Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
title:
this is an example of a LCA with binary
latent class indicators using automatic
starting values with random starts with a
covariate and a direct effect
montecarlo:
names are u1-u4 x;
generate = u1-u4(1);
categorical = u1-u4;
genclasses = c(2);
classes = c(2);
nobs = 500;
seed = 3454367;
nrep = 1;
save = ex7.12.dat;
analysis:
type = mixture;
model population:
%overall%
[x@0]; x@1;
[c#1*0];
c#1 on x*1;
u4 on x*.5;
%c#1%
[u1$1*1 u2$1*1 u3$1*-1 u4$1*-1];
%c#2%
[u1$1*-1 u2$1*-1 u3$1*1 u4$1*1];
model:
%overall%
[c#1*0];
c#1 on x*1;
u4 on x*.5;
%c#1%
[u1$1*1 u2$1*1 u3$1*-1 u4$1*-1];
%c#2%
[u1$1*-1 u2$1*-1 u3$1*1 u4$1*1];
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a LCA with binary
latent class indicators using automatic
starting values with random starts with a
covariate and a direct effect
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 1
Number of continuous latent variables 0
Number of categorical latent variables 1
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4
Observed independent variables
X
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
X
________
-0.072
Covariances
X
________
X 1.014
Correlations
X
________
X 1.000
MODEL FIT INFORMATION
Number of Free Parameters 11
Loglikelihood
H0 Value
Mean -1255.396
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -1255.396 -1255.396
0.980 0.000 -1255.396 -1255.396
0.950 0.000 -1255.396 -1255.396
0.900 0.000 -1255.396 -1255.396
0.800 0.000 -1255.396 -1255.396
0.700 0.000 -1255.396 -1255.396
0.500 0.000 -1255.396 -1255.396
0.300 0.000 -1255.396 -1255.396
0.200 0.000 -1255.396 -1255.396
0.100 0.000 -1255.396 -1255.396
0.050 0.000 -1255.396 -1255.396
0.020 0.000 -1255.396 -1255.396
0.010 0.000 -1255.396 -1255.396
Information Criteria
Akaike (AIC)
Mean 2532.793
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 2532.793 2532.793
0.980 0.000 2532.793 2532.793
0.950 0.000 2532.793 2532.793
0.900 0.000 2532.793 2532.793
0.800 0.000 2532.793 2532.793
0.700 0.000 2532.793 2532.793
0.500 0.000 2532.793 2532.793
0.300 0.000 2532.793 2532.793
0.200 0.000 2532.793 2532.793
0.100 0.000 2532.793 2532.793
0.050 0.000 2532.793 2532.793
0.020 0.000 2532.793 2532.793
0.010 0.000 2532.793 2532.793
Bayesian (BIC)
Mean 2579.153
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 2579.153 2579.153
0.980 0.000 2579.153 2579.153
0.950 0.000 2579.153 2579.153
0.900 0.000 2579.153 2579.153
0.800 0.000 2579.153 2579.153
0.700 0.000 2579.153 2579.153
0.500 0.000 2579.153 2579.153
0.300 0.000 2579.153 2579.153
0.200 0.000 2579.153 2579.153
0.100 0.000 2579.153 2579.153
0.050 0.000 2579.153 2579.153
0.020 0.000 2579.153 2579.153
0.010 0.000 2579.153 2579.153
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 2544.239
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 2544.239 2544.239
0.980 0.000 2544.239 2544.239
0.950 0.000 2544.239 2544.239
0.900 0.000 2544.239 2544.239
0.800 0.000 2544.239 2544.239
0.700 0.000 2544.239 2544.239
0.500 0.000 2544.239 2544.239
0.300 0.000 2544.239 2544.239
