Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:09 PM
INPUT INSTRUCTIONS
TITLE: this is an example of non-linear
constraint on the logit parameters of an
unordered categorical (nominal) variable
DATA: FILE IS ex3.10.dat;
VARIABLE: NAMES ARE u;
NOMINAL = u;
MODEL: [u#1] (p1);
[u#2] (p2);
[u#3] (p2);
MODEL CONSTRAINT:
p2 = log ((exp (p1) - 1)/2 - 1);
INPUT READING TERMINATED NORMALLY
this is an example of non-linear
constraint on the logit parameters of an
unordered categorical (nominal) variable
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of dependent variables 1
Number of independent variables 0
Number of continuous latent variables 0
Observed dependent variables
Unordered categorical (nominal)
U
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 0
Adaptive quadrature ON
Cholesky OFF
Input data file(s)
ex3.10.dat
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U
Category 1 0.620 310.000
Category 2 0.110 55.000
Category 3 0.100 50.000
Category 4 0.170 85.000
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 1
Loglikelihood
H0 Value -536.568
H0 Scaling Correction Factor 0.9447
for MLR
Information Criteria
Akaike (AIC) 1075.136
Bayesian (BIC) 1079.351
Sample-Size Adjusted BIC 1076.176
(n* = (n + 2) / 24)
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Means
U#1 1.469 0.040 36.927 0.000
U#2 -0.398 0.129 -3.097 0.002
U#3 -0.398 0.129 -3.097 0.002
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.167E-02
(ratio of smallest to largest eigenvalue)
Beginning Time: 23:09:14
Ending Time: 23:09:14
Elapsed Time: 00:00:00
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