Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
title:
this is an example of LCA with partial
conditional independence
! this is the Qu-Tan-Kutner (1996) Biometrics
! model
montecarlo:
names are u1-u4;
generate = u1-u4(1);
categorical = u1-u4;
genclasses = c(2);
classes = c(2);
nobs = 1000;
seed = 3454367;
nrep = 1;
save = ex7.16.dat;
analysis:
type = mixture;
parameterization = rescovariances;
model population:
%overall%
%c#1%
[u1$1-u4$1*-1];
u2 WITH u3*0.3;
%c#2%
[u1$1-u4$1*1];
model:
%overall%
%c#1%
[u1$1-u4$1*-1];
u2 WITH u3;
%c#2%
[u1$1-u4$1*1];
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of LCA with partial
conditional independence
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 4
Number of independent variables 0
Number of continuous latent variables 0
Number of categorical latent variables 1
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4
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-02
Relative loglikelihood change 0.100D-05
Derivative 0.100D-02
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-02
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-02
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
Integration Specifications
Type STANDARD
Number of integration points 15
Dimensions of numerical integration 0
Adaptive quadrature ON
Link LOGIT
Cholesky ON
MODEL FIT INFORMATION
Number of Free Parameters 10
Loglikelihood
H0 Value
Mean -2598.123
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -2598.123 -2598.123
0.980 0.000 -2598.123 -2598.123
0.950 0.000 -2598.123 -2598.123
0.900 0.000 -2598.123 -2598.123
0.800 0.000 -2598.123 -2598.123
0.700 0.000 -2598.123 -2598.123
0.500 0.000 -2598.123 -2598.123
0.300 0.000 -2598.123 -2598.123
0.200 0.000 -2598.123 -2598.123
0.100 0.000 -2598.123 -2598.123
0.050 0.000 -2598.123 -2598.123
0.020 0.000 -2598.123 -2598.123
0.010 0.000 -2598.123 -2598.123
Information Criteria
Akaike (AIC)
Mean 5216.247
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 5216.247 5216.247
0.980 0.000 5216.247 5216.247
0.950 0.000 5216.247 5216.247
0.900 0.000 5216.247 5216.247
0.800 0.000 5216.247 5216.247
0.700 0.000 5216.247 5216.247
0.500 0.000 5216.247 5216.247
0.300 0.000 5216.247 5216.247
0.200 0.000 5216.247 5216.247
0.100 0.000 5216.247 5216.247
0.050 0.000 5216.247 5216.247
0.020 0.000 5216.247 5216.247
0.010 0.000 5216.247 5216.247
Bayesian (BIC)
Mean 5265.325
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 5265.325 5265.325
0.980 0.000 5265.325 5265.325
0.950 0.000 5265.325 5265.325
0.900 0.000 5265.325 5265.325
0.800 0.000 5265.325 5265.325
0.700 0.000 5265.325 5265.325
0.500 0.000 5265.325 5265.325
0.300 0.000 5265.325 5265.325
0.200 0.000 5265.325 5265.325
0.100 0.000 5265.325 5265.325
0.050 0.000 5265.325 5265.325
0.020 0.000 5265.325 5265.325
0.010 0.000 5265.325 5265.325
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 5233.564
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 5233.564 5233.564
0.980 0.000 5233.564 5233.564
0.950 0.000 5233.564 5233.564
0.900 0.000 5233.564 5233.564
0.800 0.000 5233.564 5233.564
0.700 0.000 5233.564 5233.564
0.500 0.000 5233.564 5233.564
0.300 0.000 5233.564 5233.564
0.200 0.000 5233.564 5233.564
0.100 0.000 5233.564 5233.564
0.050 0.000 5233.564 5233.564
0.020 0.000 5233.564 5233.564
0.010 0.000 5233.564 5233.564
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Mean 11.084
Std Dev 0.000
Degrees of freedom 5
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 0.554 11.084
0.980 1.000 0.752 11.084
0.950 1.000 1.145 11.084
0.900 1.000 1.610 11.084
0.800 1.000 2.343 11.084
0.700 1.000 3.000 11.084
0.500 1.000 4.351 11.084
0.300 1.000 6.064 11.084
0.200 1.000 7.289 11.084
0.100 1.000 9.236 11.084
0.050 1.000 11.070 11.084
0.020 0.000 13.388 11.084
0.010 0.000 15.086 11.084
Likelihood Ratio Chi-Square
Mean 10.882
Std Dev 0.000
Degrees of freedom 5
