0.750 0.000
Y4 0.000 1.000
Y5 0.000 0.850
Y6 0.000 0.850
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.250
Y2 0.000 0.250
Y3 0.000 0.000 0.250
Y4 0.000 0.000 0.000 0.250
Y5 0.000 0.000 0.000 0.000 0.250
Y6 0.000 0.000 0.000 0.000 0.000
THETA
Y6
________
Y6 0.250
ALPHA
F1 F2
________ ________
0.000 0.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 0.500 0.000
PSI
F1 F2
________ ________
F1 1.000
F2 0.000 1.000
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
0.000 0.000
POPULATION VALUES FOR LATENT CLASS 1
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y6
________
0.000
LAMBDA
F1 F2
________ ________
Y1 1.000 0.000
Y2 0.750 0.000
Y3 0.750 0.000
Y4 0.000 1.000
Y5 0.000 0.850
Y6 0.000 0.850
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.250
Y2 0.000 0.250
Y3 0.000 0.000 0.250
Y4 0.000 0.000 0.000 0.250
Y5 0.000 0.000 0.000 0.000 0.250
Y6 0.000 0.000 0.000 0.000 0.000
THETA
Y6
________
Y6 0.250
ALPHA
F1 F2
________ ________
1.000 -2.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 -0.500 0.000
PSI
F1 F2
________ ________
F1 1.000
F2 0.000 1.000
POPULATION VALUES FOR LATENT CLASS 2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y6
________
0.000
LAMBDA
F1 F2
________ ________
Y1 1.000 0.000
Y2 0.750 0.000
Y3 0.750 0.000
Y4 0.000 1.000
Y5 0.000 0.850
Y6 0.000 0.850
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.250
Y2 0.000 0.250
Y3 0.000 0.000 0.250
Y4 0.000 0.000 0.000 0.250
Y5 0.000 0.000 0.000 0.000 0.250
Y6 0.000 0.000 0.000 0.000 0.000
THETA
Y6
________
Y6 0.250
ALPHA
F1 F2
________ ________
0.000 0.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 0.500 0.000
PSI
F1 F2
________ ________
F1 1.000
F2 0.000 1.000
POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 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 -0.70866512D+04 0.0000000 0.0000000 EM
2 -0.70765515D+04 10.0997349 0.0014252 EM
3 -0.70763580D+04 0.1934084 0.0000273 EM
4 -0.70762868D+04 0.0712578 0.0000101 EM
5 -0.70762547D+04 0.0320500 0.0000045 EM
6 -0.70762374D+04 0.0173182 0.0000024 EM
7 -0.70762265D+04 0.0109595 0.0000015 EM
8 -0.70762188D+04 0.0077107 0.0000011 EM
9 -0.70762130D+04 0.0057546 0.0000008 EM
10 -0.70762086D+04 0.0044236 0.0000006 EM
11 -0.70762051D+04 0.0034495 0.0000005 EM
12 -0.70762024D+04 0.0027088 0.0000004 EM
13 -0.70762003D+04 0.0021346 0.0000003 EM
14 -0.70761986D+04 0.0016854 0.0000002 EM
15 -0.70761973D+04 0.0013321 0.0000002 EM
16 -0.70761962D+04 0.0010537 0.0000001 EM
17 -0.70761954D+04 0.0008339 0.0000001 EM
18 -0.70761947D+04 0.0006601 0.0000001 EM
19 -0.70761942D+04 0.0005228 0.0000001 EM
20 -0.70761938D+04 0.0004141 0.0000001 EM
21 -0.70761934D+04 0.0003281 0.0000000 EM
22 -0.70761932D+04 0.0002600 0.0000000 EM
23 -0.70761930D+04 0.0002060 0.0000000 EM
24 -0.70761928D+04 0.0001633 0.0000000 EM
25 -0.70761927D+04 0.0001294 0.0000000 EM
26 -0.70761926D+04 0.0001026 0.0000000 EM
27 -0.70761925D+04 0.0000814 0.0000000 EM
28 -0.70761924D+04 0.0000645 0.0000000 EM
29 -0.70761924D+04 0.0000512 0.0000000 EM
30 -0.70761924D+04 0.0000406 0.0000000 EM
31 -0.70761923D+04 0.0000322 0.0000000 EM
32 -0.70761923D+04 0.0000255 0.0000000 EM
33 -0.70761923D+04 0.0000202 0.0000000 EM
34 -0.70761923D+04 0.0000161 0.0000000 EM
35 -0.70761922D+04 0.0000127 0.0000000 EM
36 -0.70761922D+04 0.0000101 0.0000000 EM
37 -0.70761922D+04 0.0000362 0.0000000 FS
38 -0.70761922D+04 0.0000022 0.0000000 FS
39 -0.70761922D+04 0.0000003 0.0000000 FS
40 -0.70761922D+04 0.0000001 0.0000000 FS
41 -0.70761922D+04 0.0000000 0.0000000 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
Y5
Y6
C
Save file
ex7.20.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
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