Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
title:
this is an example of a GMM for a
continuous outcome using automatic
starting values and random starts
montecarlo:
names are y1-y4 x;
genclasses = c(2);
classes = c(2);
nobs = 500;
seed = 3454367;
nrep = 1;
save = ex8.1.dat;
analysis:
type = mixture;
model population:
%overall%
[x@0]; x@1;
y1-y4*.5;
i s | y1@0 y2@1 y3@2 y4@3;
i*1; s*.2;
c#1 on x*1;
i on x*.5;
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*.2;
c#1 on x*1;
i on x*.5;
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
continuous outcome using 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
Continuous
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-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
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
1.907 2.697 3.336 4.087 -0.060
Covariances
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 2.443
Y2 2.099 3.205
Y3 2.303 3.140 4.350
Y4 2.463 3.534 4.576 6.031
X 0.086 0.360 0.601 0.750 0.982
Correlations
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 1.000
Y2 0.750 1.000
Y3 0.706 0.841 1.000
Y4 0.642 0.804 0.894 1.000
X 0.055 0.203 0.291 0.308 1.000
MODEL FIT INFORMATION
Number of Free Parameters 15
Loglikelihood
H0 Value
Mean -3183.703
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -3183.703 -3183.703
0.980 0.000 -3183.703 -3183.703
0.950 0.000 -3183.703 -3183.703
0.900 0.000 -3183.703 -3183.703
0.800 0.000 -3183.703 -3183.703
0.700 0.000 -3183.703 -3183.703
0.500 0.000 -3183.703 -3183.703
0.300 0.000 -3183.703 -3183.703
0.200 0.000 -3183.703 -3183.703
0.100 0.000 -3183.703 -3183.703
0.050 0.000 -3183.703 -3183.703
0.020 0.000 -3183.703 -3183.703
0.010 0.000 -3183.703 -3183.703
Information Criteria
Akaike (AIC)
Mean 6397.407
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 6397.407 6397.407
0.980 0.000 6397.407 6397.407
0.950 0.000 6397.407 6397.407
0.900 0.000 6397.407 6397.407
0.800 0.000 6397.407 6397.407
0.700 0.000 6397.407 6397.407
0.500 0.000 6397.407 6397.407
0.300 0.000 6397.407 6397.407
0.200 0.000 6397.407 6397.407
0.100 0.000 6397.407 6397.407
0.050 0.000 6397.407 6397.407
0.020 0.000 6397.407 6397.407
0.010 0.000 6397.407 6397.407
Bayesian (BIC)
Mean 6460.626
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 6460.626 6460.626
0.980 0.000 6460.626 6460.626
0.950 0.000 6460.626 6460.626
0.900 0.000 6460.626 6460.626
0.800 0.000 6460.626 6460.626
0.700 0.000 6460.626 6460.626
0.500 0.000 6460.626 6460.626
0.300 0.000 6460.626 6460.626
0.200 0.000 6460.626 6460.626
0.100 0.000 6460.626 6460.626
0.050 0.000 6460.626 6460.626
0.020 0.000 6460.626 6460.626
0.010 0.000 6460.626 6460.626
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 6413.015
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 6413.015 6413.015
0.980 0.000 6413.015 6413.015
0.950 0.000 6413.015 6413.015
0.900 0.000 6413.015 6413.015
0.800 0.000 6413.015 6413.015
0.700 0.000 6413.015 6413.015
0.500 0.000 6413.015 6413.015
0.300 0.000 6413.015 6413.015
0.200 0.000 6413.015 6413.015
0.100 0.000 6413.015 6413.015
0.050 0.000 6413.015 6413.015
0.020 0.000 6413.015 6413.015
0.010 0.000 6413.015 6413.015
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 239.53368 0.47907
2 260.46632 0.52093
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 239.53371 0.47907
