```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 with a
covariate and a direct effect

montecarlo:
names are u1-u4 x;
generate = u1-u4(1);
categorical = u1-u4;
genclasses = c(2);
classes = c(2);
nobs = 500;
seed = 3454367;
nrep = 1;
save = ex7.12.dat;

analysis:
type = mixture;

model population:

%overall%

[x@0]; x@1;

[c#1*0];

c#1 on x*1;

u4 on x*.5;

%c#1%
[u1\$1*1 u2\$1*1 u3\$1*-1 u4\$1*-1];

%c#2%
[u1\$1*-1 u2\$1*-1 u3\$1*1 u4\$1*1];

model:

%overall%

[c#1*0];

c#1 on x*1;

u4 on x*.5;

%c#1%
[u1\$1*1 u2\$1*1 u3\$1*-1 u4\$1*-1];

%c#2%
[u1\$1*-1 u2\$1*-1 u3\$1*1 u4\$1*1];

output:
tech8 tech9;

this is an example of a LCA with binary
latent class indicators using automatic
starting values with random starts with a
covariate and a direct effect

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                                    4
Number of independent variables                                  1
Number of continuous latent variables                            0
Number of categorical latent variables                           1

Observed dependent variables

Binary and ordered categorical (ordinal)
U1          U2          U3          U4

Observed independent variables
X

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
X
________
-0.072

Covariances
X
________
X              1.014

Correlations
X
________
X              1.000

MODEL FIT INFORMATION

Number of Free Parameters                       11

Loglikelihood

H0 Value

Mean                             -1255.396
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000        -1255.396      -1255.396
0.980       0.000        -1255.396      -1255.396
0.950       0.000        -1255.396      -1255.396
0.900       0.000        -1255.396      -1255.396
0.800       0.000        -1255.396      -1255.396
0.700       0.000        -1255.396      -1255.396
0.500       0.000        -1255.396      -1255.396
0.300       0.000        -1255.396      -1255.396
0.200       0.000        -1255.396      -1255.396
0.100       0.000        -1255.396      -1255.396
0.050       0.000        -1255.396      -1255.396
0.020       0.000        -1255.396      -1255.396
0.010       0.000        -1255.396      -1255.396

Information Criteria

Akaike (AIC)

Mean                              2532.793
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         2532.793       2532.793
0.980       0.000         2532.793       2532.793
0.950       0.000         2532.793       2532.793
0.900       0.000         2532.793       2532.793
0.800       0.000         2532.793       2532.793
0.700       0.000         2532.793       2532.793
0.500       0.000         2532.793       2532.793
0.300       0.000         2532.793       2532.793
0.200       0.000         2532.793       2532.793
0.100       0.000         2532.793       2532.793
0.050       0.000         2532.793       2532.793
0.020       0.000         2532.793       2532.793
0.010       0.000         2532.793       2532.793

Bayesian (BIC)

Mean                              2579.153
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         2579.153       2579.153
0.980       0.000         2579.153       2579.153
0.950       0.000         2579.153       2579.153
0.900       0.000         2579.153       2579.153
0.800       0.000         2579.153       2579.153
0.700       0.000         2579.153       2579.153
0.500       0.000         2579.153       2579.153
0.300       0.000         2579.153       2579.153
0.200       0.000         2579.153       2579.153
0.100       0.000         2579.153       2579.153
0.050       0.000         2579.153       2579.153
0.020       0.000         2579.153       2579.153
0.010       0.000         2579.153       2579.153

Sample-Size Adjusted BIC (n* = (n + 2) / 24)

Mean                              2544.239
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         2544.239       2544.239
0.980       0.000         2544.239       2544.239
0.950       0.000         2544.239       2544.239
0.900       0.000         2544.239       2544.239
0.800       0.000         2544.239       2544.239
0.700       0.000         2544.239       2544.239
0.500       0.000         2544.239       2544.239
0.300       0.000         2544.239       2544.239
0.200       0.000         2544.239       2544.239
0.100       0.000         2544.239       2544.239
0.050       0.000         2544.239       2544.239
0.020       0.000         2544.239       2544.239
0.010       0.000         2544.239       2544.239

FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL

Latent
Classes

1        249.27676          0.49855
2        250.72324          0.50145

FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES

Latent
Classes

