Mplus VERSION 7.2
MUTHEN & MUTHEN
05/07/2014   2:38 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:  14:38:05
        Ending Time:  14:38:05
       Elapsed Time:  00:00:00



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