```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;

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

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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Los Angeles, CA  90066

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Fax: (310) 391-8971
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Copyright (c) 1998-2022 Muthen & Muthen
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