2 260.46629 0.52093
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 241 0.48200
2 259 0.51800
CLASSIFICATION QUALITY
Entropy 0.608
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.878 0.122
2 0.108 0.892
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.883 0.117
2 0.113 0.887
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 2.024 0.000
2 -2.061 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 0.500 0.4721 0.0000 0.1026 0.0008 1.000 1.000
S ON
X 0.300 0.3057 0.0000 0.0337 0.0000 1.000 1.000
S WITH
I 0.000 -0.0218 0.0000 0.0424 0.0005 1.000 0.000
Intercepts
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
I 1.000 0.8860 0.0000 0.0950 0.0130 1.000 1.000
S 0.500 0.5016 0.0000 0.0609 0.0000 1.000 1.000
Residual Variances
Y1 0.500 0.5744 0.0000 0.0655 0.0055 1.000 1.000
Y2 0.500 0.5751 0.0000 0.0452 0.0056 1.000 1.000
Y3 0.500 0.4435 0.0000 0.0471 0.0032 1.000 1.000
Y4 0.500 0.5651 0.0000 0.0811 0.0042 1.000 1.000
I 1.000 0.9606 0.0000 0.1497 0.0016 1.000 1.000
S 0.200 0.1747 0.0000 0.0226 0.0006 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 0.500 0.4721 0.0000 0.1026 0.0008 1.000 1.000
S ON
X 0.300 0.3057 0.0000 0.0337 0.0000 1.000 1.000
S WITH
I 0.000 -0.0218 0.0000 0.0424 0.0005 1.000 0.000
Intercepts
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
I 3.000 2.9431 0.0000 0.1473 0.0032 1.000 1.000
S 1.000 0.9497 0.0000 0.0407 0.0025 1.000 1.000
Residual Variances
Y1 0.500 0.5744 0.0000 0.0655 0.0055 1.000 1.000
Y2 0.500 0.5751 0.0000 0.0452 0.0056 1.000 1.000
Y3 0.500 0.4435 0.0000 0.0471 0.0032 1.000 1.000
Y4 0.500 0.5651 0.0000 0.0811 0.0042 1.000 1.000
I 1.000 0.9606 0.0000 0.1497 0.0016 1.000 1.000
S 0.200 0.1747 0.0000 0.0226 0.0006 1.000 1.000
Categorical Latent Variables
C#1 ON
X 1.000 0.7757 0.0000 0.2556 0.0503 1.000 1.000
Intercepts
C#1 0.000 -0.0488 0.0000 0.2025 0.0024 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.592E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
NU
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
I S X
________ ________ ________
Y1 0 0 0
Y2 0 0 0
Y3 0 0 0
Y4 0 0 0
X 0 0 0
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 1
Y2 0 2
Y3 0 0 3
Y4 0 0 0 4
X 0 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 Y2 Y3 Y4 X
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
I S X
________ ________ ________
Y1 0 0 0
Y2 0 0 0
Y3 0 0 0
Y4 0 0 0
X 0 0 0
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 1
Y2 0 2
Y3 0 0 3
Y4 0 0 0 4
X 0 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)
X
________
C#1 15
C#2 0
STARTING VALUES FOR LATENT CLASS 1
NU
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
I S X
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
Y3 1.000 2.000 0.000
Y4 1.000 3.000 0.000
X 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
X 0.000 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 0.500
S 0.000 0.000 0.300
X 0.000 0.000 0.000
PSI
I S X
________ ________ ________
I 1.000
S 0.000 0.200
X 0.000 0.000 0.500
STARTING VALUES FOR LATENT CLASS 2
NU
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
I S X
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
Y3 1.000 2.000 0.000
Y4 1.000 3.000 0.000
X 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
X 0.000 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 0.500
