Mplus VERSION 6
MUTHEN & MUTHEN
04/22/2010 6:15 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);
*** WARNING in VARIABLE command
Variable DZ, used in KNOWNCLASS specification, has been removed from the
USEVARIABLES list. Subsequent errors may occur if this variable is used
elsewhere.
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
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
TESTS OF MODEL FIT
Loglikelihood
H0 Value -24258.023
H0 Scaling Correction Factor 1.005
for MLR
Information Criteria
Number of Free Parameters 11
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
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 2030.00000 0.50750
2 1970.00000 0.49250
CLASSIFICATION QUALITY
Entropy 1.000
CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 2030 0.50750
2 1970 0.49250
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 1.000 0.000
2 0.000 1.000
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Latent Class 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 0.632 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
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: 18:15:30
Ending Time: 18:15:58
Elapsed Time: 00:00:28
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