Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:13 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 -24258.020
H0 Scaling Correction Factor 1.0055
for MLR
Information Criteria
Akaike (AIC) 48538.040
Bayesian (BIC) 48607.275
Sample-Size Adjusted BIC 48572.322
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 465.492
Degrees of Freedom 500
P-Value 0.8635
Likelihood Ratio Chi-Square
Value 473.897
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 0.969 0.075 12.881 0.000
U13 0.977 0.078 12.504 0.000
U14 0.932 0.076 12.295 0.000
F2 BY
U21 1.000 0.000 999.000 999.000
U22 0.969 0.075 12.881 0.000
U23 0.977 0.078 12.504 0.000
U24 0.932 0.076 12.295 0.000
F2 WITH
F1 0.633 0.080 7.870 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 -0.692 0.489
U14$1 0.028 0.028 1.002 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 -0.692 0.489
U24$1 0.028 0.028 1.002 0.317
Variances
F1 1.041 0.112 9.266 0.000
F2 1.041 0.112 9.266 0.000
Latent Class 2 (1)
F1 BY
U11 1.000 0.000 999.000 999.000
U12 0.969 0.075 12.881 0.000
U13 0.977 0.078 12.504 0.000
U14 0.932 0.076 12.295 0.000
F2 BY
U21 1.000 0.000 999.000 999.000
U22 0.969 0.075 12.881 0.000
U23 0.977 0.078 12.504 0.000
U24 0.932 0.076 12.295 0.000
F2 WITH
F1 0.398 0.063 6.296 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 -0.692 0.489
U14$1 0.028 0.028 1.002 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 -0.692 0.489
U24$1 0.028 0.028 1.002 0.317
Variances
F1 1.041 0.112 9.266 0.000
F2 1.041 0.112 9.266 0.000
Categorical Latent Variables
Means
CDZ#1 0.030 0.032 0.949 0.343
New/Additional Parameters
A 0.684 0.109 6.300 0.000
C 0.405 0.139 2.923 0.003
E 0.639 0.053 12.150 0.000
H 0.450 0.133 3.382 0.001
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.452E-03
(ratio of smallest to largest eigenvalue)
RESULTS IN PROBABILITY SCALE
Estimate
Latent Class 1 (0)
U11
Category 1 0.506
Category 2 0.494
U12
Category 1 0.505
Category 2 0.495
U13
Category 1 0.496
Category 2 0.504
U14
Category 1 0.506
Category 2 0.494
U21
Category 1 0.506
Category 2 0.494
U22
Category 1 0.505
Category 2 0.495
U23
Category 1 0.496
Category 2 0.504
U24
Category 1 0.506
Category 2 0.494
Latent Class 2 (1)
U11
Category 1 0.506
Category 2 0.494
U12
Category 1 0.505
Category 2 0.495
U13
Category 1 0.496
Category 2 0.504
U14
Category 1 0.506
Category 2 0.494
U21
Category 1 0.506
Category 2 0.494
U22
Category 1 0.505
Category 2 0.495
U23
Category 1 0.496
Category 2 0.504
U24
Category 1 0.506
Category 2 0.494
LATENT CLASS INDICATOR ODDS RATIOS FOR THE LATENT CLASSES
95% C.I.
Estimate S.E. Lower 2.5% Upper 2.5%
Latent Class 1 Compared to Latent Class 2
U11
Category > 1 1.000 0.000 1.000 1.000
U12
Category > 1 1.000 0.000 1.000 1.000
U13
Category > 1 1.000 0.000 1.000 1.000
U14
Category > 1 1.000 0.000 1.000 1.000
U21
Category > 1 1.000 0.000 1.000 1.000
U22
Category > 1 1.000 0.000 1.000 1.000
U23
Category > 1 1.000 0.000 1.000 1.000
U24
Category > 1 1.000 0.000 1.000 1.000
Beginning Time: 23:13:20
Ending Time: 23:13:22
Elapsed Time: 00:00:02
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