Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:25 PM
INPUT INSTRUCTIONS
title: this is an example of a LCGA for a binary
outcome
montecarlo:
names are u1-u4;
generate = u1-u4(1);
categorical = u1-u4;
genclasses = c(2);
classes = c(2);
nobs = 500;
seed = 3454367;
nrep = 1;
save = ex8.9.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] (1);
%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);
%c#2%
[i@0 s*0];
OUTPUT:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a LCGA for a binary
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 5
Loglikelihood
H0 Value
Mean -1272.307
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -1272.307 -1272.307
0.980 0.000 -1272.307 -1272.307
0.950 0.000 -1272.307 -1272.307
0.900 0.000 -1272.307 -1272.307
0.800 0.000 -1272.307 -1272.307
0.700 0.000 -1272.307 -1272.307
0.500 0.000 -1272.307 -1272.307
0.300 0.000 -1272.307 -1272.307
0.200 0.000 -1272.307 -1272.307
0.100 0.000 -1272.307 -1272.307
0.050 0.000 -1272.307 -1272.307
0.020 0.000 -1272.307 -1272.307
0.010 0.000 -1272.307 -1272.307
Information Criteria
Akaike (AIC)
Mean 2554.614
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 2554.614 2554.614
0.980 0.000 2554.614 2554.614
0.950 0.000 2554.614 2554.614
0.900 0.000 2554.614 2554.614
0.800 0.000 2554.614 2554.614
0.700 0.000 2554.614 2554.614
0.500 0.000 2554.614 2554.614
0.300 0.000 2554.614 2554.614
0.200 0.000 2554.614 2554.614
0.100 0.000 2554.614 2554.614
0.050 0.000 2554.614 2554.614
0.020 0.000 2554.614 2554.614
0.010 0.000 2554.614 2554.614
Bayesian (BIC)
Mean 2575.687
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 2575.687 2575.687
0.980 0.000 2575.687 2575.687
0.950 0.000 2575.687 2575.687
0.900 0.000 2575.687 2575.687
0.800 0.000 2575.687 2575.687
0.700 0.000 2575.687 2575.687
0.500 0.000 2575.687 2575.687
0.300 0.000 2575.687 2575.687
0.200 0.000 2575.687 2575.687
0.100 0.000 2575.687 2575.687
0.050 0.000 2575.687 2575.687
0.020 0.000 2575.687 2575.687
0.010 0.000 2575.687 2575.687
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 2559.817
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 2559.817 2559.817
0.980 0.000 2559.817 2559.817
0.950 0.000 2559.817 2559.817
0.900 0.000 2559.817 2559.817
0.800 0.000 2559.817 2559.817
0.700 0.000 2559.817 2559.817
0.500 0.000 2559.817 2559.817
0.300 0.000 2559.817 2559.817
0.200 0.000 2559.817 2559.817
0.100 0.000 2559.817 2559.817
0.050 0.000 2559.817 2559.817
0.020 0.000 2559.817 2559.817
0.010 0.000 2559.817 2559.817
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Mean 6.013
Std Dev 0.000
Degrees of freedom 10
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 2.558 6.013
0.980 1.000 3.059 6.013
0.950 1.000 3.940 6.013
0.900 1.000 4.865 6.013
0.800 0.000 6.179 6.013
0.700 0.000 7.267 6.013
0.500 0.000 9.342 6.013
0.300 0.000 11.781 6.013
0.200 0.000 13.442 6.013
0.100 0.000 15.987 6.013
0.050 0.000 18.307 6.013
0.020 0.000 21.161 6.013
0.010 0.000 23.209 6.013
Likelihood Ratio Chi-Square
Mean 6.044
Std Dev 0.000
Degrees of freedom 10
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 2.558 6.044
0.980 1.000 3.059 6.044
0.950 1.000 3.940 6.044
0.900 1.000 4.865 6.044
0.800 0.000 6.179 6.044
0.700 0.000 7.267 6.044
0.500 0.000 9.342 6.044
0.300 0.000 11.781 6.044
0.200 0.000 13.442 6.044
0.100 0.000 15.987 6.044
0.050 0.000 18.307 6.044
0.020 0.000 21.161 6.044
0.010 0.000 23.209 6.044
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 230.84750 0.46169
2 269.15250 0.53831
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 230.84750 0.46169
2 269.15250 0.53831
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 234 0.46800
2 266 0.53200
CLASSIFICATION QUALITY
Entropy 0.648
