Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a LCGA for a three-
category outcome
montecarlo:
names are u1-u4;
generate = u1-u4(2);
categorical = u1-u4;
genclasses = c(2);
classes = c(2);
nobs = 500;
seed = 3454367;
nrep = 1;
save = ex8.10.dat;
ANALYSIS:
TYPE = MIXTURE;
model population:
%overall%
i s | u1@0 u2@1 u3@2 u4@3;
[i*1 s*1];
[u1$1-u4$1*1];
[u1$2-u4$2*1.5];
%c#2%
[i@0 s*0];
MODEL:
%overall%
i s | u1@0 u2@1 u3@2 u4@3;
[i*1 s*1];
[u1$1-u4$1*1] (1);
[u1$2-u4$2*1.5] (2);
%c#2%
[i@0 s*0];
OUTPUT:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a LCGA for a three-
category outcome
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of replications
Requested 1
Completed 1
Value of seed 3454367
Number of dependent variables 4
Number of independent variables 0
Number of continuous latent variables 2
Number of categorical latent variables 1
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4
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
MODEL FIT INFORMATION
Number of Free Parameters 6
Loglikelihood
H0 Value
Mean -1706.048
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -1706.048 -1706.048
0.980 0.000 -1706.048 -1706.048
0.950 0.000 -1706.048 -1706.048
0.900 0.000 -1706.048 -1706.048
0.800 0.000 -1706.048 -1706.048
0.700 0.000 -1706.048 -1706.048
0.500 0.000 -1706.048 -1706.048
0.300 0.000 -1706.048 -1706.048
0.200 0.000 -1706.048 -1706.048
0.100 0.000 -1706.048 -1706.048
0.050 0.000 -1706.048 -1706.048
0.020 0.000 -1706.048 -1706.048
0.010 0.000 -1706.048 -1706.048
Information Criteria
Akaike (AIC)
Mean 3424.096
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 3424.096 3424.096
0.980 0.000 3424.096 3424.096
0.950 0.000 3424.096 3424.096
0.900 0.000 3424.096 3424.096
0.800 0.000 3424.096 3424.096
0.700 0.000 3424.096 3424.096
0.500 0.000 3424.096 3424.096
0.300 0.000 3424.096 3424.096
0.200 0.000 3424.096 3424.096
0.100 0.000 3424.096 3424.096
0.050 0.000 3424.096 3424.096
0.020 0.000 3424.096 3424.096
0.010 0.000 3424.096 3424.096
Bayesian (BIC)
Mean 3449.384
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 3449.384 3449.384
0.980 0.000 3449.384 3449.384
0.950 0.000 3449.384 3449.384
0.900 0.000 3449.384 3449.384
0.800 0.000 3449.384 3449.384
0.700 0.000 3449.384 3449.384
0.500 0.000 3449.384 3449.384
0.300 0.000 3449.384 3449.384
0.200 0.000 3449.384 3449.384
0.100 0.000 3449.384 3449.384
0.050 0.000 3449.384 3449.384
0.020 0.000 3449.384 3449.384
0.010 0.000 3449.384 3449.384
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 3430.339
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 3430.339 3430.339
0.980 0.000 3430.339 3430.339
0.950 0.000 3430.339 3430.339
0.900 0.000 3430.339 3430.339
0.800 0.000 3430.339 3430.339
0.700 0.000 3430.339 3430.339
0.500 0.000 3430.339 3430.339
0.300 0.000 3430.339 3430.339
0.200 0.000 3430.339 3430.339
0.100 0.000 3430.339 3430.339
0.050 0.000 3430.339 3430.339
0.020 0.000 3430.339 3430.339
0.010 0.000 3430.339 3430.339
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Mean 69.894
Std Dev 0.000
Degrees of freedom 74
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 48.666 69.894
0.980 1.000 51.208 69.894
0.950 1.000 55.189 69.894
0.900 1.000 58.900 69.894
0.800 1.000 63.616 69.894
0.700 1.000 67.170 69.894
0.500 0.000 73.334 69.894
0.300 0.000 79.865 69.894
0.200 0.000 83.997 69.894
0.100 0.000 89.956 69.894
0.050 0.000 95.081 69.894
0.020 0.000 101.074 69.894
0.010 0.000 105.202 69.894
Likelihood Ratio Chi-Square
Mean 74.075
Std Dev 0.000
Degrees of freedom 74
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 48.666 74.075
0.980 1.000 51.208 74.075
0.950 1.000 55.189 74.075
0.900 1.000 58.900 74.075
0.800 1.000 63.616 74.075
0.700 1.000 67.170 74.075