1        249.27676          0.49855
2        250.72324          0.50145

FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP

Class Counts and Proportions

Latent
Classes

1              248          0.49600
2              252          0.50400

CLASSIFICATION QUALITY

Entropy                         0.586

Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)

1        2

1   0.882    0.118
2   0.122    0.878

Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)

1        2

1   0.877    0.123
2   0.117    0.883

Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)

1        2

1      1.964    0.000
2     -2.019    0.000

MODEL RESULTS

ESTIMATES              S. E.     M. S. E.  95%  % Sig
Population   Average   Std. Dev.   Average             Cover Coeff

Latent Class 1

U4         ON
X                   0.500     0.5786     0.0000     0.1283     0.0062 1.000 1.000

Thresholds
U1\$1                1.000     1.3370     0.0000     0.2455     0.1136 1.000 1.000
U2\$1                1.000     0.9287     0.0000     0.1974     0.0051 1.000 1.000
U3\$1               -1.000    -0.9464     0.0000     0.2048     0.0029 1.000 1.000
U4\$1               -1.000    -0.6627     0.0000     0.2118     0.1138 1.000 1.000

Latent Class 2

U4         ON
X                   0.500     0.5786     0.0000     0.1283     0.0062 1.000 1.000

Thresholds
U1\$1               -1.000    -1.4517     0.0000     0.2912     0.2040 1.000 1.000
U2\$1               -1.000    -1.1716     0.0000     0.2174     0.0294 1.000 1.000
U3\$1                1.000     1.0828     0.0000     0.2006     0.0069 1.000 1.000
U4\$1                1.000     0.9580     0.0000     0.2016     0.0018 1.000 1.000

Categorical Latent Variables

C#1        ON
X                   1.000     1.0247     0.0000     0.1510     0.0006 1.000 1.000

Intercepts
C#1                 0.000     0.0667     0.0000     0.2393     0.0045 1.000 0.000

QUALITY OF NUMERICAL RESULTS

Average Condition Number for the Information Matrix      0.762E-01
(ratio of smallest to largest eigenvalue)

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION FOR LATENT CLASS 1

NU
X
________
0

LAMBDA
X
________
X                  0

THETA
X
________
X                  0

ALPHA
X
________
0

BETA
X
________
X                  0

PSI
X
________
X                  0

PARAMETER SPECIFICATION FOR LATENT CLASS 2

NU
X
________
0

LAMBDA
X
________
X                  0

THETA
X
________
X                  0

ALPHA
X
________
0

BETA
X
________
X                  0

PSI
X
________
X                  0

PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART

TAU(U) FOR LATENT CLASS 1
U1\$1          U2\$1          U3\$1          U4\$1
________      ________      ________      ________
1             2             3             4

TAU(U) FOR LATENT CLASS 2
U1\$1          U2\$1          U3\$1          U4\$1
________      ________      ________      ________
6             7             8             9

PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART

ALPHA(C)
C#1           C#2
________      ________
10             0

GAMMA(C)
X
________
C#1               11
C#2                0

PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR GROWTH MODEL PART

LAMBDA(F) FOR LATENT CLASS 1
U4
________
U1                 0
U2                 0
U3                 0
U4                 0

ALPHA(F) FOR LATENT CLASS 1
U4
________
0

GAMMA(F) FOR LATENT CLASS 1
X
________
U4                 5

LAMBDA(F) FOR LATENT CLASS 2
U4
________
U1                 0
U2                 0
U3                 0
U4                 0

ALPHA(F) FOR LATENT CLASS 2
U4
________
0

GAMMA(F) FOR LATENT CLASS 2
X
________
U4                 5

STARTING VALUES FOR LATENT CLASS 1

NU
X
________
0.000

LAMBDA
X
________
X              1.000

THETA
X
________
X              0.000

ALPHA
X
________
0.000

BETA
X
________
X              0.000

PSI
X
________
X              0.500

STARTING VALUES FOR LATENT CLASS 2

NU
X
________
0.000

LAMBDA
X
________
X              1.000

THETA
X
________
X              0.000

ALPHA
X
________
0.000

BETA
X
________
X              0.000

PSI
X
________
X              0.500

STARTING VALUES FOR LATENT CLASS INDICATOR MODEL PART

TAU(U) FOR LATENT CLASS 1
U1\$1          U2\$1          U3\$1          U4\$1
________      ________      ________      ________
1.000         1.000        -1.000        -1.000

TAU(U) FOR LATENT CLASS 2
U1\$1          U2\$1          U3\$1          U4\$1
________      ________      ________      ________
-1.000        -1.000         1.000         1.000

STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART

ALPHA(C)
C#1           C#2
________      ________
0.000         0.000

GAMMA(C)
X
________
C#1            1.000
