Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
title:
this is an example of a LCA with three-
category latent class indicators using
user-specified starting values without
random starts
montecarlo:
names are u1-u4;
generate = u1-u4(2);
categorical = u1-u4;
genclasses = c(2);
classes = c(2);
nobs = 5000;
seed = 3454367;
nrep = 1;
save = ex7.6.dat;
analysis:
type = mixture;
model population:
%overall%
[c#1*0];
%c#1%
[u1$1*.5 u2$1*.5 u3$1*-.5 u4$1*-.5];
[u1$2*1 u2$2*1 u3$2*0 u4$2*0];
%c#2%
[u1$1*-.5 u2$1*-.5 u3$1*.5 u4$1*.5];
[u1$2*0 u2$2*0 u3$2*1 u4$2*1];
model:
%overall%
[c#1*0];
%c#1%
[u1$1*.5 u2$1*.5 u3$1*-.5 u4$1*-.5];
[u1$2*1 u2$2*1 u3$2*0 u4$2*0];
%c#2%
[u1$1*-.5 u2$1*-.5 u3$1*.5 u4$1*.5];
[u1$2*0 u2$2*0 u3$2*1 u4$2*1];
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a LCA with three-
category latent class indicators using
user-specified starting values without
random starts
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 5000
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-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
MODEL FIT INFORMATION
Number of Free Parameters 17
Loglikelihood
H0 Value
Mean -19214.480
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -19214.480 -19214.480
0.980 0.000 -19214.480 -19214.480
0.950 0.000 -19214.480 -19214.480
0.900 0.000 -19214.480 -19214.480
0.800 0.000 -19214.480 -19214.480
0.700 0.000 -19214.480 -19214.480
0.500 0.000 -19214.480 -19214.480
0.300 0.000 -19214.480 -19214.480
0.200 0.000 -19214.480 -19214.480
0.100 0.000 -19214.480 -19214.480
0.050 0.000 -19214.480 -19214.480
0.020 0.000 -19214.480 -19214.480
0.010 0.000 -19214.480 -19214.480
Information Criteria
Akaike (AIC)
Mean 38462.961
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 38462.961 38462.961
0.980 0.000 38462.961 38462.961
0.950 0.000 38462.961 38462.961
0.900 0.000 38462.961 38462.961
0.800 0.000 38462.961 38462.961
0.700 0.000 38462.961 38462.961
0.500 0.000 38462.961 38462.961
0.300 0.000 38462.961 38462.961
0.200 0.000 38462.961 38462.961
0.100 0.000 38462.961 38462.961
0.050 0.000 38462.961 38462.961
0.020 0.000 38462.961 38462.961
0.010 0.000 38462.961 38462.961
Bayesian (BIC)
Mean 38573.753
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 38573.753 38573.753
0.980 0.000 38573.753 38573.753
0.950 0.000 38573.753 38573.753
0.900 0.000 38573.753 38573.753
0.800 0.000 38573.753 38573.753
0.700 0.000 38573.753 38573.753
0.500 0.000 38573.753 38573.753
0.300 0.000 38573.753 38573.753
0.200 0.000 38573.753 38573.753
0.100 0.000 38573.753 38573.753
0.050 0.000 38573.753 38573.753
0.020 0.000 38573.753 38573.753
0.010 0.000 38573.753 38573.753
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 38519.733
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 38519.733 38519.733
0.980 0.000 38519.733 38519.733
0.950 0.000 38519.733 38519.733
0.900 0.000 38519.733 38519.733
0.800 0.000 38519.733 38519.733
0.700 0.000 38519.733 38519.733
0.500 0.000 38519.733 38519.733
0.300 0.000 38519.733 38519.733
0.200 0.000 38519.733 38519.733
0.100 0.000 38519.733 38519.733
0.050 0.000 38519.733 38519.733
