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;
LINK = PROBIT;
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);
INPUT READING TERMINATED NORMALLY
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
Adaptive quadrature ON
Link PROBIT
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
Sample-Size Adjusted BIC 19876.474
(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
New/Additional Parameters
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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