0.500 1.000 73.334 74.075
0.300 0.000 79.865 74.075
0.200 0.000 83.997 74.075
0.100 0.000 89.956 74.075
0.050 0.000 95.081 74.075
0.020 0.000 101.074 74.075
0.010 0.000 105.202 74.075
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 240.72044 0.48144
2 259.27956 0.51856
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 240.72044 0.48144
2 259.27956 0.51856
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 244 0.48800
2 256 0.51200
CLASSIFICATION QUALITY
Entropy 0.705
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.913 0.087
2 0.070 0.930
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.925 0.075
2 0.082 0.918
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 2.516 0.000
2 -2.415 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Latent Class 1
I |
U1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U3 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
S |
U1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
U2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U3 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
U4 3.000 3.0000 0.0000 0.0000 0.0000 1.000 0.000
Means
I 1.000 0.7172 0.0000 0.1793 0.0800 1.000 1.000
S 1.000 1.0696 0.0000 0.1140 0.0048 1.000 1.000
Thresholds
U1$1 1.000 0.7461 0.0000 0.1180 0.0645 0.000 1.000
U1$2 1.500 1.2762 0.0000 0.1184 0.0501 1.000 1.000
U2$1 1.000 0.7461 0.0000 0.1180 0.0645 0.000 1.000
U2$2 1.500 1.2762 0.0000 0.1184 0.0501 1.000 1.000
U3$1 1.000 0.7461 0.0000 0.1180 0.0645 0.000 1.000
U3$2 1.500 1.2762 0.0000 0.1184 0.0501 1.000 1.000
U4$1 1.000 0.7461 0.0000 0.1180 0.0645 0.000 1.000
U4$2 1.500 1.2762 0.0000 0.1184 0.0501 1.000 1.000
Latent Class 2
I |
U1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U3 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
S |
U1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
U2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U3 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
U4 3.000 3.0000 0.0000 0.0000 0.0000 1.000 0.000
Means
I 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
S 0.000 -0.1175 0.0000 0.0771 0.0138 1.000 0.000
Thresholds
U1$1 1.000 0.7461 0.0000 0.1180 0.0645 0.000 1.000
U1$2 1.500 1.2762 0.0000 0.1184 0.0501 1.000 1.000
U2$1 1.000 0.7461 0.0000 0.1180 0.0645 0.000 1.000
U2$2 1.500 1.2762 0.0000 0.1184 0.0501 1.000 1.000
U3$1 1.000 0.7461 0.0000 0.1180 0.0645 0.000 1.000
U3$2 1.500 1.2762 0.0000 0.1184 0.0501 1.000 1.000
U4$1 1.000 0.7461 0.0000 0.1180 0.0645 0.000 1.000
U4$2 1.500 1.2762 0.0000 0.1184 0.0501 1.000 1.000
Categorical Latent Variables
Means
C#1 0.000 -0.0743 0.0000 0.1374 0.0055 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.118E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
PARAMETER SPECIFICATION FOR LATENT CLASS 2
PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1 U1$2 U2$1 U2$2 U3$1
________ ________ ________ ________ ________
1 2 1 2 1
TAU(U) FOR LATENT CLASS 1
U3$2 U4$1 U4$2
________ ________ ________
2 1 2
TAU(U) FOR LATENT CLASS 2
U1$1 U1$2 U2$1 U2$2 U3$1
________ ________ ________ ________ ________
1 2 1 2 1
TAU(U) FOR LATENT CLASS 2
U3$2 U4$1 U4$2
________ ________ ________
2 1 2
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
6 0
PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR GROWTH MODEL PART
LAMBDA(F) FOR LATENT CLASS 1
I S
________ ________
U1 0 0
U2 0 0
U3 0 0
U4 0 0
ALPHA(F) FOR LATENT CLASS 1
I S
________ ________
3 4
LAMBDA(F) FOR LATENT CLASS 2
I S
________ ________
U1 0 0
U2 0 0
U3 0 0
U4 0 0
ALPHA(F) FOR LATENT CLASS 2
I S
________ ________
0 5
STARTING VALUES FOR LATENT CLASS 1
STARTING VALUES FOR LATENT CLASS 2
STARTING VALUES FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1 U1$2 U2$1 U2$2 U3$1