0.200 0.000 2544.239 2544.239
0.100 0.000 2544.239 2544.239
0.050 0.000 2544.239 2544.239
0.020 0.000 2544.239 2544.239
0.010 0.000 2544.239 2544.239
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 249.27676 0.49855
2 250.72324 0.50145
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 249.27676 0.49855
2 250.72324 0.50145
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 248 0.49600
2 252 0.50400
CLASSIFICATION QUALITY
Entropy 0.586
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.882 0.118
2 0.122 0.878
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.877 0.123
2 0.117 0.883
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 1.964 0.000
2 -2.019 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Latent Class 1
U4 ON
X 0.500 0.5786 0.0000 0.1283 0.0062 1.000 1.000
Thresholds
U1$1 1.000 1.3370 0.0000 0.2455 0.1136 1.000 1.000
U2$1 1.000 0.9287 0.0000 0.1974 0.0051 1.000 1.000
U3$1 -1.000 -0.9464 0.0000 0.2048 0.0029 1.000 1.000
U4$1 -1.000 -0.6627 0.0000 0.2118 0.1138 1.000 1.000
Latent Class 2
U4 ON
X 0.500 0.5786 0.0000 0.1283 0.0062 1.000 1.000
Thresholds
U1$1 -1.000 -1.4517 0.0000 0.2912 0.2040 1.000 1.000
U2$1 -1.000 -1.1716 0.0000 0.2174 0.0294 1.000 1.000
U3$1 1.000 1.0828 0.0000 0.2006 0.0069 1.000 1.000
U4$1 1.000 0.9580 0.0000 0.2016 0.0018 1.000 1.000
Categorical Latent Variables
C#1 ON
X 1.000 1.0247 0.0000 0.1510 0.0006 1.000 1.000
Intercepts
C#1 0.000 0.0667 0.0000 0.2393 0.0045 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.762E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
NU
X
________
0
LAMBDA
X
________
X 0
THETA
X
________
X 0
ALPHA
X
________
0
BETA
X
________
X 0
PSI
X
________
X 0
PARAMETER SPECIFICATION FOR LATENT CLASS 2
NU
X
________
0
LAMBDA
X
________
X 0
THETA
X
________
X 0
ALPHA
X
________
0
BETA
X
________
X 0
PSI
X
________
X 0
PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
1 2 3 4
TAU(U) FOR LATENT CLASS 2
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
6 7 8 9
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
10 0
GAMMA(C)
X
________
C#1 11
C#2 0
PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR GROWTH MODEL PART
LAMBDA(F) FOR LATENT CLASS 1
U4
________
U1 0
U2 0
U3 0
U4 0
ALPHA(F) FOR LATENT CLASS 1
U4
________
0
GAMMA(F) FOR LATENT CLASS 1
X
________
U4 5
LAMBDA(F) FOR LATENT CLASS 2
U4
________
U1 0
U2 0
U3 0
U4 0
ALPHA(F) FOR LATENT CLASS 2
U4
________
0
GAMMA(F) FOR LATENT CLASS 2
X
________
U4 5
STARTING VALUES FOR LATENT CLASS 1
NU
X
________
0.000
LAMBDA
X
________
X 1.000
THETA
X
________
X 0.000
ALPHA
X
________
0.000
BETA
X
________
X 0.000
PSI
X
________
X 0.500
STARTING VALUES FOR LATENT CLASS 2
NU
X
________
0.000
LAMBDA
X
________
X 1.000
THETA
X
________
X 0.000
ALPHA
X
________
0.000
BETA
X
________
X 0.000
PSI
X
________
X 0.500
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
GAMMA(C)
X
________
C#1 1.000
C#2 0.000
STARTING VALUES FOR LATENT CLASS INDICATOR GROWTH MODEL PART
LAMBDA(F) FOR CLASS LATENT CLASS 1
U4
________
U1 0.000
U2 0.000
U3 0.000
U4 1.000
ALPHA(F) FOR LATENT CLASS 1
U4