C#2            0.000

STARTING VALUES FOR LATENT CLASS INDICATOR GROWTH MODEL PART

LAMBDA(F) FOR CLASS LATENT CLASS 1
U4
________
U1             0.000
U2             0.000
U3             0.000
U4             1.000

ALPHA(F) FOR LATENT CLASS 1
U4
________
0.000

GAMMA(F) FOR LATENT CLASS 1
X
________
U4             0.500

LAMBDA(F) FOR CLASS LATENT CLASS 2
U4
________
U1             0.000
U2             0.000
U3             0.000
U4             1.000

ALPHA(F) FOR LATENT CLASS 2
U4
________
0.000

GAMMA(F) FOR LATENT CLASS 2
X
________
U4             0.500

POPULATION VALUES FOR LATENT CLASS 1

NU
X
________
0.000

LAMBDA
X
________
X              1.000

THETA
X
________
X              0.000

ALPHA
X
________
0.000

BETA
X
________
X              0.000

PSI
X
________
X              1.000

POPULATION VALUES FOR LATENT CLASS 2

NU
X
________
0.000

LAMBDA
X
________
X              1.000

THETA
X
________
X              0.000

ALPHA
X
________
0.000

BETA
X
________
X              0.000

PSI
X
________
X              1.000

POPULATION VALUES FOR LATENT CLASS INDICATOR MODEL PART

TAU(U) FOR LATENT CLASS 1
U1\$1          U2\$1          U3\$1          U4\$1
________      ________      ________      ________
1.000         1.000        -1.000        -1.000

TAU(U) FOR LATENT CLASS 2
U1\$1          U2\$1          U3\$1          U4\$1
________      ________      ________      ________
-1.000        -1.000         1.000         1.000

POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART

ALPHA(C)
C#1           C#2
________      ________
0.000         0.000

GAMMA(C)
X
________
C#1            1.000
C#2            0.000

POPULATION VALUES FOR LATENT CLASS INDICATOR GROWTH MODEL PART

LAMBDA(F) FOR LATENT CLASS 1
U4
________
U1             0.000
U2             0.000
U3             0.000
U4             1.000

ALPHA(F) FOR LATENT CLASS 1
U4
________
0.000

GAMMA(F) FOR LATENT CLASS 1
X
________
U4             0.500

LAMBDA(F) FOR LATENT CLASS 2
U4
________
U1             0.000
U2             0.000
U3             0.000
U4             1.000

ALPHA(F) FOR LATENT CLASS 2
U4
________
0.000

GAMMA(F) FOR LATENT CLASS 2
X
________
U4             0.500

TECHNICAL 8 OUTPUT

TECHNICAL 8 OUTPUT FOR REPLICATION 1

E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
1 -0.12598594D+04    0.0000000    0.0000000  EM
2 -0.12566708D+04    3.1886149    0.0025309  EM
3 -0.12559336D+04    0.7372358    0.0005867  EM
4 -0.12556664D+04    0.2671668    0.0002127  EM
5 -0.12555545D+04    0.1118609    0.0000891  EM
6 -0.12555009D+04    0.0536395    0.0000427  EM
7 -0.12554714D+04    0.0294607    0.0000235  EM
8 -0.12554531D+04    0.0183427    0.0000146  EM
9 -0.12554405D+04    0.0126080    0.0000100  EM
10 -0.12554312D+04    0.0092662    0.0000074  EM
11 -0.12554241D+04    0.0070917    0.0000056  EM
12 -0.12554186D+04    0.0055529    0.0000044  EM
13 -0.12554142D+04    0.0044024    0.0000035  EM
14 -0.12554107D+04    0.0035138    0.0000028  EM
15 -0.12554079D+04    0.0028146    0.0000022  EM
16 -0.12554056D+04    0.0022590    0.0000018  EM
17 -0.12554038D+04    0.0018151    0.0000014  EM
18 -0.12554023D+04    0.0014594    0.0000012  EM
19 -0.12554011D+04    0.0011739    0.0000009  EM
20 -0.12554002D+04    0.0009445    0.0000008  EM
21 -0.12553994D+04    0.0007601    0.0000006  EM
22 -0.12553988D+04    0.0006118    0.0000005  EM
23 -0.12553983D+04    0.0004925    0.0000004  EM
24 -0.12553979D+04    0.0003965    0.0000003  EM
25 -0.12553976D+04    0.0003193    0.0000003  EM
26 -0.12553974D+04    0.0002571    0.0000002  EM
27 -0.12553972D+04    0.0002071    0.0000002  EM
28 -0.12553970D+04    0.0001668    0.0000001  EM
29 -0.12553969D+04    0.0001343    0.0000001  EM
30 -0.12553967D+04    0.0001082    0.0000001  EM
31 -0.12553967D+04    0.0000872    0.0000001  EM
32 -0.12553966D+04    0.0000702    0.0000001  EM
33 -0.12553965D+04    0.0000566    0.0000000  EM
34 -0.12553965D+04    0.0000456    0.0000000  EM
35 -0.12553965D+04    0.0000367    0.0000000  EM
36 -0.12553964D+04    0.0000296    0.0000000  EM
37 -0.12553964D+04    0.0000238    0.0000000  EM
38 -0.12553963D+04    0.0000961    0.0000001  FS
39 -0.12553963D+04    0.0000027    0.0000000  FS
40 -0.12553963D+04    0.0000001    0.0000000  FS
41 -0.12553963D+04    0.0000000    0.0000000  FS

TECHNICAL 9 OUTPUT

Error messages for each replication (if any)

SAVEDATA INFORMATION

Order of variables

U1
U2
U3
U4
X
C

Save file
ex7.12.dat

Save file format           Free
Save file record length    10000

Beginning Time:  22:24:28
Ending Time:  22:24:28
Elapsed Time:  00:00:00

MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA  90066

Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com

Copyright (c) 1998-2022 Muthen & Muthen
```