Mplus VERSION 7.3
MUTHEN & MUTHEN
09/22/2014   5:17 PM

INPUT INSTRUCTIONS

  title:	this is an example of a threshold
  	structure CFA for categorical factor indicators

  montecarlo:
  	names = u1a u1b u1c u2a u2b u2c;
  	generate = u1a-u2c(1);
  	categorical = u1a-u2c;
  	nobs = 500;
  	nreps = 1;
  	save = ex5.10.dat;

  model population:

  	f1 by u1a-u1c@1;
  	f2 by u2a-u2c@1;
  	[u1a$1*-.5 u1b$1*-.5 u1c$1*-.5] (1);	
  	[u2a$1*.5 u2b$1*.5 u2c$1*.5] (2);

  	u1a-u2c*.5;

  	f1-f2*.5; f1 with f2*.2;

  	! note that u* variances should be 1
  	! in order for the Delta parameterization
  	! to give estimates in the correct metric


  model:

  	f1 by u1a-u1c@1;
  	f2 by u2a-u2c@1;
  	[u1a$1*-.5 u1b$1*-.5 u1c$1*-.5] (1);	
  	[u2a$1*.5 u2b$1*.5 u2c$1*.5] (2);


  	f1-f2*.5; f1 with f2*.2;




INPUT READING TERMINATED NORMALLY



this is an example of a threshold
structure CFA for categorical factor indicators

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

Number of replications
    Requested                                                    1
    Completed                                                    1
Value of seed                                                    0

Number of dependent variables                                    6
Number of independent variables                                  0
Number of continuous latent variables                            2

Observed dependent variables

  Binary and ordered categorical (ordinal)
   U1A         U1B         U1C         U2A         U2B         U2C

Continuous latent variables
   F1          F2


Estimator                                                    WLSMV
Maximum number of iterations                                  1000
Convergence criterion                                    0.500D-04
Maximum number of steepest descent iterations                   20
Parameterization                                             DELTA



SAMPLE STATISTICS FOR THE FIRST REPLICATION


     SAMPLE STATISTICS


           Means/Intercepts/Thresholds
              U1A$1         U1B$1         U1C$1         U2A$1         U2B$1
              ________      ________      ________      ________      ________
      1        -0.479        -0.577        -0.490         0.577         0.536


           Means/Intercepts/Thresholds
              U2C$1
              ________
      1         0.507


           Covariances/Correlations/Residual Correlations
              U1A           U1B           U1C           U2A           U2B
              ________      ________      ________      ________      ________
 U1A
 U1B            0.504
 U1C            0.464         0.513
 U2A            0.215         0.085         0.154
 U2B            0.196         0.082         0.204         0.470
 U2C            0.303         0.211         0.110         0.514         0.579


           Covariances/Correlations/Residual Correlations
              U2C
              ________


MODEL FIT INFORMATION

Number of Free Parameters                        5

Chi-Square Test of Model Fit

        Degrees of freedom                      16

        Mean                                15.119
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000            5.812         15.119
           0.980       1.000            6.614         15.119
           0.950       1.000            7.962         15.119
           0.900       1.000            9.312         15.119
           0.800       1.000           11.152         15.119
           0.700       1.000           12.624         15.119
           0.500       0.000           15.338         15.119
           0.300       0.000           18.418         15.119
           0.200       0.000           20.465         15.119
           0.100       0.000           23.542         15.119
           0.050       0.000           26.296         15.119
           0.020       0.000           29.633         15.119
           0.010       0.000           32.000         15.119

RMSEA (Root Mean Square Error Of Approximation)

        Mean                                 0.000
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000            0.000          0.000
           0.980       0.000            0.000          0.000
           0.950       0.000            0.000          0.000
           0.900       0.000            0.000          0.000
           0.800       0.000            0.000          0.000
           0.700       0.000            0.000          0.000
           0.500       0.000            0.000          0.000
           0.300       0.000            0.000          0.000
           0.200       0.000            0.000          0.000
           0.100       0.000            0.000          0.000
           0.050       0.000            0.000          0.000
           0.020       0.000            0.000          0.000
           0.010       0.000            0.000          0.000

WRMR (Weighted Root Mean Square Residual)

        Mean                                 0.742
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000            0.742          0.742
           0.980       0.000            0.742          0.742
           0.950       0.000            0.742          0.742
           0.900       0.000            0.742          0.742
           0.800       0.000            0.742          0.742
           0.700       0.000            0.742          0.742
           0.500       0.000            0.742          0.742
           0.300       0.000            0.742          0.742
           0.200       0.000            0.742          0.742
           0.100       0.000            0.742          0.742
           0.050       0.000            0.742          0.742
           0.020       0.000            0.742          0.742
           0.010       0.000            0.742          0.742


MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff
 F1       BY
  U1A                 1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  U1B                 1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  U1C                 1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

 F2       BY
  U2A                 1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  U2B                 1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  U2C                 1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

 F1       WITH
  F2                  0.200     0.1760     0.0000     0.0400     0.0006 1.000 1.000

 Thresholds
  U1A$1              -0.500    -0.5146     0.0000     0.0433     0.0002 1.000 1.000
  U1B$1              -0.500    -0.5146     0.0000     0.0433     0.0002 1.000 1.000
  U1C$1              -0.500    -0.5146     0.0000     0.0433     0.0002 1.000 1.000
  U2A$1               0.500     0.5397     0.0000     0.0441     0.0016 1.000 1.000
  U2B$1               0.500     0.5397     0.0000     0.0441     0.0016 1.000 1.000
  U2C$1               0.500     0.5397     0.0000     0.0441     0.0016 1.000 1.000

 Variances
  F1                  0.500     0.4940     0.0000     0.0431     0.0000 1.000 1.000
  F2                  0.500     0.5257     0.0000     0.0435     0.0007 1.000 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.504E+00
       (ratio of smallest to largest eigenvalue)


TECHNICAL OUTPUT


     PARAMETER SPECIFICATION


           TAU
              U1A$1         U1B$1         U1C$1         U2A$1         U2B$1
              ________      ________      ________      ________      ________
      1           1             1             1             2             2


           TAU
              U2C$1
              ________
      1           2


           NU
              U1A           U1B           U1C           U2A           U2B
              ________      ________      ________      ________      ________
      1           0             0             0             0             0


           NU
              U2C
              ________
      1           0


           LAMBDA
              F1            F2
              ________      ________
 U1A                0             0
 U1B                0             0
 U1C                0             0
 U2A                0             0
 U2B                0             0
 U2C                0             0


           ALPHA
              F1            F2
              ________      ________
      1           0             0


           BETA
              F1            F2
              ________      ________
 F1                 0             0
 F2                 0             0


           PSI
              F1            F2
              ________      ________
 F1                 3
 F2                 4             5


     STARTING VALUES


           TAU
              U1A$1         U1B$1         U1C$1         U2A$1         U2B$1
              ________      ________      ________      ________      ________
      1        -0.500        -0.500        -0.500         0.500         0.500


           TAU
              U2C$1
              ________
      1         0.500


           NU
              U1A           U1B           U1C           U2A           U2B
              ________      ________      ________      ________      ________
      1         0.000         0.000         0.000         0.000         0.000


           NU
              U2C
              ________
      1         0.000


           LAMBDA
              F1            F2
              ________      ________
 U1A            1.000         0.000
 U1B            1.000         0.000
 U1C            1.000         0.000
 U2A            0.000         1.000
 U2B            0.000         1.000
 U2C            0.000         1.000


           ALPHA
              F1            F2
              ________      ________
      1         0.000         0.000


           BETA
              F1            F2
              ________      ________
 F1             0.000         0.000
 F2             0.000         0.000


           PSI
              F1            F2
              ________      ________
 F1             0.500
 F2             0.200         0.500


     POPULATION VALUES


           TAU
              U1A$1         U1B$1         U1C$1         U2A$1         U2B$1
              ________      ________      ________      ________      ________
 1             -0.500        -0.500        -0.500         0.500         0.500


           TAU
              U2C$1
              ________
 1              0.500


           NU
              U1A           U1B           U1C           U2A           U2B
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           NU
              U2C
              ________
 1              0.000


           LAMBDA
              F1            F2
              ________      ________
 U1A            1.000         0.000
 U1B            1.000         0.000
 U1C            1.000         0.000
 U2A            0.000         1.000
 U2B            0.000         1.000
 U2C            0.000         1.000


           THETA
              U1A           U1B           U1C           U2A           U2B
              ________      ________      ________      ________      ________
 U1A            0.500
 U1B            0.000         0.500
 U1C            0.000         0.000         0.500
 U2A            0.000         0.000         0.000         0.500
 U2B            0.000         0.000         0.000         0.000         0.500
 U2C            0.000         0.000         0.000         0.000         0.000


           THETA
              U2C
              ________
 U2C            0.500


           ALPHA
              F1            F2
              ________      ________
 1              0.000         0.000


           BETA
              F1            F2
              ________      ________
 F1             0.000         0.000
 F2             0.000         0.000


           PSI
              F1            F2
              ________      ________
 F1             0.500
 F2             0.200         0.500


SAVEDATA INFORMATION

  Order of variables

    U1A
    U1B
    U1C
    U2A
    U2B
    U2C

  Save file
    ex5.10.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  17:17:48
        Ending Time:  17:17:48
       Elapsed Time:  00:00:00



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