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
montecarlo:
NAMES = u1-u4 x1-x10;
generate = u1-u4(1);
categorical = u1-u4;
genclasses = c(2);
classes = c(2);
nobs = 500;
seed = 3454367;
nrep = 1;
save = ex7.3.dat;
analysis:
type = mixture;
model population:
%overall%
[c#1*1];
x1-x10*1;
%c#1%
[u1$1*2 u2$1*2 u3$1*-2 u4$1*-2];
[x1-x2*-2 x3-x4*-1 x5-x6*0 x7-x8*1 x9-x10*2];
%c#2%
[u1$1*-2 u2$1*-2 u3$1*2 u4$1*2];
[x1-x2*2 x3-x4*1 x5-x6*0 x7-x8*-1 x9-x10*-2];
model:
%overall%
[c#1*1];
x1-x10*1;
%c#1%
[u1$1*2 u2$1*2 u3$1*-2 u4$1*-2];
[x1-x2*-2 x3-x4*-1 x5-x6*0 x7-x8*1 x9-x10*2];
%c#2%
[u1$1*-2 u2$1*-2 u3$1*2 u4$1*2];
[x1-x2*2 x3-x4*1 x5-x6*0 x7-x8*-1 x9-x10*-2];
output:
tech8 tech9;
*** WARNING in MODEL command
All variables are uncorrelated with all other variables within class.
Check that this is what is intended.
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
this is an example of a LCA with binary
latent class indicators using automatic
starting values with 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 14
Number of independent variables 0
Number of continuous latent variables 0
Number of categorical latent variables 1
Observed dependent variables
Continuous
X1 X2 X3 X4 X5 X6
X7 X8 X9 X10
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-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
X1 X2 X3 X4 X5
________ ________ ________ ________ ________
-0.987 -0.993 -0.464 -0.508 -0.004
Means
X6 X7 X8 X9 X10
________ ________ ________ ________ ________
-0.030 0.483 0.439 0.940 0.945
Covariances
X1 X2 X3 X4 X5
________ ________ ________ ________ ________
X1 4.303
X2 3.173 4.120
X3 1.585 1.526 1.790
X4 1.475 1.455 0.686 1.590
X5 0.132 0.125 -0.038 0.078 1.067
X6 -0.033 0.052 -0.044 -0.011 0.024
X7 -1.426 -1.431 -0.761 -0.650 -0.116
X8 -1.542 -1.546 -0.844 -0.658 -0.115
X9 -3.113 -3.013 -1.542 -1.437 -0.126
X10 -3.263 -3.249 -1.651 -1.506 -0.116
Covariances
X6 X7 X8 X9 X10
________ ________ ________ ________ ________
X6 0.928
X7 -0.072 1.632
X8 0.025 0.668 1.727
X9 -0.011 1.376 1.469 3.823
X10 -0.050 1.364 1.581 3.092 4.289
Correlations
X1 X2 X3 X4 X5
________ ________ ________ ________ ________
X1 1.000
X2 0.754 1.000
X3 0.571 0.562 1.000
X4 0.564 0.568 0.407 1.000
X5 0.062 0.060 -0.028 0.060 1.000
X6 -0.016 0.026 -0.034 -0.009 0.024
X7 -0.538 -0.552 -0.445 -0.403 -0.088
X8 -0.566 -0.579 -0.480 -0.397 -0.085
X9 -0.768 -0.759 -0.590 -0.583 -0.062
X10 -0.759 -0.773 -0.596 -0.577 -0.054
Correlations
X6 X7 X8 X9 X10
________ ________ ________ ________ ________
X6 1.000
X7 -0.059 1.000
X8 0.019 0.398 1.000
X9 -0.006 0.551 0.572 1.000
X10 -0.025 0.516 0.581 0.764 1.000
MODEL FIT INFORMATION
Number of Free Parameters 39
Loglikelihood
H0 Value
Mean -8071.281
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -8071.281 -8071.281
