Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
title:
this is an example of a GMM for a censored
outcome using a censored model with
automatic starting values and random starts
montecarlo:
names are y1-y4 x;
generate = y1-y4(cb 0);
censored = y1-y4(b);
genclasses = c(2);
classes = c(2);
nobs = 500;
seed = 3454367;
nrep = 1;
save = ex8.3.dat;
analysis:
type = mixture;
algorithm = integration;
model population:
%overall%
[x@0]; x@1;
y1-y4*.5;
i s | y1@0 y2@1 y3@2 y4@3;
i*1; s*.5;
c#1 on x*1;
i on x*.4;
s on x*.3;
%c#1%
[i*1 s*.5];
%c#2%
[i*3 s*1];
model:
%overall%
y1-y4*.5;
i s | y1@0 y2@1 y3@2 y4@3;
i*1; s*.5;
c#1 on x*1;
i on x*.4;
s on x*.3;
%c#1%
[i*1 s*.5];
%c#2%
[i*3 s*1];
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a GMM for a censored
outcome using a censored model with
automatic starting values and random starts
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 2
Number of categorical latent variables 1
Observed dependent variables
Censored
Y1 Y2 Y3 Y4
Observed independent variables
X
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-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 2
Adaptive quadrature ON
Cholesky ON
SUMMARY OF CENSORED LIMITS
Y1 0.000
Y2 0.000
Y3 0.000
Y4 0.000
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
X
________
-0.008
Covariances
X
________
X 1.001
Correlations
X
________
X 1.000
MODEL FIT INFORMATION
Number of Free Parameters 15
Loglikelihood
H0 Value
Mean -3211.439
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -3211.439 -3211.439
0.980 0.000 -3211.439 -3211.439
0.950 0.000 -3211.439 -3211.439
0.900 0.000 -3211.439 -3211.439
0.800 0.000 -3211.439 -3211.439
0.700 0.000 -3211.439 -3211.439
0.500 0.000 -3211.439 -3211.439
0.300 0.000 -3211.439 -3211.439
0.200 0.000 -3211.439 -3211.439
0.100 0.000 -3211.439 -3211.439
0.050 0.000 -3211.439 -3211.439
0.020 0.000 -3211.439 -3211.439
0.010 0.000 -3211.439 -3211.439
Information Criteria
Akaike (AIC)
Mean 6452.878
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 6452.878 6452.878
0.980 0.000 6452.878 6452.878
0.950 0.000 6452.878 6452.878
0.900 0.000 6452.878 6452.878
0.800 0.000 6452.878 6452.878
0.700 0.000 6452.878 6452.878
0.500 0.000 6452.878 6452.878
0.300 0.000 6452.878 6452.878
0.200 0.000 6452.878 6452.878
0.100 0.000 6452.878 6452.878
0.050 0.000 6452.878 6452.878
0.020 0.000 6452.878 6452.878
0.010 0.000 6452.878 6452.878
Bayesian (BIC)
Mean 6516.097
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 6516.097 6516.097
0.980 0.000 6516.097 6516.097
0.950 0.000 6516.097 6516.097
0.900 0.000 6516.097 6516.097
0.800 0.000 6516.097 6516.097
0.700 0.000 6516.097 6516.097
0.500 0.000 6516.097 6516.097
0.300 0.000 6516.097 6516.097
0.200 0.000 6516.097 6516.097
0.100 0.000 6516.097 6516.097
0.050 0.000 6516.097 6516.097
0.020 0.000 6516.097 6516.097
0.010 0.000 6516.097 6516.097
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 6468.486
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 6468.486 6468.486
0.980 0.000 6468.486 6468.486
0.950 0.000 6468.486 6468.486
0.900 0.000 6468.486 6468.486
0.800 0.000 6468.486 6468.486
0.700 0.000 6468.486 6468.486
