Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:22 PM
INPUT INSTRUCTIONS
title:
this is an example of a factor mixture analysis
with continuous latent class indicators
montecarlo:
names are y1-y8;
genclasses = c(2);
classes = c(2);
nobs = 2000;
seed = 3454367;
nrep = 1;
save = ex4.4.dat;
model population:
%overall%
f1 by y1-y4*1;
f2 by y5-y8*1;
y1-y8*.5;
f1-f2@1;
[f1-f2@0];
[c#1*0];
%c#1%
f1 by y1-y4*1;
f2 by y5-y8*.5;
[y1*2 y2*2 y3*2 y4*2 y5*-1 y6*-1 y7*-1 y8*-1];
%c#2%
f1 by y1-y4*.5;
f2 by y5-y8*1;
[y1*-1 y2*-1 y3*-1 y4*-1 y5*2 y6*2 y7*2 y8*2];
analysis:
type = mixture;
model:
%overall%
f1 by y1-y4*1;
f2 by y5-y8*1;
y1-y8*.5;
f1-f2@1;
[f1-f2@0];
[c#1*0];
%c#1%
f1 by y1-y4*1;
f2 by y5-y8*.5;
[y1*2 y2*2 y3*2 y4*2 y5*-1 y6*-1 y7*-1 y8*-1];
%c#2%
f1 by y1-y4*.5;
f2 by y5-y8*1;
[y1*-1 y2*-1 y3*-1 y4*-1 y5*2 y6*2 y7*2 y8*2];
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a factor mixture analysis
with continuous latent class indicators
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 2000
Number of replications
Requested 1
Completed 1
Value of seed 3454367
Number of dependent variables 8
Number of independent variables 0
Number of continuous latent variables 2
Number of categorical latent variables 1
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5 Y6
Y7 Y8
Continuous latent variables
F1 F2
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 Y5
________ ________ ________ ________ ________
0.504 0.478 0.515 0.512 0.459
Means
Y6 Y7 Y8
________ ________ ________
0.476 0.464 0.418
Covariances
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 3.347
Y2 2.785 3.259
Y3 2.839 2.806 3.368
Y4 2.807 2.793 2.861 3.326
Y5 -2.211 -2.205 -2.204 -2.217 3.309
Y6 -2.160 -2.129 -2.174 -2.180 2.771
Y7 -2.194 -2.141 -2.157 -2.185 2.788
Y8 -2.217 -2.171 -2.202 -2.213 2.781
Covariances
Y6 Y7 Y8
________ ________ ________
Y6 3.194
Y7 2.753 3.298
Y8 2.740 2.798 3.306
Correlations
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.843 1.000
Y3 0.846 0.847 1.000
Y4 0.841 0.848 0.855 1.000
Y5 -0.664 -0.671 -0.660 -0.668 1.000
Y6 -0.661 -0.660 -0.663 -0.669 0.852
Y7 -0.660 -0.653 -0.647 -0.660 0.844
Y8 -0.666 -0.661 -0.660 -0.667 0.841
Correlations
Y6 Y7 Y8
________ ________ ________
Y6 1.000
Y7 0.848 1.000
Y8 0.843 0.848 1.000
MODEL FIT INFORMATION
Number of Free Parameters 42
Loglikelihood
H0 Value
Mean -21822.867
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -21822.867 -21822.867
0.980 0.000 -21822.867 -21822.867
0.950 0.000 -21822.867 -21822.867
0.900 0.000 -21822.867 -21822.867
0.800 0.000 -21822.867 -21822.867
0.700 0.000 -21822.867 -21822.867
0.500 0.000 -21822.867 -21822.867
0.300 0.000 -21822.867 -21822.867
0.200 0.000 -21822.867 -21822.867
0.100 0.000 -21822.867 -21822.867
0.050 0.000 -21822.867 -21822.867
0.020 0.000 -21822.867 -21822.867
0.010 0.000 -21822.867 -21822.867
Information Criteria
Akaike (AIC)
Mean 43729.735
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 43729.735 43729.735
0.980 0.000 43729.735 43729.735
0.950 0.000 43729.735 43729.735
0.900 0.000 43729.735 43729.735
0.800 0.000 43729.735 43729.735
0.700 0.000 43729.735 43729.735
0.500 0.000 43729.735 43729.735
0.300 0.000 43729.735 43729.735
0.200 0.000 43729.735 43729.735
0.100 0.000 43729.735 43729.735
