Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
title:
this is an example of a LCA with unordered
categorical latent class indicators using
automatic starting values with random
starts
! using the population threshold values
! in ex 7.6 as intercept values
! so that in effect ordinal outcomes
! are treated as unordered in the analysis.
! note that intercept values need not be
! ordered with nominal outcomes.
montecarlo:
names are u1-u4;
generate = u1-u4(n 2);
nominal = u1-u4;
genclasses = c(2);
classes = c(2);
nobs = 5000;
seed = 3454367;
nrep = 1;
save = ex7.7.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 unordered
categorical latent class indicators using
automatic starting values with 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
Unordered categorical (nominal)
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
MODEL FIT INFORMATION
Number of Free Parameters 17
Loglikelihood
H0 Value
Mean -21408.482
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -21408.482 -21408.482
0.980 0.000 -21408.482 -21408.482
0.950 0.000 -21408.482 -21408.482
0.900 0.000 -21408.482 -21408.482
0.800 0.000 -21408.482 -21408.482
0.700 0.000 -21408.482 -21408.482
0.500 0.000 -21408.482 -21408.482
0.300 0.000 -21408.482 -21408.482
0.200 0.000 -21408.482 -21408.482
0.100 0.000 -21408.482 -21408.482
0.050 0.000 -21408.482 -21408.482
0.020 0.000 -21408.482 -21408.482
0.010 0.000 -21408.482 -21408.482
Information Criteria
Akaike (AIC)
Mean 42850.964
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 42850.964 42850.964
0.980 0.000 42850.964 42850.964
0.950 0.000 42850.964 42850.964
0.900 0.000 42850.964 42850.964
0.800 0.000 42850.964 42850.964
0.700 0.000 42850.964 42850.964
0.500 0.000 42850.964 42850.964
0.300 0.000 42850.964 42850.964
0.200 0.000 42850.964 42850.964
0.100 0.000 42850.964 42850.964
0.050 0.000 42850.964 42850.964
0.020 0.000 42850.964 42850.964
0.010 0.000 42850.964 42850.964
Bayesian (BIC)
Mean 42961.756
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 42961.756 42961.756
0.980 0.000 42961.756 42961.756
0.950 0.000 42961.756 42961.756
0.900 0.000 42961.756 42961.756
0.800 0.000 42961.756 42961.756
0.700 0.000 42961.756 42961.756
0.500 0.000 42961.756 42961.756
0.300 0.000 42961.756 42961.756
0.200 0.000 42961.756 42961.756
0.100 0.000 42961.756 42961.756
0.050 0.000 42961.756 42961.756
0.020 0.000 42961.756 42961.756
0.010 0.000 42961.756 42961.756
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 42907.736
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 42907.736 42907.736
0.980 0.000 42907.736 42907.736
0.950 0.000 42907.736 42907.736
0.900 0.000 42907.736 42907.736
0.800 0.000 42907.736 42907.736
0.700 0.000 42907.736 42907.736
0.500 0.000 42907.736 42907.736
0.300 0.000 42907.736 42907.736
0.200 0.000 42907.736 42907.736
0.100 0.000 42907.736 42907.736
0.050 0.000 42907.736 42907.736
0.020 0.000 42907.736 42907.736
0.010 0.000 42907.736 42907.736
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 1286.98163 0.25740