0.980 0.000 -8071.281 -8071.281
0.950 0.000 -8071.281 -8071.281
0.900 0.000 -8071.281 -8071.281
0.800 0.000 -8071.281 -8071.281
0.700 0.000 -8071.281 -8071.281
0.500 0.000 -8071.281 -8071.281
0.300 0.000 -8071.281 -8071.281
0.200 0.000 -8071.281 -8071.281
0.100 0.000 -8071.281 -8071.281
0.050 0.000 -8071.281 -8071.281
0.020 0.000 -8071.281 -8071.281
0.010 0.000 -8071.281 -8071.281
Information Criteria
Akaike (AIC)
Mean 16220.562
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 16220.562 16220.562
0.980 0.000 16220.562 16220.562
0.950 0.000 16220.562 16220.562
0.900 0.000 16220.562 16220.562
0.800 0.000 16220.562 16220.562
0.700 0.000 16220.562 16220.562
0.500 0.000 16220.562 16220.562
0.300 0.000 16220.562 16220.562
0.200 0.000 16220.562 16220.562
0.100 0.000 16220.562 16220.562
0.050 0.000 16220.562 16220.562
0.020 0.000 16220.562 16220.562
0.010 0.000 16220.562 16220.562
Bayesian (BIC)
Mean 16384.932
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 16384.932 16384.932
0.980 0.000 16384.932 16384.932
0.950 0.000 16384.932 16384.932
0.900 0.000 16384.932 16384.932
0.800 0.000 16384.932 16384.932
0.700 0.000 16384.932 16384.932
0.500 0.000 16384.932 16384.932
0.300 0.000 16384.932 16384.932
0.200 0.000 16384.932 16384.932
0.100 0.000 16384.932 16384.932
0.050 0.000 16384.932 16384.932
0.020 0.000 16384.932 16384.932
0.010 0.000 16384.932 16384.932
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 16261.143
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 16261.143 16261.143
0.980 0.000 16261.143 16261.143
0.950 0.000 16261.143 16261.143
0.900 0.000 16261.143 16261.143
0.800 0.000 16261.143 16261.143
0.700 0.000 16261.143 16261.143
0.500 0.000 16261.143 16261.143
0.300 0.000 16261.143 16261.143
0.200 0.000 16261.143 16261.143
0.100 0.000 16261.143 16261.143
0.050 0.000 16261.143 16261.143
0.020 0.000 16261.143 16261.143
0.010 0.000 16261.143 16261.143
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Mean 7.597
Std Dev 0.000
Degrees of freedom 6
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 0.872 7.597
0.980 1.000 1.134 7.597
0.950 1.000 1.635 7.597
0.900 1.000 2.204 7.597
0.800 1.000 3.070 7.597
0.700 1.000 3.828 7.597
0.500 1.000 5.348 7.597
0.300 1.000 7.231 7.597
0.200 0.000 8.558 7.597
0.100 0.000 10.645 7.597
0.050 0.000 12.592 7.597
0.020 0.000 15.033 7.597
0.010 0.000 16.812 7.597
Likelihood Ratio Chi-Square
Mean 6.993
Std Dev 0.000
Degrees of freedom 6
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 0.872 6.993
0.980 1.000 1.134 6.993
0.950 1.000 1.635 6.993
0.900 1.000 2.204 6.993
0.800 1.000 3.070 6.993
0.700 1.000 3.828 6.993
0.500 1.000 5.348 6.993
0.300 0.000 7.231 6.993
0.200 0.000 8.558 6.993
0.100 0.000 10.645 6.993
0.050 0.000 12.592 6.993
0.020 0.000 15.033 6.993
0.010 0.000 16.812 6.993