0.500 0.000 6468.486 6468.486
0.300 0.000 6468.486 6468.486
0.200 0.000 6468.486 6468.486
0.100 0.000 6468.486 6468.486
0.050 0.000 6468.486 6468.486
0.020 0.000 6468.486 6468.486
0.010 0.000 6468.486 6468.486
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 256.65808 0.51332
2 243.34192 0.48668
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 256.65809 0.51332
2 243.34191 0.48668
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 253 0.50600
2 247 0.49400
CLASSIFICATION QUALITY
Entropy 0.600
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.892 0.108
2 0.126 0.874
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.879 0.121
2 0.112 0.888
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 1.984 0.000
2 -2.066 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Latent Class 1
I |
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
S |
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 3.000 3.0000 0.0000 0.0000 0.0000 1.000 0.000
I ON
X 0.400 0.2883 0.0000 0.0812 0.0125 1.000 1.000
S ON
X 0.300 0.3050 0.0000 0.0457 0.0000 1.000 1.000
S WITH
I 0.000 -0.0539 0.0000 0.0580 0.0029 1.000 0.000
Intercepts
I 1.000 0.9430 0.0000 0.1086 0.0032 1.000 1.000
S 0.500 0.4214 0.0000 0.0756 0.0062 1.000 1.000
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Residual Variances
I 1.000 0.8936 0.0000 0.1473 0.0113 1.000 1.000
S 0.500 0.4948 0.0000 0.0504 0.0000 1.000 1.000
Y1 0.500 0.5898 0.0000 0.0801 0.0081 1.000 1.000
Y2 0.500 0.4791 0.0000 0.0447 0.0004 1.000 1.000
Y3 0.500 0.4913 0.0000 0.0583 0.0001 1.000 1.000
Y4 0.500 0.4662 0.0000 0.1007 0.0011 1.000 1.000
Latent Class 2
I |
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
S |
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 3.000 3.0000 0.0000 0.0000 0.0000 1.000 0.000
I ON
X 0.400 0.2883 0.0000 0.0812 0.0125 1.000 1.000
S ON
X 0.300 0.3050 0.0000 0.0457 0.0000 1.000 1.000
S WITH
I 0.000 -0.0539 0.0000 0.0580 0.0029 1.000 0.000
Intercepts
I 3.000 3.0519 0.0000 0.1273 0.0027 1.000 1.000
S 1.000 1.0004 0.0000 0.0758 0.0000 1.000 1.000
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Residual Variances
I 1.000 0.8936 0.0000 0.1473 0.0113 1.000 1.000
S 0.500 0.4948 0.0000 0.0504 0.0000 1.000 1.000
Y1 0.500 0.5898 0.0000 0.0801 0.0081 1.000 1.000
Y2 0.500 0.4791 0.0000 0.0447 0.0004 1.000 1.000
Y3 0.500 0.4913 0.0000 0.0583 0.0001 1.000 1.000
Y4 0.500 0.4662 0.0000 0.1007 0.0011 1.000 1.000
Categorical Latent Variables
C#1 ON
X 1.000 0.8000 0.0000 0.1736 0.0400 1.000 1.000
Intercepts
C#1 0.000 0.0696 0.0000 0.1730 0.0048 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.169E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
NU
Y1#1 Y1 Y2#1 Y2 Y3#1
________ ________ ________ ________ ________
0 0 0 0 0
NU
Y3 Y4#1 Y4 X
________ ________ ________ ________
0 0 0 0
LAMBDA
I S X
________ ________ ________
Y1#1 0 0 0
Y1 0 0 0
Y2#1 0 0 0
Y2 0 0 0
Y3#1 0 0 0
Y3 0 0 0
Y4#1 0 0 0
Y4 0 0 0
X 0 0 0
THETA
Y1#1 Y1 Y2#1 Y2 Y3#1
________ ________ ________ ________ ________
Y1#1 0
Y1 0 1
Y2#1 0 0 0
Y2 0 0 0 2
Y3#1 0 0 0 0 0
Y3 0 0 0 0 0
Y4#1 0 0 0 0 0
Y4 0 0 0 0 0
X 0 0 0 0 0
THETA
Y3 Y4#1 Y4 X