S 0.000 0.000 0.300
X 0.000 0.000 0.000
PSI
I S X
________ ________ ________
I 1.000
S 0.000 0.200
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)
X
________
C#1 1.000
C#2 0.000
POPULATION VALUES FOR LATENT CLASS 1
NU
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
I S X
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
Y3 1.000 2.000 0.000
Y4 1.000 3.000 0.000
X 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
X 0.000 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 0.500
S 0.000 0.000 0.300
X 0.000 0.000 0.000
PSI
I S X
________ ________ ________
I 1.000
S 0.000 0.200
X 0.000 0.000 1.000
POPULATION VALUES FOR LATENT CLASS 2
NU
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
I S X
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
Y3 1.000 2.000 0.000
Y4 1.000 3.000 0.000
X 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
X 0.000 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 0.500
S 0.000 0.000 0.300
X 0.000 0.000 0.000
PSI
I S X
________ ________ ________
I 1.000
S 0.000 0.200
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)
X
________
C#1 1.000
C#2 0.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.31907108D+04 0.0000000 0.0000000 EM
2 -0.31841268D+04 6.5839861 0.0020635 EM
3 -0.31840124D+04 0.1144477 0.0000359 EM
4 -0.31839346D+04 0.0777789 0.0000244 EM
5 -0.31838777D+04 0.0568433 0.0000179 EM
6 -0.31838356D+04 0.0421072 0.0000132 EM
7 -0.31838041D+04 0.0315174 0.0000099 EM
8 -0.31837803D+04 0.0237755 0.0000075 EM
9 -0.31837623D+04 0.0180374 0.0000057 EM
10 -0.31837486D+04 0.0137413 0.0000043 EM
11 -0.31837381D+04 0.0104992 0.0000033 EM
12 -0.31837300D+04 0.0080389 0.0000025 EM
13 -0.31837239D+04 0.0061654 0.0000019 EM
14 -0.31837191D+04 0.0047341 0.0000015 EM
15 -0.31837155D+04 0.0036383 0.0000011 EM
16 -0.31837127D+04 0.0027984 0.0000009 EM
17 -0.31837105D+04 0.0021537 0.0000007 EM
18 -0.31837089D+04 0.0016583 0.0000005 EM
19 -0.31837076D+04 0.0012774 0.0000004 EM
20 -0.31837066D+04 0.0009844 0.0000003 EM
21 -0.31837059D+04 0.0007588 0.0000002 EM
22 -0.31837053D+04 0.0005850 0.0000002 EM
23 -0.31837048D+04 0.0004512 0.0000001 EM
24 -0.31837045D+04 0.0003480 0.0000001 EM
25 -0.31837042D+04 0.0002685 0.0000001 EM
26 -0.31837040D+04 0.0002072 0.0000001 EM
27 -0.31837038D+04 0.0001599 0.0000001 EM
28 -0.31837037D+04 0.0001234 0.0000000 EM
29 -0.31837036D+04 0.0000953 0.0000000 EM
30 -0.31837036D+04 0.0000736 0.0000000 EM
31 -0.31837035D+04 0.0000569 0.0000000 EM
32 -0.31837034D+04 0.0000439 0.0000000 EM
33 -0.31837034D+04 0.0000339 0.0000000 EM
34 -0.31837034D+04 0.0000261 0.0000000 EM
35 -0.31837033D+04 0.0000796 0.0000000 FS
36 -0.31837033D+04 0.0000077 0.0000000 FS
37 -0.31837033D+04 0.0000010 0.0000000 FS
38 -0.31837033D+04 0.0000002 0.0000000 FS
39 -0.31837033D+04 0.0000001 0.0000000 FS
40 -0.31837033D+04 0.0000000 0.0000000 EM
41 -0.31837033D+04 0.0000000 0.0000000 EM
42 -0.31837033D+04 0.0000000 0.0000000 EM
43 -0.31837033D+04 0.0000000 0.0000000 EM
44 -0.31837033D+04 0.0000000 0.0000000 EM
45 -0.31837033D+04 0.0000000 0.0000000 EM
46 -0.31837033D+04 0.0000000 0.0000000 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
X
C
Save file
ex8.1.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:42
Ending Time: 22:24:42
Elapsed Time: 00:00:00
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