```Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   4:43 AM

INPUT INSTRUCTIONS

TITLE:	this is an example of a two-group IRT
twin model for factors with categorical factor
indicators using parameter constraints
DATA:	FILE = ex7.29.dat;
VARIABLE:	NAMES = u11-u14 u21-u24 dz;
CATEGORICAL = u11-u24;
CLASSES = cdz (2);
KNOWNCLASS = cdz (dz = 0 dz = 1);
ANALYSIS:	TYPE = MIXTURE;
ALGORITHM = INTEGRATION;
MODEL:	%OVERALL%
f1 BY u11
u12-u14 (lam2-lam4);
f2 BY u21
u22-u24 (lam2-lam4);
[f1-f2@0];
f1-f2 (var);
[u11\$1-u14\$1] (t1-t4);
[u21\$1-u24\$1] (t1-t4);
%cdz#1%
f1 WITH f2(covmz);
%cdz#2%
f1 WITH f2(covdz);
MODEL CONSTRAINT:
NEW(a c e h);
var = a**2 + c**2 + e**2;
covmz = a**2 + c**2;
covdz = 0.5*a**2 + c**2;
h = a**2/(a**2 + c**2 + e**2);

this is an example of a two-group IRT
twin model for factors with categorical factor
indicators using parameter constraints

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        4000

Number of dependent variables                                    8
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)
U11         U12         U13         U14         U21         U22
U23         U24

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                            15
Minimum value for logit thresholds                           -15
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)
ex7.29.dat
Input data format  FREE

UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

U11
Category 1    0.503         2014.000
Category 2    0.496         1986.000
U12
Category 1    0.499         1997.000
Category 2    0.501         2003.000
U13
Category 1    0.489         1956.000
Category 2    0.511         2044.000
U14
Category 1    0.504         2015.000
Category 2    0.496         1985.000
U21
Category 1    0.508         2031.000
Category 2    0.492         1969.000
U22
Category 1    0.510         2041.000
Category 2    0.490         1959.000
U23
Category 1    0.503         2011.000
Category 2    0.497         1989.000
U24
Category 1    0.508         2031.000
Category 2    0.492         1969.000

THE MODEL ESTIMATION TERMINATED NORMALLY

MODEL FIT INFORMATION

Number of Free Parameters                       11

Loglikelihood

H0 Value                      -24258.023
H0 Scaling Correction Factor      1.0050
for MLR

Information Criteria

Akaike (AIC)                   48538.045
Bayesian (BIC)                 48607.280
(n* = (n + 2) / 24)

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

Pearson Chi-Square

Value                            465.386
Degrees of Freedom                   500
P-Value                           0.8643

Likelihood Ratio Chi-Square

Value                            473.902
Degrees of Freedom                   500
P-Value                           0.7936

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

Latent
Classes

1       2030.00000          0.50750
2       1970.00000          0.49250

MODEL RESULTS

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

Latent Class 1 (0)

F1       BY
U11                1.000      0.000    999.000    999.000
U12                0.970      0.075     12.952      0.000
U13                0.978      0.078     12.559      0.000
U14                0.934      0.076     12.335      0.000

F2       BY
U21                1.000      0.000    999.000    999.000
U22                0.970      0.075     12.952      0.000
U23                0.978      0.078     12.559      0.000
U24                0.934      0.076     12.335      0.000

F2       WITH
F1                 0.632      0.080      7.888      0.000

Means
F1                 0.000      0.000    999.000    999.000
F2                 0.000      0.000    999.000    999.000

Thresholds
U11\$1              0.028      0.028      0.984      0.325
U12\$1              0.023      0.028      0.835      0.404
U13\$1             -0.020      0.028     -0.693      0.488
U14\$1              0.028      0.028      1.001      0.317
U21\$1              0.028      0.028      0.984      0.325
U22\$1              0.023      0.028      0.835      0.404
U23\$1             -0.020      0.028     -0.693      0.488
U24\$1              0.028      0.028      1.001      0.317

Variances
F1                 1.037      0.111      9.322      0.000
F2                 1.037      0.111      9.322      0.000

Latent Class 2 (1)

F1       BY
U11                1.000      0.000    999.000    999.000
U12                0.970      0.075     12.952      0.000
U13                0.978      0.078     12.559      0.000
U14                0.934      0.076     12.335      0.000

F2       BY
U21                1.000      0.000    999.000    999.000
U22                0.970      0.075     12.952      0.000
U23                0.978      0.078     12.559      0.000
U24                0.934      0.076     12.335      0.000

F2       WITH
F1                 0.399      0.063      6.326      0.000

Means
F1                 0.000      0.000    999.000    999.000
F2                 0.000      0.000    999.000    999.000

Thresholds
U11\$1              0.028      0.028      0.984      0.325
U12\$1              0.023      0.028      0.835      0.404
U13\$1             -0.020      0.028     -0.693      0.488
U14\$1              0.028      0.028      1.001      0.317
U21\$1              0.028      0.028      0.984      0.325
U22\$1              0.023      0.028      0.835      0.404
U23\$1             -0.020      0.028     -0.693      0.488
U24\$1              0.028      0.028      1.001      0.317

Variances
F1                 1.037      0.111      9.322      0.000
F2                 1.037      0.111      9.322      0.000

Categorical Latent Variables

Means
CDZ#1              0.030      0.032      0.949      0.343

A                  0.683      0.109      6.287      0.000
C                  0.407      0.137      2.963      0.003
E                  0.636      0.052     12.135      0.000
H                  0.450      0.133      3.370      0.001

QUALITY OF NUMERICAL RESULTS

Condition Number for the Information Matrix              0.451E-03
(ratio of smallest to largest eigenvalue)

Beginning Time:  04:43:41
Ending Time:  04:43:50
Elapsed Time:  00:00:09

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Copyright (c) 1998-2017 Muthen & Muthen
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