________ ________ ________ ________
Y3 3
Y4#1 0 0
Y4 0 0 4
X 0 0 0 0
ALPHA
I S X
________ ________ ________
5 6 0
BETA
I S X
________ ________ ________
I 0 0 7
S 0 0 8
X 0 0 0
PSI
I S X
________ ________ ________
I 9
S 10 11
X 0 0 0
PARAMETER SPECIFICATION FOR LATENT CLASS 2
NU
Y1#1 Y1 Y2#1 Y2 Y3#1
________ ________ ________ ________ ________
0 0 0 0 0
NU
Y3 Y4#1 Y4 X
________ ________ ________ ________
0 0 0 0
LAMBDA
I S X
________ ________ ________
Y1#1 0 0 0
Y1 0 0 0
Y2#1 0 0 0
Y2 0 0 0
Y3#1 0 0 0
Y3 0 0 0
Y4#1 0 0 0
Y4 0 0 0
X 0 0 0
THETA
Y1#1 Y1 Y2#1 Y2 Y3#1
________ ________ ________ ________ ________
Y1#1 0
Y1 0 1
Y2#1 0 0 0
Y2 0 0 0 2
Y3#1 0 0 0 0 0
Y3 0 0 0 0 0
Y4#1 0 0 0 0 0
Y4 0 0 0 0 0
X 0 0 0 0 0
THETA
Y3 Y4#1 Y4 X
________ ________ ________ ________
Y3 3
Y4#1 0 0
Y4 0 0 4
X 0 0 0 0
ALPHA
I S X
________ ________ ________
12 13 0
BETA
I S X
________ ________ ________
I 0 0 7
S 0 0 8
X 0 0 0
PSI
I S X
________ ________ ________
I 9
S 10 11
X 0 0 0
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
14 0
GAMMA(C)
I S X
________ ________ ________
C#1 0 0 15
C#2 0 0 0
STARTING VALUES FOR LATENT CLASS 1
NU
Y1#1 Y1 Y2#1 Y2 Y3#1
________ ________ ________ ________ ________
-20.000 0.000 -20.000 0.000 -20.000
NU
Y3 Y4#1 Y4 X
________ ________ ________ ________
0.000 -20.000 0.000 0.000
LAMBDA
I S X
________ ________ ________
Y1#1 0.000 0.000 0.000
Y1 1.000 0.000 0.000
Y2#1 0.000 0.000 0.000
Y2 1.000 1.000 0.000
Y3#1 0.000 0.000 0.000
Y3 1.000 2.000 0.000
Y4#1 0.000 0.000 0.000
Y4 1.000 3.000 0.000
X 0.000 0.000 1.000
THETA
Y1#1 Y1 Y2#1 Y2 Y3#1
________ ________ ________ ________ ________
Y1#1 0.000
Y1 0.000 0.500
Y2#1 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.500
Y3#1 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4#1 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
THETA
Y3 Y4#1 Y4 X
________ ________ ________ ________
Y3 0.500
Y4#1 0.000 0.000
Y4 0.000 0.000 0.500
X 0.000 0.000 0.000 0.000
ALPHA
I S X
________ ________ ________
1.000 0.500 0.000
BETA
I S X
________ ________ ________
I 0.000 0.000 0.400
S 0.000 0.000 0.300
X 0.000 0.000 0.000
PSI
I S X
________ ________ ________
I 1.000
S 0.000 0.500
X 0.000 0.000 0.500
STARTING VALUES FOR LATENT CLASS 2
NU
Y1#1 Y1 Y2#1 Y2 Y3#1
________ ________ ________ ________ ________
-20.000 0.000 -20.000 0.000 -20.000
NU
Y3 Y4#1 Y4 X
________ ________ ________ ________
0.000 -20.000 0.000 0.000
LAMBDA
I S X
________ ________ ________
Y1#1 0.000 0.000 0.000
Y1 1.000 0.000 0.000
Y2#1 0.000 0.000 0.000
Y2 1.000 1.000 0.000
Y3#1 0.000 0.000 0.000
Y3 1.000 2.000 0.000
Y4#1 0.000 0.000 0.000
Y4 1.000 3.000 0.000
X 0.000 0.000 1.000
THETA
Y1#1 Y1 Y2#1 Y2 Y3#1
________ ________ ________ ________ ________
Y1#1 0.000
Y1 0.000 0.500
Y2#1 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.500
Y3#1 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4#1 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
THETA
Y3 Y4#1 Y4 X
________ ________ ________ ________
Y3 0.500
Y4#1 0.000 0.000
Y4 0.000 0.000 0.500
X 0.000 0.000 0.000 0.000
ALPHA
I S X
________ ________ ________
3.000 1.000 0.000
BETA
I S X
________ ________ ________
I 0.000 0.000 0.400