________ ________ ________ ________ ________
1.000 1.500 1.000 1.500 1.000
TAU(U) FOR LATENT CLASS 1
U3$2 U4$1 U4$2
________ ________ ________
1.500 1.000 1.500
TAU(U) FOR LATENT CLASS 2
U1$1 U1$2 U2$1 U2$2 U3$1
________ ________ ________ ________ ________
1.000 1.500 1.000 1.500 1.000
TAU(U) FOR LATENT CLASS 2
U3$2 U4$1 U4$2
________ ________ ________
1.500 1.000 1.500
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
0.000 0.000
STARTING VALUES FOR LATENT CLASS INDICATOR GROWTH MODEL PART
LAMBDA(F) FOR CLASS LATENT CLASS 1
I S
________ ________
U1 1.000 0.000
U2 1.000 1.000
U3 1.000 2.000
U4 1.000 3.000
ALPHA(F) FOR LATENT CLASS 1
I S
________ ________
1.000 1.000
LAMBDA(F) FOR CLASS LATENT CLASS 2
I S
________ ________
U1 1.000 0.000
U2 1.000 1.000
U3 1.000 2.000
U4 1.000 3.000
ALPHA(F) FOR LATENT CLASS 2
I S
________ ________
0.000 0.000
POPULATION VALUES FOR LATENT CLASS 1
POPULATION VALUES FOR LATENT CLASS 2
POPULATION VALUES FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1 U1$2 U2$1 U2$2 U3$1
________ ________ ________ ________ ________
1.000 1.500 1.000 1.500 1.000
TAU(U) FOR LATENT CLASS 1
U3$2 U4$1 U4$2
________ ________ ________
1.500 1.000 1.500
TAU(U) FOR LATENT CLASS 2
U1$1 U1$2 U2$1 U2$2 U3$1
________ ________ ________ ________ ________
1.000 1.500 1.000 1.500 1.000
TAU(U) FOR LATENT CLASS 2
U3$2 U4$1 U4$2
________ ________ ________
1.500 1.000 1.500
POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
0.000 0.000
POPULATION VALUES FOR LATENT CLASS INDICATOR GROWTH MODEL PART
LAMBDA(F) FOR LATENT CLASS 1
I S
________ ________
U1 1.000 0.000
U2 1.000 1.000
U3 1.000 2.000
U4 1.000 3.000
ALPHA(F) FOR LATENT CLASS 1
I S
________ ________
1.000 1.000
LAMBDA(F) FOR LATENT CLASS 2
I S
________ ________
U1 1.000 0.000
U2 1.000 1.000
U3 1.000 2.000
U4 1.000 3.000
ALPHA(F) FOR LATENT CLASS 2
I S
________ ________
0.000 0.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.17086500D+04 0.0000000 0.0000000 EM
2 -0.17062090D+04 2.4409741 0.0014286 EM
3 -0.17060918D+04 0.1172387 0.0000687 EM
4 -0.17060716D+04 0.0202001 0.0000118 EM
5 -0.17060634D+04 0.0081486 0.0000048 EM
6 -0.17060584D+04 0.0050191 0.0000029 EM
7 -0.17060551D+04 0.0033547 0.0000020 EM
8 -0.17060528D+04 0.0022682 0.0000013 EM
9 -0.17060513D+04 0.0015359 0.0000009 EM
10 -0.17060502D+04 0.0010403 0.0000006 EM
11 -0.17060495D+04 0.0007046 0.0000004 EM
12 -0.17060490D+04 0.0004773 0.0000003 EM
13 -0.17060487D+04 0.0003233 0.0000002 EM
14 -0.17060485D+04 0.0002190 0.0000001 EM
15 -0.17060483D+04 0.0001484 0.0000001 EM
16 -0.17060482D+04 0.0001005 0.0000001 EM
17 -0.17060482D+04 0.0000681 0.0000000 EM
18 -0.17060481D+04 0.0000461 0.0000000 EM
19 -0.17060481D+04 0.0000313 0.0000000 EM
20 -0.17060481D+04 0.0000212 0.0000000 EM
21 -0.17060481D+04 0.0000143 0.0000000 EM
22 -0.17060481D+04 0.0000097 0.0000000 EM
23 -0.17060480D+04 0.0000066 0.0000000 EM
24 -0.17060480D+04 0.0000045 0.0000000 EM
25 -0.17060480D+04 0.0000030 0.0000000 EM
26 -0.17060480D+04 0.0000020 0.0000000 EM
27 -0.17060480D+04 0.0000014 0.0000000 EM
28 -0.17060480D+04 0.0000009 0.0000000 EM
29 -0.17060480D+04 0.0000006 0.0000000 EM
30 -0.17060480D+04 0.0000004 0.0000000 EM
31 -0.17060480D+04 0.0000003 0.0000000 EM
32 -0.17060480D+04 0.0000002 0.0000000 EM
33 -0.17060480D+04 0.0000001 0.0000000 EM
34 -0.17060480D+04 0.0000001 0.0000000 EM
35 -0.17060480D+04 0.0000001 0.0000000 EM
36 -0.17060480D+04 0.0000000 0.0000000 EM
37 -0.17060480D+04 0.0000001 0.0000000 FS
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
U1
U2
U3
U4
C
Save file
ex8.10.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:42
Ending Time: 22:24:43
Elapsed Time: 00:00:01
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