0.050 0.000 43729.735 43729.735
0.020 0.000 43729.735 43729.735
0.010 0.000 43729.735 43729.735
Bayesian (BIC)
Mean 43964.972
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 43964.972 43964.972
0.980 0.000 43964.972 43964.972
0.950 0.000 43964.972 43964.972
0.900 0.000 43964.972 43964.972
0.800 0.000 43964.972 43964.972
0.700 0.000 43964.972 43964.972
0.500 0.000 43964.972 43964.972
0.300 0.000 43964.972 43964.972
0.200 0.000 43964.972 43964.972
0.100 0.000 43964.972 43964.972
0.050 0.000 43964.972 43964.972
0.020 0.000 43964.972 43964.972
0.010 0.000 43964.972 43964.972
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 43831.536
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 43831.536 43831.536
0.980 0.000 43831.536 43831.536
0.950 0.000 43831.536 43831.536
0.900 0.000 43831.536 43831.536
0.800 0.000 43831.536 43831.536
0.700 0.000 43831.536 43831.536
0.500 0.000 43831.536 43831.536
0.300 0.000 43831.536 43831.536
0.200 0.000 43831.536 43831.536
0.100 0.000 43831.536 43831.536
0.050 0.000 43831.536 43831.536
0.020 0.000 43831.536 43831.536
0.010 0.000 43831.536 43831.536
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 1009.33383 0.50467
2 990.66617 0.49533
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 1009.33383 0.50467
2 990.66617 0.49533
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 1012 0.50600
2 988 0.49400
CLASSIFICATION QUALITY
Entropy 0.974
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.992 0.008
2 0.006 0.994
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.994 0.006
2 0.008 0.992
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 5.187 0.000
2 -4.777 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Latent Class 1
F1 BY
Y1 1.000 0.9814 0.0000 0.0340 0.0003 1.000 1.000
Y2 1.000 0.9857 0.0000 0.0342 0.0002 1.000 1.000
Y3 1.000 1.0042 0.0000 0.0374 0.0000 1.000 1.000
Y4 1.000 1.0055 0.0000 0.0328 0.0000 1.000 1.000
F2 BY
Y5 0.500 0.4930 0.0000 0.0315 0.0000 1.000 1.000
Y6 0.500 0.4870 0.0000 0.0316 0.0002 1.000 1.000
Y7 0.500 0.4679 0.0000 0.0317 0.0010 1.000 1.000
Y8 0.500 0.4697 0.0000 0.0329 0.0009 1.000 1.000
F2 WITH
F1 0.000 -0.0032 0.0000 0.0303 0.0000 1.000 0.000
Means
F1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
F2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Intercepts
Y1 2.000 1.9759 0.0000 0.0399 0.0006 1.000 1.000
Y2 2.000 1.9348 0.0000 0.0393 0.0043 1.000 1.000
Y3 2.000 1.9933 0.0000 0.0399 0.0000 1.000 1.000
Y4 2.000 1.9894 0.0000 0.0398 0.0001 1.000 1.000
Y5 -1.000 -1.0047 0.0000 0.0275 0.0000 1.000 1.000
Y6 -1.000 -0.9677 0.0000 0.0270 0.0010 1.000 1.000
Y7 -1.000 -0.9978 0.0000 0.0271 0.0000 1.000 1.000
Y8 -1.000 -1.0369 0.0000 0.0278 0.0014 1.000 1.000
Variances
F1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
F2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Residual Variances
Y1 0.500 0.5463 0.0000 0.0222 0.0021 0.000 1.000
Y2 0.500 0.5077 0.0000 0.0225 0.0001 1.000 1.000
Y3 0.500 0.4867 0.0000 0.0230 0.0002 1.000 1.000
Y4 0.500 0.4943 0.0000 0.0207 0.0000 1.000 1.000
Y5 0.500 0.5110 0.0000 0.0218 0.0001 1.000 1.000
Y6 0.500 0.4729 0.0000 0.0214 0.0007 1.000 1.000
Y7 0.500 0.5029 0.0000 0.0217 0.0000 1.000 1.000
Y8 0.500 0.5314 0.0000 0.0224 0.0010 1.000 1.000
Latent Class 2
F1 BY
Y1 0.500 0.4669 0.0000 0.0332 0.0011 1.000 1.000