S 0.000 0.000 0.300
X 0.000 0.000 0.000
PSI
I S X
________ ________ ________
I 1.000
S 0.000 0.500
X 0.000 0.000 0.500
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
0.000 0.000
GAMMA(C)
I S X
________ ________ ________
C#1 0.000 0.000 1.000
C#2 0.000 0.000 0.000
POPULATION VALUES FOR LATENT CLASS 1
NU
Y1#1 Y1 Y2#1 Y2 Y3#1
________ ________ ________ ________ ________
-20.000 0.000 -20.000 0.000 -20.000
NU
Y3 Y4#1 Y4 X
________ ________ ________ ________
0.000 -20.000 0.000 0.000
LAMBDA
I S X
________ ________ ________
Y1#1 0.000 0.000 0.000
Y1 1.000 0.000 0.000
Y2#1 0.000 0.000 0.000
Y2 1.000 1.000 0.000
Y3#1 0.000 0.000 0.000
Y3 1.000 2.000 0.000
Y4#1 0.000 0.000 0.000
Y4 1.000 3.000 0.000
X 0.000 0.000 1.000
THETA
Y1#1 Y1 Y2#1 Y2 Y3#1
________ ________ ________ ________ ________
Y1#1 0.000
Y1 0.000 0.500
Y2#1 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.500
Y3#1 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4#1 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
THETA
Y3 Y4#1 Y4 X
________ ________ ________ ________
Y3 0.500
Y4#1 0.000 0.000
Y4 0.000 0.000 0.500
X 0.000 0.000 0.000 0.000
ALPHA
I S X
________ ________ ________
1.000 0.500 0.000
BETA
I S X
________ ________ ________
I 0.000 0.000 0.400
S 0.000 0.000 0.300
X 0.000 0.000 0.000
PSI
I S X
________ ________ ________
I 1.000
S 0.000 0.500
X 0.000 0.000 1.000
POPULATION VALUES FOR LATENT CLASS 2
NU
Y1#1 Y1 Y2#1 Y2 Y3#1
________ ________ ________ ________ ________
-20.000 0.000 -20.000 0.000 -20.000
NU
Y3 Y4#1 Y4 X
________ ________ ________ ________
0.000 -20.000 0.000 0.000
LAMBDA
I S X
________ ________ ________
Y1#1 0.000 0.000 0.000
Y1 1.000 0.000 0.000
Y2#1 0.000 0.000 0.000
Y2 1.000 1.000 0.000
Y3#1 0.000 0.000 0.000
Y3 1.000 2.000 0.000
Y4#1 0.000 0.000 0.000
Y4 1.000 3.000 0.000
X 0.000 0.000 1.000
THETA
Y1#1 Y1 Y2#1 Y2 Y3#1
________ ________ ________ ________ ________
Y1#1 0.000
Y1 0.000 0.500
Y2#1 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.500
Y3#1 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4#1 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
THETA
Y3 Y4#1 Y4 X
________ ________ ________ ________
Y3 0.500
Y4#1 0.000 0.000
Y4 0.000 0.000 0.500
X 0.000 0.000 0.000 0.000
ALPHA
I S X
________ ________ ________
3.000 1.000 0.000
BETA
I S X
________ ________ ________
I 0.000 0.000 0.400
S 0.000 0.000 0.300
X 0.000 0.000 0.000
PSI
I S X
________ ________ ________
I 1.000
S 0.000 0.500
X 0.000 0.000 1.000
POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
0.000 0.000
GAMMA(C)
I S X
________ ________ ________
C#1 0.000 0.000 1.000
C#2 0.000 0.000 0.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.32165851D+04 0.0000000 0.0000000 EM
2 -0.32121936D+04 4.3914287 0.0013652 FS
3 -0.32114579D+04 0.7356865 0.0002290 FS
4 -0.32114415D+04 0.0164969 0.0000051 FS
5 -0.32114382D+04 0.0032608 0.0000010 FS
6 -0.32114388D+04 -0.0005785 -0.0000002 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
X
C
Save file
ex8.3.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:53
Ending Time: 22:24:55
Elapsed Time: 00:00:02
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