2 3713.01837 0.74260
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 1286.98163 0.25740
2 3713.01837 0.74260
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 683 0.13660
2 4317 0.86340
CLASSIFICATION QUALITY
Entropy 0.343
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.584 0.416
2 0.206 0.794
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.310 0.690
2 0.076 0.924
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 -0.800 0.000
2 -2.491 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Latent Class 1
Means
U1#1 0.500 0.9666 0.0000 0.9629 0.2178 1.000 0.000
U1#2 1.000 1.4079 0.0000 0.8821 0.1664 1.000 0.000
U2#1 0.500 2.3526 0.0000 3.9184 3.4320 1.000 0.000
U2#2 1.000 2.8377 0.0000 3.8780 3.3772 1.000 0.000
U3#1 -0.500 -0.7716 0.0000 0.4872 0.0738 1.000 0.000
U3#2 0.000 -0.0428 0.0000 0.2357 0.0018 1.000 0.000
U4#1 -0.500 -0.6820 0.0000 0.4242 0.0331 1.000 0.000
U4#2 0.000 -0.1610 0.0000 0.4161 0.0259 1.000 0.000
Latent Class 2
Means
U1#1 -0.500 -0.3794 0.0000 0.1624 0.0145 1.000 1.000
U1#2 0.000 0.1451 0.0000 0.1672 0.0210 1.000 0.000
U2#1 -0.500 -0.4979 0.0000 0.2871 0.0000 1.000 0.000
U2#2 0.000 0.0706 0.0000 0.2755 0.0050 1.000 0.000
U3#1 0.500 0.1446 0.0000 0.1680 0.1263 0.000 0.000
U3#2 1.000 0.6192 0.0000 0.1687 0.1450 0.000 1.000
U4#1 0.500 0.1955 0.0000 0.1560 0.0927 1.000 0.000
U4#2 1.000 0.6398 0.0000 0.1441 0.1297 0.000 1.000
Categorical Latent Variables
Means
C#1 0.000 -1.0595 0.0000 1.1926 1.1226 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.443E-04
(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 REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
1 0
PARAMETER SPECIFICATION FOR THE CENSORED/NOMINAL/COUNT MODEL PART
NU(P) FOR LATENT CLASS 1
U1#1 U1#2 U2#1 U2#2 U3#1
________ ________ ________ ________ ________
2 3 4 5 6
NU(P) FOR LATENT CLASS 1
U3#2 U4#1 U4#2
________ ________ ________
7 8 9
NU(P) FOR LATENT CLASS 2
U1#1 U1#2 U2#1 U2#2 U3#1
________ ________ ________ ________ ________
10 11 12 13 14
NU(P) FOR LATENT CLASS 2
U3#2 U4#1 U4#2
________ ________ ________
15 16 17
STARTING VALUES FOR LATENT CLASS 1
STARTING VALUES FOR LATENT CLASS 2
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
0.000 0.000
STARTING VALUES FOR THE CENSORED/NOMINAL/COUNT MODEL PART
NU(P) FOR LATENT CLASS 1
U1#1 U1#2 U2#1 U2#2 U3#1
________ ________ ________ ________ ________
0.500 1.000 0.500 1.000 -0.500
NU(P) FOR LATENT CLASS 1
U3#2 U4#1 U4#2
________ ________ ________
0.000 -0.500 0.000
NU(P) FOR LATENT CLASS 2
U1#1 U1#2 U2#1 U2#2 U3#1
________ ________ ________ ________ ________
-0.500 0.000 -0.500 0.000 0.500
NU(P) FOR LATENT CLASS 2
U3#2 U4#1 U4#2
________ ________ ________
1.000 0.500 1.000
POPULATION VALUES FOR LATENT CLASS 1
POPULATION VALUES FOR LATENT CLASS 2
POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
0.000 0.000
POPULATION VALUES FOR THE CENSORED/NOMINAL/COUNT MODEL PART
NU(P) FOR LATENT CLASS 1
U1#1 U1#2 U2#1 U2#2 U3#1
________ ________ ________ ________ ________
0.500 1.000 0.500 1.000 -0.500