Y2 0.500 0.4497 0.0000 0.0327 0.0025 1.000 1.000
Y3 0.500 0.5420 0.0000 0.0324 0.0018 1.000 1.000
Y4 0.500 0.4458 0.0000 0.0336 0.0029 1.000 1.000
F2 BY
Y5 1.000 0.9959 0.0000 0.0355 0.0000 1.000 1.000
Y6 1.000 0.9841 0.0000 0.0346 0.0003 1.000 1.000
Y7 1.000 1.0107 0.0000 0.0339 0.0001 1.000 1.000
Y8 1.000 1.0106 0.0000 0.0346 0.0001 1.000 1.000
F2 WITH
F1 0.000 -0.0032 0.0000 0.0303 0.0000 1.000 0.000
Means
F1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
F2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Intercepts
Y1 -1.000 -0.9953 0.0000 0.0278 0.0000 1.000 1.000
Y2 -1.000 -1.0052 0.0000 0.0272 0.0000 1.000 1.000
Y3 -1.000 -0.9912 0.0000 0.0285 0.0001 1.000 1.000
Y4 -1.000 -0.9928 0.0000 0.0270 0.0001 1.000 1.000
Y5 2.000 1.9509 0.0000 0.0404 0.0024 1.000 1.000
Y6 2.000 1.9459 0.0000 0.0391 0.0029 1.000 1.000
Y7 2.000 1.9541 0.0000 0.0402 0.0021 1.000 1.000
Y8 2.000 1.9005 0.0000 0.0407 0.0099 0.000 1.000
Variances
F1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
F2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Residual Variances
Y1 0.500 0.5463 0.0000 0.0222 0.0021 0.000 1.000
Y2 0.500 0.5077 0.0000 0.0225 0.0001 1.000 1.000
Y3 0.500 0.4867 0.0000 0.0230 0.0002 1.000 1.000
Y4 0.500 0.4943 0.0000 0.0207 0.0000 1.000 1.000
Y5 0.500 0.5110 0.0000 0.0218 0.0001 1.000 1.000
Y6 0.500 0.4729 0.0000 0.0214 0.0007 1.000 1.000
Y7 0.500 0.5029 0.0000 0.0217 0.0000 1.000 1.000
Y8 0.500 0.5314 0.0000 0.0224 0.0010 1.000 1.000
Categorical Latent Variables
Means
C#1 0.000 0.0187 0.0000 0.0454 0.0003 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.749E-03
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
NU
Y6 Y7 Y8
________ ________ ________
6 7 8
LAMBDA
F1 F2
________ ________
Y1 9 0
Y2 10 0
Y3 11 0
Y4 12 0
Y5 0 13
Y6 0 14
Y7 0 15
Y8 0 16
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 17
Y2 0 18
Y3 0 0 19
Y4 0 0 0 20
Y5 0 0 0 0 21
Y6 0 0 0 0 0
Y7 0 0 0 0 0
Y8 0 0 0 0 0
THETA
Y6 Y7 Y8
________ ________ ________
Y6 22
Y7 0 23
Y8 0 0 24
ALPHA
F1 F2
________ ________
0 0
BETA
F1 F2
________ ________
F1 0 0
F2 0 0
PSI
F1 F2
________ ________
F1 0
F2 25 0
PARAMETER SPECIFICATION FOR LATENT CLASS 2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
26 27 28 29 30
NU
Y6 Y7 Y8
________ ________ ________
31 32 33
LAMBDA
F1 F2
________ ________
Y1 34 0
Y2 35 0
Y3 36 0
Y4 37 0
Y5 0 38
Y6 0 39
Y7 0 40
Y8 0 41
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 17
Y2 0 18
Y3 0 0 19
Y4 0 0 0 20
Y5 0 0 0 0 21
Y6 0 0 0 0 0
Y7 0 0 0 0 0
Y8 0 0 0 0 0
THETA
Y6 Y7 Y8
________ ________ ________
Y6 22
Y7 0 23
Y8 0 0 24
ALPHA
F1 F2
________ ________
0 0
BETA
F1 F2
________ ________
F1 0 0
F2 0 0
PSI
F1 F2
________ ________
F1 0
F2 25 0
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
42 0
STARTING VALUES FOR LATENT CLASS 1
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
2.000 2.000 2.000 2.000 -1.000
NU
Y6 Y7 Y8
________ ________ ________
-1.000 -1.000 -1.000
LAMBDA
F1 F2
________ ________
Y1 1.000 0.000
Y2 1.000 0.000
Y3 1.000 0.000
Y4 1.000 0.000
Y5 0.000 0.500
Y6 0.000 0.500
Y7 0.000 0.500
Y8 0.000 0.500
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
Y5 0.000 0.000 0.000 0.000 0.500
Y6 0.000 0.000 0.000 0.000 0.000
Y7 0.000 0.000 0.000 0.000 0.000