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 367.00000 0.73400
2 133.00000 0.26600
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 367.00000 0.73400
2 133.00000 0.26600
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 367 0.73400
2 133 0.26600
CLASSIFICATION QUALITY
Entropy 1.000
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 1.000 0.000
2 0.000 1.000
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 1.000 0.000
2 0.000 1.000
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 13.816 0.000
2 -13.816 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Latent Class 1
Means
X1 -2.000 -2.0608 0.0000 0.0554 0.0037 1.000 1.000
X2 -2.000 -2.0644 0.0000 0.0504 0.0042 1.000 1.000
X3 -1.000 -0.9884 0.0000 0.0546 0.0001 1.000 1.000
X4 -1.000 -0.9948 0.0000 0.0515 0.0000 1.000 1.000
X5 0.000 -0.0396 0.0000 0.0527 0.0016 1.000 0.000
X6 0.000 -0.0368 0.0000 0.0496 0.0014 1.000 0.000
X7 1.000 0.9563 0.0000 0.0509 0.0019 1.000 1.000
X8 1.000 0.9667 0.0000 0.0527 0.0011 1.000 1.000
X9 2.000 1.9576 0.0000 0.0507 0.0018 1.000 1.000
X10 2.000 2.0433 0.0000 0.0518 0.0019 1.000 1.000
Thresholds
U1$1 2.000 2.0195 0.0000 0.1623 0.0004 1.000 1.000
U2$1 2.000 2.0733 0.0000 0.1657 0.0054 1.000 1.000
U3$1 -2.000 -2.0733 0.0000 0.1657 0.0054 1.000 1.000
U4$1 -2.000 -1.9428 0.0000 0.1577 0.0033 1.000 1.000
Variances
X1 1.000 1.1187 0.0000 0.0730 0.0141 1.000 1.000
X2 1.000 0.9514 0.0000 0.0570 0.0024 1.000 1.000
X3 1.000 1.0312 0.0000 0.0593 0.0010 1.000 1.000
X4 1.000 0.9370 0.0000 0.0583 0.0040 1.000 1.000
X5 1.000 1.0638 0.0000 0.0675 0.0041 1.000 1.000
X6 1.000 0.9277 0.0000 0.0556 0.0052 1.000 1.000
X7 1.000 1.0126 0.0000 0.0680 0.0002 1.000 1.000
X8 1.000 0.9604 0.0000 0.0598 0.0016 1.000 1.000
X9 1.000 0.9678 0.0000 0.0572 0.0010 1.000 1.000
X10 1.000 0.9601 0.0000 0.0556 0.0016 1.000 1.000
Latent Class 2
Means
X1 2.000 1.9776 0.0000 0.0910 0.0005 1.000 1.000
X2 2.000 1.9641 0.0000 0.0869 0.0013 1.000 1.000
X3 1.000 0.9826 0.0000 0.0802 0.0003 1.000 1.000
X4 1.000 0.8343 0.0000 0.0793 0.0275 0.000 1.000
X5 0.000 0.0951 0.0000 0.0943 0.0090 1.000 0.000
X6 0.000 -0.0106 0.0000 0.0864 0.0001 1.000 0.000
X7 -1.000 -0.8246 0.0000 0.0943 0.0308 1.000 1.000
X8 -1.000 -1.0154 0.0000 0.0776 0.0002 1.000 1.000
X9 -2.000 -1.8663 0.0000 0.0882 0.0179 1.000 1.000
X10 -2.000 -2.0858 0.0000 0.0821 0.0074 1.000 1.000
Thresholds
U1$1 -2.000 -2.0626 0.0000 0.2741 0.0039 1.000 1.000
U2$1 -2.000 -1.9204 0.0000 0.2597 0.0063 1.000 1.000
U3$1 2.000 2.2225 0.0000 0.2920 0.0495 1.000 1.000
U4$1 2.000 2.3109 0.0000 0.3027 0.0966 1.000 1.000
Variances
X1 1.000 1.1187 0.0000 0.0730 0.0141 1.000 1.000
X2 1.000 0.9514 0.0000 0.0570 0.0024 1.000 1.000
X3 1.000 1.0312 0.0000 0.0593 0.0010 1.000 1.000
X4 1.000 0.9370 0.0000 0.0583 0.0040 1.000 1.000
