Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:13 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
DATA: FILE IS ex7.6.dat;
VARIABLE: NAMES ARE u1-u4 c;
USEVARIABLES ARE u1-u4;
CLASSES = c (2);
CATEGORICAL = u1-u4;
ANALYSIS: TYPE = MIXTURE;
STARTS = 0;
MODEL:
%OVERALL%
%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: TECH1 TECH8;
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 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
Input data file(s)
ex7.6.dat
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.487 2435.000
Category 2 0.120 600.000
Category 3 0.393 1965.000
U2
Category 1 0.508 2540.000
Category 2 0.114 570.000
Category 3 0.378 1890.000
U3
Category 1 0.490 2452.000
Category 2 0.112 560.000
Category 3 0.398 1988.000
U4
Category 1 0.499 2496.000
Category 2 0.116 578.000
Category 3 0.385 1926.000
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 17
Loglikelihood
H0 Value -19214.480
H0 Scaling Correction Factor 1.0208
for MLR
Information Criteria
Akaike (AIC) 38462.961
Bayesian (BIC) 38573.753
Sample-Size Adjusted BIC 38519.733
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 65.388
Degrees of Freedom 63
P-Value 0.3938
Likelihood Ratio Chi-Square
Value 62.447
Degrees of Freedom 63
P-Value 0.4960
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
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Latent Class 1
Thresholds
U1$1 0.615 0.192 3.203 0.001
U1$2 1.147 0.224 5.123 0.000
U2$1 0.604 0.179 3.379 0.001
U2$2 1.144 0.214 5.339 0.000
U3$1 -0.713 0.182 -3.918 0.000
U3$2 -0.197 0.154 -1.284 0.199
U4$1 -0.556 0.174 -3.203 0.001
U4$2 -0.052 0.159 -0.327 0.744
Latent Class 2
Thresholds
U1$1 -0.523 0.141 -3.702 0.000
U1$2 -0.002 0.128 -0.016 0.987
U2$1 -0.364 0.114 -3.203 0.001
U2$2 0.102 0.109 0.935 0.350
U3$1 0.425 0.147 2.888 0.004
U3$2 0.894 0.163 5.499 0.000
U4$1 0.383 0.109 3.503 0.000
U4$2 0.872 0.116 7.510 0.000
Categorical Latent Variables
Means
C#1 -0.346 0.474 -0.730 0.466
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.788E-03
(ratio of smallest to largest eigenvalue)
RESULTS IN PROBABILITY SCALE
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Latent Class 1
U1
Category 1 0.649 0.044 14.834 0.000
Category 2 0.110 0.015 7.417 0.000
Category 3 0.241 0.041 5.887 0.000
U2
Category 1 0.646 0.041 15.835 0.000
Category 2 0.112 0.014 8.031 0.000
Category 3 0.242 0.039 6.156 0.000
U3
Category 1 0.329 0.040 8.185 0.000
Category 2 0.122 0.014 8.729 0.000
Category 3 0.549 0.038 14.446 0.000
U4
Category 1 0.365 0.040 9.068 0.000
Category 2 0.123 0.014 8.912 0.000
Category 3 0.513 0.040 12.896 0.000
Latent Class 2
U1
Category 1 0.372 0.033 11.281 0.000
Category 2 0.127 0.011 11.576 0.000
Category 3 0.501 0.032 15.617 0.000
U2
Category 1 0.410 0.027 14.918 0.000
Category 2 0.115 0.010 11.137 0.000
Category 3 0.474 0.027 17.428 0.000
U3
Category 1 0.605 0.035 17.184 0.000
Category 2 0.105 0.010 10.330 0.000
Category 3 0.290 0.033 8.671 0.000
U4
Category 1 0.595 0.026 22.571 0.000
Category 2 0.111 0.010 10.727 0.000
Category 3 0.295 0.024 12.207 0.000
LATENT CLASS INDICATOR ODDS RATIOS FOR THE LATENT CLASSES
95% C.I.
Estimate S.E. Lower 2.5% Upper 2.5%
Latent Class 1 Compared to Latent Class 2
U1
Category > 1 0.320 0.055 0.229 0.448
Category > 2 0.317 0.063 0.214 0.469
U2
Category > 1 0.380 0.062 0.276 0.524
Category > 2 0.353 0.067 0.243 0.512
U3
Category > 1 3.122 0.520 2.252 4.327
Category > 2 2.977 0.479 2.171 4.081
U4
Category > 1 2.556 0.404 1.875 3.486
Category > 2 2.520 0.379 1.878 3.383
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
TECHNICAL 8 OUTPUT
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
Beginning Time: 23:13:23
Ending Time: 23:13:23
Elapsed Time: 00:00:00
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