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.889 0.111
2 0.086 0.914
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.901 0.099
2 0.097 0.903
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 2.206 0.000
2 -2.233 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 0.7993 0.0000 0.2003 0.0403 1.000 1.000
S 1.000 1.0968 0.0000 0.2002 0.0094 1.000 1.000
Thresholds
U1$1 1.000 0.7761 0.0000 0.1237 0.0501 1.000 1.000
U2$1 1.000 0.7761 0.0000 0.1237 0.0501 1.000 1.000
U3$1 1.000 0.7761 0.0000 0.1237 0.0501 1.000 1.000
U4$1 1.000 0.7761 0.0000 0.1237 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 -0.0682 0.0000 0.0860 0.0047 1.000 0.000
Thresholds
U1$1 1.000 0.7761 0.0000 0.1237 0.0501 1.000 1.000
U2$1 1.000 0.7761 0.0000 0.1237 0.0501 1.000 1.000
U3$1 1.000 0.7761 0.0000 0.1237 0.0501 1.000 1.000
U4$1 1.000 0.7761 0.0000 0.1237 0.0501 1.000 1.000
Categorical Latent Variables
Means
C#1 0.000 -0.1535 0.0000 0.1985 0.0236 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.247E-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 U2$1 U3$1 U4$1
________ ________ ________ ________
1 1 1 1
TAU(U) FOR LATENT CLASS 2
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
1 1 1 1
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
5 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
________ ________
2 3
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 4
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 U2$1 U3$1 U4$1
________ ________ ________ ________
1.000 1.000 1.000 1.000
TAU(U) FOR LATENT CLASS 2
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
1.000 1.000 1.000 1.000
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 U2$1 U3$1 U4$1
________ ________ ________ ________
1.000 1.000 1.000 1.000
TAU(U) FOR LATENT CLASS 2
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
1.000 1.000 1.000 1.000
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 -0.12740621D+04 0.0000000 0.0000000 EM
2 -0.12725843D+04 1.4777716 0.0011599 EM
3 -0.12725080D+04 0.0762856 0.0000599 EM
4 -0.12724721D+04 0.0359594 0.0000283 EM
5 -0.12724459D+04 0.0261224 0.0000205 EM
6 -0.12724245D+04 0.0214066 0.0000168 EM
7 -0.12724065D+04 0.0180166 0.0000142 EM
8 -0.12723913D+04 0.0152468 0.0000120 EM
9 -0.12723783D+04 0.0129155 0.0000102 EM
10 -0.12723674D+04 0.0109412 0.0000086 EM
11 -0.12723581D+04 0.0092674 0.0000073 EM
12 -0.12723503D+04 0.0078483 0.0000062 EM
13 -0.12723436D+04 0.0066456 0.0000052 EM
14 -0.12723380D+04 0.0056264 0.0000044 EM
15 -0.12723333D+04 0.0047629 0.0000037 EM
16 -0.12723292D+04 0.0040314 0.0000032 EM
17 -0.12723258D+04 0.0034120 0.0000027 EM
18 -0.12723229D+04 0.0028874 0.0000023 EM
19 -0.12723205D+04 0.0024434 0.0000019 EM
20 -0.12723184D+04 0.0020674 0.0000016 EM
21 -0.12723167D+04 0.0017492 0.0000014 EM
22 -0.12723152D+04 0.0014799 0.0000012 EM
23 -0.12723139D+04 0.0012519 0.0000010 EM
24 -0.12723129D+04 0.0010591 0.0000008 EM
25 -0.12723120D+04 0.0008959 0.0000007 EM
26 -0.12723112D+04 0.0007578 0.0000006 EM
27 -0.12723106D+04 0.0006409 0.0000005 EM
28 -0.12723100D+04 0.0005421 0.0000004 EM
29 -0.12723096D+04 0.0004585 0.0000004 EM
30 -0.12723092D+04 0.0003878 0.0000003 EM
31 -0.12723089D+04 0.0003280 0.0000003 EM
32 -0.12723086D+04 0.0002774 0.0000002 EM
33 -0.12723083D+04 0.0002346 0.0000002 EM
34 -0.12723082D+04 0.0001984 0.0000002 EM
35 -0.12723080D+04 0.0001677 0.0000001 EM
36 -0.12723071D+04 0.0009052 0.0000007 FS
37 -0.12723071D+04 0.0000133 0.0000000 FS
38 -0.12723071D+04 0.0000002 0.0000000 FS
39 -0.12723071D+04 0.0000000 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
ex8.9.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:25:07
Ending Time: 22:25:09
Elapsed Time: 00:00:02
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