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 0.554 10.882
0.980 1.000 0.752 10.882
0.950 1.000 1.145 10.882
0.900 1.000 1.610 10.882
0.800 1.000 2.343 10.882
0.700 1.000 3.000 10.882
0.500 1.000 4.351 10.882
0.300 1.000 6.064 10.882
0.200 1.000 7.289 10.882
0.100 1.000 9.236 10.882
0.050 0.000 11.070 10.882
0.020 0.000 13.388 10.882
0.010 0.000 15.086 10.882
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 467.70875 0.46771
2 532.29125 0.53229
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 467.70874 0.46771
2 532.29126 0.53229
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 471 0.47100
2 529 0.52900
CLASSIFICATION QUALITY
Entropy 0.561
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.866 0.134
2 0.113 0.887
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.872 0.128
2 0.118 0.882
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 1.922 0.000
2 -2.009 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Latent Class 1
U2 WITH
U3 0.000 0.5067 0.0000 0.8508 0.2568 1.000 0.000
Thresholds
U1$1 -1.000 -1.0602 0.0000 0.1572 0.0036 1.000 1.000
U2$1 -1.000 -0.9014 0.0000 1.6980 0.0097 1.000 0.000
U3$1 -1.000 -0.8974 0.0000 1.7042 0.0105 1.000 0.000
U4$1 -1.000 -1.0163 0.0000 0.1330 0.0003 1.000 1.000
Latent Class 2
Thresholds
U1$1 1.000 0.8462 0.0000 0.1376 0.0237 1.000 1.000
U2$1 1.000 0.8349 0.0000 0.1519 0.0273 1.000 1.000
U3$1 1.000 0.9351 0.0000 0.1418 0.0042 1.000 1.000
U4$1 1.000 0.7751 0.0000 0.1462 0.0506 1.000 1.000
Categorical Latent Variables
Means
C#1 0.000 -0.1293 0.0000 0.1530 0.0167 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.230E-03
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
NU
U1 U2 U3 U4
________ ________ ________ ________
0 0 0 0
THETA
U1 U2 U3 U4
________ ________ ________ ________
U1 0
U2 0 0
U3 0 1 0
U4 0 0 0 0
PARAMETER SPECIFICATION FOR LATENT CLASS 2
NU
U1 U2 U3 U4
________ ________ ________ ________
0 0 0 0
THETA
U1 U2 U3 U4
________ ________ ________ ________
U1 0
U2 0 0
U3 0 0 0
U4 0 0 0 0
PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
2 3 4 5
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
STARTING VALUES FOR LATENT CLASS 1
NU
U1 U2 U3 U4
________ ________ ________ ________
0.000 0.000 0.000 0.000
THETA
U1 U2 U3 U4
________ ________ ________ ________
U1 1.000
U2 0.000 1.000
U3 0.000 0.000 1.000
U4 0.000 0.000 0.000 1.000
STARTING VALUES FOR LATENT CLASS 2
NU
U1 U2 U3 U4
________ ________ ________ ________
0.000 0.000 0.000 0.000
THETA
U1 U2 U3 U4
________ ________ ________ ________
U1 1.000
U2 0.000 1.000
U3 0.000 0.000 1.000
U4 0.000 0.000 0.000 1.000
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
POPULATION VALUES FOR LATENT CLASS 1
NU
U1 U2 U3 U4
________ ________ ________ ________
0.000 0.000 0.000 0.000
THETA
U1 U2 U3 U4
________ ________ ________ ________
U1 0.000
U2 0.000 0.000
U3 0.000 0.300 0.000
U4 0.000 0.000 0.000 0.000
POPULATION VALUES FOR LATENT CLASS 2
NU
U1 U2 U3 U4
________ ________ ________ ________
0.000 0.000 0.000 0.000
THETA
U1 U2 U3 U4
________ ________ ________ ________
U1 0.000
U2 0.000 0.000
U3 0.000 0.000 0.000
U4 0.000 0.000 0.000 0.000
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
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.26230473D+04 0.0000000 0.0000000 EM
2 -0.26003271D+04 22.7201985 0.0086618 EM
3 -0.25995987D+04 0.7283835 0.0002801 EM
4 -0.25992899D+04 0.3087793 0.0001188 EM
5 -0.25991092D+04 0.1807334 0.0000695 EM
6 -0.25989819D+04 0.1272928 0.0000490 EM
7 -0.25982628D+04 0.7191166 0.0002767 FS
8 -0.25981375D+04 0.1253028 0.0000482 EM
9 -0.25981238D+04 0.0137065 0.0000053 EM
10 -0.25981235D+04 0.0002893 0.0000001 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
U1
U2
U3
U4
C
Save file
ex7.16.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:29
Ending Time: 22:24:29
Elapsed Time: 00:00:00
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