```Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  11:13 PM

INPUT INSTRUCTIONS

TITLE:	this is an example of a two-group twin
model for categorical outcomes using
maximum likelihood and parameter constraints
DATA:		FILE = ex7.28.dat;
VARIABLE:	NAMES = u1 u2 dz;
CATEGORICAL = u1 u2;
CLASSES = cdz (2);
KNOWNCLASS = cdz (dz = 0 dz = 1);
ANALYSIS:	TYPE = MIXTURE;
ALGORITHM = INTEGRATION;
MODEL:	%OVERALL%
[u1\$1-u2\$1] (1);
f1 BY u1;
f2 BY u2;
[f1-f2@0];
f1-f2 (varf);
%cdz#1%
f1 WITH f2(covmz);
%cdz#2%
f1 WITH f2(covdz);
MODEL CONSTRAINT:
NEW(a c h);
varf = a**2 + c**2 + .001;
covmz = a**2 + c**2;
covdz = 0.5*a**2 + c**2;
h = a**2/(a**2 + c**2 + 1);

this is an example of a two-group twin
model for categorical outcomes using
maximum likelihood and parameter constraints

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        5000

Number of dependent variables                                    2
Number of independent variables                                  0
Number of continuous latent variables                            2
Number of categorical latent variables                           1

Observed dependent variables

Binary and ordered categorical (ordinal)
U1          U2

Continuous latent variables
F1          F2

Categorical latent variables
CDZ

Knownclass            CDZ

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-02
Relative loglikelihood change                        0.100D-05
Derivative                                           0.100D-02
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-02
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-02
Basis for M step termination                           ITERATION
Maximum value for logit thresholds                            10
Minimum value for logit thresholds                           -10
Minimum expected cell size for chi-square              0.100D-01
Optimization algorithm                                         EMA
Integration Specifications
Type                                                    STANDARD
Number of integration points                                  15
Dimensions of numerical integration                            2
Cholesky                                                        ON

Input data file(s)
ex7.28.dat
Input data format  FREE

UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

U1
Category 1    0.500         2501.000
Category 2    0.500         2499.000
U2
Category 1    0.507         2535.000
Category 2    0.493         2465.000

THE MODEL ESTIMATION TERMINATED NORMALLY

MODEL FIT INFORMATION

Number of Free Parameters                        4

Loglikelihood

H0 Value                       -9927.558
H0 Scaling Correction Factor      0.9922
for MLR

Information Criteria

Akaike (AIC)                   19863.116
Bayesian (BIC)                 19889.185
(n* = (n + 2) / 24)

Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes

Pearson Chi-Square

Value                              3.633
Degrees of Freedom                     3
P-Value                           0.3039

Likelihood Ratio Chi-Square

Value                              3.635
Degrees of Freedom                     3
P-Value                           0.3036

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

Latent
Classes

1       2566.00000          0.51320
2       2434.00000          0.48680

MODEL RESULTS

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

Latent Class 1 (0)

F1       BY
U1                 1.000      0.000    999.000    999.000

F2       BY
U2                 1.000      0.000    999.000    999.000

F2       WITH
F1                 2.933      0.262     11.202      0.000

Means
F1                 0.000      0.000    999.000    999.000
F2                 0.000      0.000    999.000    999.000

Thresholds
U1\$1               0.013      0.029      0.451      0.652
U2\$1               0.013      0.029      0.451      0.652

Variances
F1                 2.934      0.262     11.206      0.000
F2                 2.934      0.262     11.206      0.000

Latent Class 2 (1)

F1       BY
U1                 1.000      0.000    999.000    999.000

F2       BY
U2                 1.000      0.000    999.000    999.000

F2       WITH
F1                 1.524      0.151     10.075      0.000

Means
F1                 0.000      0.000    999.000    999.000
F2                 0.000      0.000    999.000    999.000

Thresholds
U1\$1               0.013      0.029      0.451      0.652
U2\$1               0.013      0.029      0.451      0.652

Variances
F1                 2.934      0.262     11.206      0.000
F2                 2.934      0.262     11.206      0.000

Categorical Latent Variables

Means
CDZ#1              0.053      0.028      1.867      0.062

A                  1.679      0.116     14.466      0.000
C                  0.339      0.340      0.997      0.319
H                  0.717      0.066     10.874      0.000

QUALITY OF NUMERICAL RESULTS

Condition Number for the Information Matrix              0.795E-03
(ratio of smallest to largest eigenvalue)

RESULTS IN PROBABILITY SCALE

Estimate

Latent Class 1 (0)

U1
Category 1         0.503
Category 2         0.497
U2
Category 1         0.503
Category 2         0.497

Latent Class 2 (1)

U1
Category 1         0.503
Category 2         0.497
U2
Category 1         0.503
Category 2         0.497

Beginning Time:  23:13:20
Ending Time:  23:13:20
Elapsed Time:  00:00:00

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```