Mplus VERSION 7.3
MUTHEN & MUTHEN
09/22/2014   5:49 PM

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);



INPUT READING TERMINATED NORMALLY



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
  Adaptive quadrature                                           ON
Link                                                         LOGIT
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
          Sample-Size Adjusted BIC       48572.327
            (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

New/Additional Parameters
    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:  17:49:50
        Ending Time:  17:50:03
       Elapsed Time:  00:00:13



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