0.020 0.000 38519.733 38519.733
0.010 0.000 38519.733 38519.733
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Mean 65.388
Std Dev 0.000
Degrees of freedom 63
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 39.855 65.388
0.980 1.000 42.143 65.388
0.950 1.000 45.741 65.388
0.900 1.000 49.111 65.388
0.800 1.000 53.412 65.388
0.700 1.000 56.666 65.388
0.500 1.000 62.335 65.388
0.300 0.000 68.369 65.388
0.200 0.000 72.201 65.388
0.100 0.000 77.745 65.388
0.050 0.000 82.529 65.388
0.020 0.000 88.137 65.388
0.010 0.000 92.010 65.388
Likelihood Ratio Chi-Square
Mean 62.447
Std Dev 0.000
Degrees of freedom 63
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 39.855 62.447
0.980 1.000 42.143 62.447
0.950 1.000 45.741 62.447
0.900 1.000 49.111 62.447
0.800 1.000 53.412 62.447
0.700 1.000 56.666 62.447
0.500 1.000 62.335 62.447
0.300 0.000 68.369 62.447
0.200 0.000 72.201 62.447
0.100 0.000 77.745 62.447
0.050 0.000 82.529 62.447
0.020 0.000 88.137 62.447
0.010 0.000 92.010 62.447
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 2072.13560 0.41443
2 2927.86440 0.58557
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 2072.13560 0.41443
2 2927.86440 0.58557
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 1889 0.37780
2 3111 0.62220
CLASSIFICATION QUALITY
Entropy 0.205
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.680 0.320
2 0.253 0.747
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.620 0.380
2 0.206 0.794
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.489 0.000
2 -1.346 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Latent Class 1
Thresholds
U1$1 0.500 0.6155 0.0000 0.1922 0.0133 1.000 1.000
U1$2 1.000 1.1468 0.0000 0.2238 0.0215 1.000 1.000
U2$1 0.500 0.6035 0.0000 0.1786 0.0107 1.000 1.000
U2$2 1.000 1.1436 0.0000 0.2142 0.0206 1.000 1.000
U3$1 -0.500 -0.7133 0.0000 0.1820 0.0455 1.000 1.000
U3$2 0.000 -0.1972 0.0000 0.1535 0.0389 1.000 0.000
U4$1 -0.500 -0.5559 0.0000 0.1735 0.0031 1.000 1.000
U4$2 0.000 -0.0520 0.0000 0.1592 0.0027 1.000 0.000
Latent Class 2
Thresholds
U1$1 -0.500 -0.5227 0.0000 0.1412 0.0005 1.000 1.000
U1$2 0.000 -0.0021 0.0000 0.1282 0.0000 1.000 0.000
U2$1 -0.500 -0.3639 0.0000 0.1136 0.0185 1.000 1.000
U2$2 0.000 0.1021 0.0000 0.1092 0.0104 1.000 0.000
U3$1 0.500 0.4252 0.0000 0.1472 0.0056 1.000 1.000
U3$2 1.000 0.8937 0.0000 0.1625 0.0113 1.000 1.000
U4$1 0.500 0.3827 0.0000 0.1093 0.0138 1.000 1.000
U4$2 1.000 0.8724 0.0000 0.1162 0.0163 1.000 1.000
Categorical Latent Variables
Means
C#1 0.000 -0.3457 0.0000 0.4738 0.1195 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.788E-03
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
PARAMETER SPECIFICATION FOR LATENT CLASS 2
PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1 U1$2 U2$1 U2$2 U3$1
________ ________ ________ ________ ________
1 2 3 4 5
TAU(U) FOR LATENT CLASS 1
U3$2 U4$1 U4$2
________ ________ ________
6 7 8
TAU(U) FOR LATENT CLASS 2
U1$1 U1$2 U2$1 U2$2 U3$1
________ ________ ________ ________ ________
9 10 11 12 13
TAU(U) FOR LATENT CLASS 2
U3$2 U4$1 U4$2
________ ________ ________
14 15 16