________
0.000
GAMMA(F) FOR LATENT CLASS 1
X
________
U4 0.500
LAMBDA(F) FOR CLASS LATENT CLASS 2
U4
________
U1 0.000
U2 0.000
U3 0.000
U4 1.000
ALPHA(F) FOR LATENT CLASS 2
U4
________
0.000
GAMMA(F) FOR LATENT CLASS 2
X
________
U4 0.500
POPULATION VALUES FOR LATENT CLASS 1
NU
X
________
0.000
LAMBDA
X
________
X 1.000
THETA
X
________
X 0.000
ALPHA
X
________
0.000
BETA
X
________
X 0.000
PSI
X
________
X 1.000
POPULATION VALUES FOR LATENT CLASS 2
NU
X
________
0.000
LAMBDA
X
________
X 1.000
THETA
X
________
X 0.000
ALPHA
X
________
0.000
BETA
X
________
X 0.000
PSI
X
________
X 1.000
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
GAMMA(C)
X
________
C#1 1.000
C#2 0.000
POPULATION VALUES FOR LATENT CLASS INDICATOR GROWTH MODEL PART
LAMBDA(F) FOR LATENT CLASS 1
U4
________
U1 0.000
U2 0.000
U3 0.000
U4 1.000
ALPHA(F) FOR LATENT CLASS 1
U4
________
0.000
GAMMA(F) FOR LATENT CLASS 1
X
________
U4 0.500
LAMBDA(F) FOR LATENT CLASS 2
U4
________
U1 0.000
U2 0.000
U3 0.000
U4 1.000
ALPHA(F) FOR LATENT CLASS 2
U4
________
0.000
GAMMA(F) FOR LATENT CLASS 2
X
________
U4 0.500
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.12598594D+04 0.0000000 0.0000000 EM
2 -0.12566708D+04 3.1886149 0.0025309 EM
3 -0.12559336D+04 0.7372358 0.0005867 EM
4 -0.12556664D+04 0.2671668 0.0002127 EM
5 -0.12555545D+04 0.1118609 0.0000891 EM
6 -0.12555009D+04 0.0536395 0.0000427 EM
7 -0.12554714D+04 0.0294607 0.0000235 EM
8 -0.12554531D+04 0.0183427 0.0000146 EM
9 -0.12554405D+04 0.0126080 0.0000100 EM
10 -0.12554312D+04 0.0092662 0.0000074 EM
11 -0.12554241D+04 0.0070917 0.0000056 EM
12 -0.12554186D+04 0.0055529 0.0000044 EM
13 -0.12554142D+04 0.0044024 0.0000035 EM
14 -0.12554107D+04 0.0035138 0.0000028 EM
15 -0.12554079D+04 0.0028146 0.0000022 EM
16 -0.12554056D+04 0.0022590 0.0000018 EM
17 -0.12554038D+04 0.0018151 0.0000014 EM
18 -0.12554023D+04 0.0014594 0.0000012 EM
19 -0.12554011D+04 0.0011739 0.0000009 EM
20 -0.12554002D+04 0.0009445 0.0000008 EM
21 -0.12553994D+04 0.0007601 0.0000006 EM
22 -0.12553988D+04 0.0006118 0.0000005 EM
23 -0.12553983D+04 0.0004925 0.0000004 EM
24 -0.12553979D+04 0.0003965 0.0000003 EM
25 -0.12553976D+04 0.0003193 0.0000003 EM
26 -0.12553974D+04 0.0002571 0.0000002 EM
27 -0.12553972D+04 0.0002071 0.0000002 EM
28 -0.12553970D+04 0.0001668 0.0000001 EM
29 -0.12553969D+04 0.0001343 0.0000001 EM
30 -0.12553967D+04 0.0001082 0.0000001 EM
31 -0.12553967D+04 0.0000872 0.0000001 EM
32 -0.12553966D+04 0.0000702 0.0000001 EM
33 -0.12553965D+04 0.0000566 0.0000000 EM
34 -0.12553965D+04 0.0000456 0.0000000 EM
35 -0.12553965D+04 0.0000367 0.0000000 EM
36 -0.12553964D+04 0.0000296 0.0000000 EM
37 -0.12553964D+04 0.0000238 0.0000000 EM
38 -0.12553963D+04 0.0000961 0.0000001 FS
39 -0.12553963D+04 0.0000027 0.0000000 FS
40 -0.12553963D+04 0.0000001 0.0000000 FS
41 -0.12553963D+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
X
C
Save file
ex7.12.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:28
Ending Time: 22:24:28
Elapsed Time: 00:00:00
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