X5 1.000 1.0638 0.0000 0.0675 0.0041 1.000 1.000
X6 1.000 0.9277 0.0000 0.0556 0.0052 1.000 1.000
X7 1.000 1.0126 0.0000 0.0680 0.0002 1.000 1.000
X8 1.000 0.9604 0.0000 0.0598 0.0016 1.000 1.000
X9 1.000 0.9678 0.0000 0.0572 0.0010 1.000 1.000
X10 1.000 0.9601 0.0000 0.0556 0.0016 1.000 1.000
Categorical Latent Variables
Means
C#1 1.000 1.0150 0.0000 0.1012 0.0002 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.224E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
NU
X1 X2 X3 X4 X5
________ ________ ________ ________ ________
1 2 3 4 5
NU
X6 X7 X8 X9 X10
________ ________ ________ ________ ________
6 7 8 9 10
THETA
X1 X2 X3 X4 X5
________ ________ ________ ________ ________
X1 11
X2 0 12
X3 0 0 13
X4 0 0 0 14
X5 0 0 0 0 15
X6 0 0 0 0 0
X7 0 0 0 0 0
X8 0 0 0 0 0
X9 0 0 0 0 0
X10 0 0 0 0 0
THETA
X6 X7 X8 X9 X10
________ ________ ________ ________ ________
X6 16
X7 0 17
X8 0 0 18
X9 0 0 0 19
X10 0 0 0 0 20
PARAMETER SPECIFICATION FOR LATENT CLASS 2
NU
X1 X2 X3 X4 X5
________ ________ ________ ________ ________
21 22 23 24 25
NU
X6 X7 X8 X9 X10
________ ________ ________ ________ ________
26 27 28 29 30
THETA
X1 X2 X3 X4 X5
________ ________ ________ ________ ________
X1 11
X2 0 12
X3 0 0 13
X4 0 0 0 14
X5 0 0 0 0 15
X6 0 0 0 0 0
X7 0 0 0 0 0
X8 0 0 0 0 0
X9 0 0 0 0 0
X10 0 0 0 0 0
THETA
X6 X7 X8 X9 X10
________ ________ ________ ________ ________
X6 16
X7 0 17
X8 0 0 18
X9 0 0 0 19
X10 0 0 0 0 20
PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
31 32 33 34
TAU(U) FOR LATENT CLASS 2
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
35 36 37 38
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
39 0
STARTING VALUES FOR LATENT CLASS 1
NU
X1 X2 X3 X4 X5
________ ________ ________ ________ ________
-2.000 -2.000 -1.000 -1.000 0.000
NU
X6 X7 X8 X9 X10
________ ________ ________ ________ ________
0.000 1.000 1.000 2.000 2.000
THETA
X1 X2 X3 X4 X5
________ ________ ________ ________ ________
X1 1.000
X2 0.000 1.000
X3 0.000 0.000 1.000
X4 0.000 0.000 0.000 1.000
X5 0.000 0.000 0.000 0.000 1.000
X6 0.000 0.000 0.000 0.000 0.000
X7 0.000 0.000 0.000 0.000 0.000
X8 0.000 0.000 0.000 0.000 0.000
X9 0.000 0.000 0.000 0.000 0.000
X10 0.000 0.000 0.000 0.000 0.000
THETA
X6 X7 X8 X9 X10
________ ________ ________ ________ ________
X6 1.000
X7 0.000 1.000
X8 0.000 0.000 1.000
X9 0.000 0.000 0.000 1.000
X10 0.000 0.000 0.000 0.000 1.000
STARTING VALUES FOR LATENT CLASS 2
NU
X1 X2 X3 X4 X5
________ ________ ________ ________ ________
2.000 2.000 1.000 1.000 0.000
NU
X6 X7 X8 X9 X10
________ ________ ________ ________ ________
0.000 -1.000 -1.000 -2.000 -2.000
THETA
X1 X2 X3 X4 X5
________ ________ ________ ________ ________
X1 1.000
X2 0.000 1.000
X3 0.000 0.000 1.000
X4 0.000 0.000 0.000 1.000
X5 0.000 0.000 0.000 0.000 1.000