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
17 0
STARTING VALUES FOR LATENT CLASS 1
STARTING VALUES FOR LATENT CLASS 2
STARTING VALUES FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1 U1$2 U2$1 U2$2 U3$1
________ ________ ________ ________ ________
0.500 1.000 0.500 1.000 -0.500
TAU(U) FOR LATENT CLASS 1
U3$2 U4$1 U4$2
________ ________ ________
0.000 -0.500 0.000
TAU(U) FOR LATENT CLASS 2
U1$1 U1$2 U2$1 U2$2 U3$1
________ ________ ________ ________ ________
-0.500 0.000 -0.500 0.000 0.500
TAU(U) FOR LATENT CLASS 2
U3$2 U4$1 U4$2
________ ________ ________
1.000 0.500 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
POPULATION VALUES FOR LATENT CLASS 2
POPULATION VALUES FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1 U1$2 U2$1 U2$2 U3$1
________ ________ ________ ________ ________
0.500 1.000 0.500 1.000 -0.500
TAU(U) FOR LATENT CLASS 1
U3$2 U4$1 U4$2
________ ________ ________
0.000 -0.500 0.000
TAU(U) FOR LATENT CLASS 2
U1$1 U1$2 U2$1 U2$2 U3$1
________ ________ ________ ________ ________
-0.500 0.000 -0.500 0.000 0.500
TAU(U) FOR LATENT CLASS 2
U3$2 U4$1 U4$2
________ ________ ________
1.000 0.500 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 -0.19220264D+05 0.0000000 0.0000000 EM
2 -0.19215521D+05 4.7428188 0.0002468 EM
3 -0.19215311D+05 0.2101882 0.0000109 EM
4 -0.19215164D+05 0.1468223 0.0000076 EM
5 -0.19215060D+05 0.1041606 0.0000054 EM
6 -0.19214985D+05 0.0749645 0.0000039 EM
7 -0.19214930D+05 0.0546586 0.0000028 EM
8 -0.19214890D+05 0.0403263 0.0000021 EM
9 -0.19214860D+05 0.0300803 0.0000016 EM
10 -0.19214837D+05 0.0226767 0.0000012 EM
11 -0.19214820D+05 0.0172794 0.0000009 EM
12 -0.19214807D+05 0.0133160 0.0000007 EM
13 -0.19214796D+05 0.0103883 0.0000005 EM
14 -0.19214788D+05 0.0082147 0.0000004 EM
15 -0.19214781D+05 0.0065943 0.0000003 EM
16 -0.19214776D+05 0.0053817 0.0000003 EM
17 -0.19214772D+05 0.0044714 0.0000002 EM
18 -0.19214768D+05 0.0037858 0.0000002 EM
19 -0.19214764D+05 0.0032679 0.0000002 EM
20 -0.19214762D+05 0.0028755 0.0000001 EM
21 -0.19214759D+05 0.0025771 0.0000001 EM
22 -0.19214757D+05 0.0023495 0.0000001 EM
23 -0.19214755D+05 0.0021750 0.0000001 EM
24 -0.19214752D+05 0.0020406 0.0000001 EM
25 -0.19214751D+05 0.0019365 0.0000001 EM
26 -0.19214749D+05 0.0018553 0.0000001 EM
27 -0.19214747D+05 0.0017913 0.0000001 EM
28 -0.19214745D+05 0.0017406 0.0000001 EM
29 -0.19214743D+05 0.0016997 0.0000001 EM
30 -0.19214742D+05 0.0016664 0.0000001 EM
31 -0.19214740D+05 0.0016389 0.0000001 EM
32 -0.19214739D+05 0.0016157 0.0000001 EM
33 -0.19214737D+05 0.0015959 0.0000001 EM
34 -0.19214735D+05 0.0015786 0.0000001 EM
35 -0.19214525D+05 0.2104860 0.0000110 FS
36 -0.19214481D+05 0.0441631 0.0000023 FS
37 -0.19214480D+05 0.0003261 0.0000000 FS
38 -0.19214480D+05 0.0000124 0.0000000 FS
39 -0.19214480D+05 0.0000006 0.0000000 FS
40 -0.19214480D+05 0.0000000 0.0000000 FS
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
U1
U2
U3
U4
C
Save file
ex7.6.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:39
Ending Time: 22:24:41
Elapsed Time: 00:00:02
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