Y8 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Y7 Y8
________ ________ ________
Y6 0.500
Y7 0.000 0.500
Y8 0.000 0.000 0.500
ALPHA
F1 F2
________ ________
0.000 0.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 0.000 0.000
PSI
F1 F2
________ ________
F1 1.000
F2 0.000 1.000
STARTING VALUES FOR LATENT CLASS 2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
-1.000 -1.000 -1.000 -1.000 2.000
NU
Y6 Y7 Y8
________ ________ ________
2.000 2.000 2.000
LAMBDA
F1 F2
________ ________
Y1 0.500 0.000
Y2 0.500 0.000
Y3 0.500 0.000
Y4 0.500 0.000
Y5 0.000 1.000
Y6 0.000 1.000
Y7 0.000 1.000
Y8 0.000 1.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
Y5 0.000 0.000 0.000 0.000 0.500
Y6 0.000 0.000 0.000 0.000 0.000
Y7 0.000 0.000 0.000 0.000 0.000
Y8 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Y7 Y8
________ ________ ________
Y6 0.500
Y7 0.000 0.500
Y8 0.000 0.000 0.500
ALPHA
F1 F2
________ ________
0.000 0.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 0.000 0.000
PSI
F1 F2
________ ________
F1 1.000
F2 0.000 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
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
2.000 2.000 2.000 2.000 -1.000
NU
Y6 Y7 Y8
________ ________ ________
-1.000 -1.000 -1.000
LAMBDA
F1 F2
________ ________
Y1 1.000 0.000
Y2 1.000 0.000
Y3 1.000 0.000
Y4 1.000 0.000
Y5 0.000 0.500
Y6 0.000 0.500
Y7 0.000 0.500
Y8 0.000 0.500
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
Y5 0.000 0.000 0.000 0.000 0.500
Y6 0.000 0.000 0.000 0.000 0.000
Y7 0.000 0.000 0.000 0.000 0.000
Y8 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Y7 Y8
________ ________ ________
Y6 0.500
Y7 0.000 0.500
Y8 0.000 0.000 0.500
ALPHA
F1 F2
________ ________
0.000 0.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 0.000 0.000
PSI
F1 F2
________ ________
F1 1.000
F2 0.000 1.000
POPULATION VALUES FOR LATENT CLASS 2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
-1.000 -1.000 -1.000 -1.000 2.000
NU
Y6 Y7 Y8
________ ________ ________
2.000 2.000 2.000
LAMBDA
F1 F2
________ ________
Y1 0.500 0.000
Y2 0.500 0.000
Y3 0.500 0.000
Y4 0.500 0.000
Y5 0.000 1.000
Y6 0.000 1.000
Y7 0.000 1.000
Y8 0.000 1.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
Y5 0.000 0.000 0.000 0.000 0.500
Y6 0.000 0.000 0.000 0.000 0.000
Y7 0.000 0.000 0.000 0.000 0.000
Y8 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Y7 Y8
________ ________ ________
Y6 0.500
Y7 0.000 0.500
Y8 0.000 0.000 0.500
ALPHA
F1 F2
________ ________
0.000 0.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 0.000 0.000
PSI
F1 F2
________ ________
F1 1.000
F2 0.000 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 -0.21841744D+05 0.0000000 0.0000000 EM
2 -0.21822882D+05 18.8618179 0.0008636 EM
3 -0.21822868D+05 0.0138847 0.0000006 EM
4 -0.21822867D+05 0.0004788 0.0000000 EM
5 -0.21822867D+05 0.0000526 0.0000000 EM
6 -0.21822867D+05 0.0000078 0.0000000 EM
7 -0.21822867D+05 0.0000012 0.0000000 EM
8 -0.21822867D+05 0.0000002 0.0000000 EM
9 -0.21822867D+05 0.0000000 0.0000000 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
Y5
Y6
Y7
Y8
C
Save file
ex4.4.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:22:51
Ending Time: 22:22:52
Elapsed Time: 00:00:01
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