X6 0.000 0.000 0.000 0.000 0.000
X7 0.000 0.000 0.000 0.000 0.000
X8 0.000 0.000 0.000 0.000 0.000
X9 0.000 0.000 0.000 0.000 0.000
X10 0.000 0.000 0.000 0.000 0.000
THETA
X6 X7 X8 X9 X10
________ ________ ________ ________ ________
X6 1.000
X7 0.000 1.000
X8 0.000 0.000 1.000
X9 0.000 0.000 0.000 1.000
X10 0.000 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
________ ________ ________ ________
2.000 2.000 -2.000 -2.000
TAU(U) FOR LATENT CLASS 2
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
-2.000 -2.000 2.000 2.000
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
1.000 0.000
POPULATION VALUES FOR LATENT CLASS 1
NU
X1 X2 X3 X4 X5
________ ________ ________ ________ ________
-2.000 -2.000 -1.000 -1.000 0.000
NU
X6 X7 X8 X9 X10
________ ________ ________ ________ ________
0.000 1.000 1.000 2.000 2.000
THETA
X1 X2 X3 X4 X5
________ ________ ________ ________ ________
X1 1.000
X2 0.000 1.000
X3 0.000 0.000 1.000
X4 0.000 0.000 0.000 1.000
X5 0.000 0.000 0.000 0.000 1.000
X6 0.000 0.000 0.000 0.000 0.000
X7 0.000 0.000 0.000 0.000 0.000
X8 0.000 0.000 0.000 0.000 0.000
X9 0.000 0.000 0.000 0.000 0.000
X10 0.000 0.000 0.000 0.000 0.000
THETA
X6 X7 X8 X9 X10
________ ________ ________ ________ ________
X6 1.000
X7 0.000 1.000
X8 0.000 0.000 1.000
X9 0.000 0.000 0.000 1.000
X10 0.000 0.000 0.000 0.000 1.000
POPULATION VALUES FOR LATENT CLASS 2
NU
X1 X2 X3 X4 X5
________ ________ ________ ________ ________
2.000 2.000 1.000 1.000 0.000
NU
X6 X7 X8 X9 X10
________ ________ ________ ________ ________
0.000 -1.000 -1.000 -2.000 -2.000
THETA
X1 X2 X3 X4 X5
________ ________ ________ ________ ________
X1 1.000
X2 0.000 1.000
X3 0.000 0.000 1.000
X4 0.000 0.000 0.000 1.000
X5 0.000 0.000 0.000 0.000 1.000
X6 0.000 0.000 0.000 0.000 0.000
X7 0.000 0.000 0.000 0.000 0.000
X8 0.000 0.000 0.000 0.000 0.000
X9 0.000 0.000 0.000 0.000 0.000
X10 0.000 0.000 0.000 0.000 0.000
THETA
X6 X7 X8 X9 X10
________ ________ ________ ________ ________
X6 1.000
X7 0.000 1.000
X8 0.000 0.000 1.000
X9 0.000 0.000 0.000 1.000
X10 0.000 0.000 0.000 0.000 1.000
POPULATION VALUES FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
2.000 2.000 -2.000 -2.000
TAU(U) FOR LATENT CLASS 2
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
-2.000 -2.000 2.000 2.000
POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
1.000 0.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.80863758D+04 0.0000000 0.0000000 EM
2 -0.80712810D+04 15.0947489 0.0018667 EM
3 -0.80712810D+04 0.0000000 0.0000000 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
U1
U2
U3
U4
X1
X2
X3
X4
X5
X6
X7
X8
X9
X10
C
Save file
ex7.3.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:38
Ending Time: 22:24:38
Elapsed Time: 00:00:00
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