NU(P) FOR LATENT CLASS 1
U3#2 U4#1 U4#2
________ ________ ________
0.000 -0.500 0.000
NU(P) FOR LATENT CLASS 2
U1#1 U1#2 U2#1 U2#2 U3#1
________ ________ ________ ________ ________
-0.500 0.000 -0.500 0.000 0.500
NU(P) FOR LATENT CLASS 2
U3#2 U4#1 U4#2
________ ________ ________
1.000 0.500 1.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.21416857D+05 0.0000000 0.0000000 EM
2 -0.21412508D+05 4.3488559 0.0002031 EM
3 -0.21411996D+05 0.5113224 0.0000239 EM
4 -0.21411591D+05 0.4053413 0.0000189 EM
5 -0.21411264D+05 0.3274560 0.0000153 EM
6 -0.21410995D+05 0.2688449 0.0000126 EM
7 -0.21410771D+05 0.2238267 0.0000105 EM
8 -0.21410582D+05 0.1886182 0.0000088 EM
9 -0.21410422D+05 0.1606294 0.0000075 EM
10 -0.21410284D+05 0.1380470 0.0000064 EM
11 -0.21410164D+05 0.1195775 0.0000056 EM
12 -0.21410060D+05 0.1042836 0.0000049 EM
13 -0.21409968D+05 0.0914767 0.0000043 EM
14 -0.21409888D+05 0.0806446 0.0000038 EM
15 -0.21409816D+05 0.0714012 0.0000033 EM
16 -0.21409753D+05 0.0634523 0.0000030 EM
17 -0.21409696D+05 0.0565707 0.0000026 EM
18 -0.21409646D+05 0.0505787 0.0000024 EM
19 -0.21409600D+05 0.0453355 0.0000021 EM
20 -0.21409560D+05 0.0407283 0.0000019 EM
21 -0.21409523D+05 0.0366652 0.0000017 EM
22 -0.21409490D+05 0.0330710 0.0000015 EM
23 -0.21409460D+05 0.0298830 0.0000014 EM
24 -0.21409433D+05 0.0270488 0.0000013 EM
25 -0.21409408D+05 0.0245238 0.0000011 EM
26 -0.21409386D+05 0.0222701 0.0000010 EM
27 -0.21409366D+05 0.0202552 0.0000009 EM
28 -0.21409347D+05 0.0184511 0.0000009 EM
29 -0.21409331D+05 0.0168332 0.0000008 EM
30 -0.21409315D+05 0.0153804 0.0000007 EM
31 -0.21409301D+05 0.0140742 0.0000007 EM
32 -0.21409288D+05 0.0128982 0.0000006 EM
33 -0.21409276D+05 0.0118382 0.0000006 EM
34 -0.21409266D+05 0.0108815 0.0000005 EM
35 -0.21409256D+05 0.0100172 0.0000005 EM
36 -0.21409246D+05 0.0092354 0.0000004 EM
37 -0.21409238D+05 0.0085274 0.0000004 EM
38 -0.21409230D+05 0.0078855 0.0000004 EM
39 -0.21409223D+05 0.0073030 0.0000003 EM
40 -0.21409216D+05 0.0067737 0.0000003 EM
41 -0.21409210D+05 0.0062922 0.0000003 EM
42 -0.21409204D+05 0.0058539 0.0000003 EM
43 -0.21409198D+05 0.0054544 0.0000003 EM
44 -0.21409193D+05 0.0050898 0.0000002 EM
45 -0.21409188D+05 0.0047569 0.0000002 EM
46 -0.21409184D+05 0.0044526 0.0000002 EM
47 -0.21409180D+05 0.0041741 0.0000002 EM
48 -0.21409176D+05 0.0039191 0.0000002 EM
49 -0.21409172D+05 0.0036853 0.0000002 EM
50 -0.21409169D+05 0.0034708 0.0000002 EM
51 -0.21409165D+05 0.0032738 0.0000002 EM
52 -0.21409162D+05 0.0030928 0.0000001 EM
53 -0.21409159D+05 0.0029263 0.0000001 EM
54 -0.21409157D+05 0.0027730 0.0000001 EM
55 -0.21409154D+05 0.0026318 0.0000001 EM
56 -0.21408482D+05 0.6719633 0.0000314 QN
57 -0.21408482D+05 0.0000000 0.0000000 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
U1
U2
U3
U4
C
Save file
ex7.7.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:41
Ending Time: 22:24:41
Elapsed Time: 00:00:00
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