Mplus VERSION 7.3
MUTHEN & MUTHEN
09/22/2014   6:01 PM

INPUT INSTRUCTIONS

  TITLE:          this is an example of IRT analysis with
                  random binary items
  DATA:           FILE = ex9.26.dat;
  VARIABLE:       NAMES = u level2a level2b;
                  CATEGORICAL = u;
                  CLUSTER = level2b level2a;
  ANALYSIS:       TYPE = CROSSCLASSIFIED RANDOM;
                  ESTIMATOR = BAYES;
                  PROCESSORS = 2;
  MODEL:          %WITHIN%
                  ! variation across subjects:
                  %BETWEEN level2a%
                  s | f BY u;
                  f@1;
                  u@0;
                  ! variation across items:
                  %BETWEEN level2b%
                  u; [u$1];
                  s; [s*1];
  OUTPUT:         TECH1 TECH8;




*** WARNING in MODEL command
  Variable is uncorrelated with all other variables: U
*** WARNING in MODEL command
  At least one variable is uncorrelated with all other variables in the model.
  Check that this is what is intended.
   2 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS



this is an example of IRT analysis with
random binary items

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        5000

Number of dependent variables                                    1
Number of independent variables                                  0
Number of continuous latent variables                            2

Observed dependent variables

  Binary and ordered categorical (ordinal)
   U

Continuous latent variables
   F           S

Variables with special functions

  Cluster variables     LEVEL2B   LEVEL2A

Estimator                                                    BAYES
Specifications for Bayesian Estimation
  Point estimate                                            MEDIAN
  Number of Markov chain Monte Carlo (MCMC) chains               2
  Random seed for the first chain                                0
  Starting value information                           UNPERTURBED
  Treatment of categorical mediator                         LATENT
  Algorithm used for Markov chain Monte Carlo           GIBBS(PX1)
  Convergence criterion                                  0.500D-01
  Maximum number of iterations                               50000
  K-th iteration used for thinning                               1

Input data file(s)
  ex9.26.dat
Input data format  FREE


SUMMARY OF DATA

     Cluster information for LEVEL2A

       Number of clusters                      100

       Size (s)    Cluster ID with Size s

         50        1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
                   22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
                   40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
                   58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
                   76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93
                   94 95 96 97 98 99 100

     Cluster information for LEVEL2B

       Number of clusters                       50

       Size (s)    Cluster ID with Size s

        100        1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
                   22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
                   40 41 42 43 44 45 46 47 48 49 50



UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

    U
      Category 1    0.418     2092.000
      Category 2    0.582     2908.000



THE MODEL ESTIMATION TERMINATED NORMALLY

     USE THE FBITERATIONS OPTION TO INCREASE THE NUMBER OF ITERATIONS BY A FACTOR
     OF AT LEAST TWO TO CHECK CONVERGENCE AND THAT THE PSR VALUE DOES NOT INCREASE.



MODEL FIT INFORMATION

Number of Free Parameters                               4



MODEL RESULTS

                                Posterior  One-Tailed         95% C.I.
                    Estimate       S.D.      P-Value   Lower 2.5%  Upper 2.5%  Significance

Within Level

Between LEVEL2A Level

 Variances
    F                  1.000       0.000      0.000       1.000       1.000

 Residual Variances
    U                  0.000       0.000      0.000       0.000       0.000

Between LEVEL2B Level

 Means
    S                  1.142       0.107      0.000       0.961       1.373      *

 Thresholds
    U$1               -0.305       0.218      0.080      -0.736       0.141

 Variances
    U                  1.834       0.441      0.000       1.204       2.897      *
    S                  0.258       0.092      0.000       0.152       0.513      *


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           TAU
              U$1
              ________
 1                  0


           NU
              U
              ________
 1                  0


           LAMBDA
              F             S
              ________      ________
 U                  0             0


           THETA
              U
              ________
 U                  0


           ALPHA
              F             S
              ________      ________
 1                  0             0


           BETA
              F             S
              ________      ________
 F                  0             0
 S                  0             0


           PSI
              F             S
              ________      ________
 F                  0
 S                  0             0


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL2A


           TAU
              U$1
              ________
 1                  0


           NU
              U
              ________
 1                  0


           LAMBDA
              F             S
              ________      ________
 U                  0             0


           THETA
              U
              ________
 U                  0


           ALPHA
              F             S
              ________      ________
 1                  0             0


           BETA
              F             S
              ________      ________
 F                  0             0
 S                  0             0


           PSI
              F             S
              ________      ________
 F                  0
 S                  0             0


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B


           TAU
              U$1
              ________
 1                  4


           NU
              U
              ________
 1                  0


           LAMBDA
              F             S
              ________      ________
 U                  0             0


           THETA
              U
              ________
 U                  1


           ALPHA
              F             S
              ________      ________
 1                  0             2


           BETA
              F             S
              ________      ________
 F                  0             0
 S                  0             0


           PSI
              F             S
              ________      ________
 F                  0
 S                  0             3


     STARTING VALUES FOR WITHIN


           TAU
              U$1
              ________
 1              0.000


           NU
              U
              ________
 1              0.000


           LAMBDA
              F             S
              ________      ________
 U              0.000         0.000


           THETA
              U
              ________
 U              1.000


           ALPHA
              F             S
              ________      ________
 1              0.000         0.000


           BETA
              F             S
              ________      ________
 F              0.000         0.000
 S              0.000         0.000


           PSI
              F             S
              ________      ________
 F              0.000
 S              0.000         0.000


     STARTING VALUES FOR BETWEEN LEVEL2A


           TAU
              U$1
              ________
 1              0.000


           NU
              U
              ________
 1              0.000


           LAMBDA
              F             S
              ________      ________
 U              0.000         0.000


           THETA
              U
              ________
 U              0.000


           ALPHA
              F             S
              ________      ________
 1              0.000         0.000


           BETA
              F             S
              ________      ________
 F              0.000         0.000
 S              0.000         0.000


           PSI
              F             S
              ________      ________
 F              1.000
 S              0.000         0.000


     STARTING VALUES FOR BETWEEN LEVEL2B


           TAU
              U$1
              ________
 1             -0.183


           NU
              U
              ________
 1              0.000


           LAMBDA
              F             S
              ________      ________
 U              0.000         0.000


           THETA
              U
              ________
 U              1.000


           ALPHA
              F             S
              ________      ________
 1              0.000         1.000


           BETA
              F             S
              ________      ________
 F              0.000         0.000
 S              0.000         0.000


           PSI
              F             S
              ________      ________
 F              0.000
 S              0.000         1.000



     PRIORS FOR ALL PARAMETERS            PRIOR MEAN      PRIOR VARIANCE     PRIOR STD. DEV.

     Parameter 1~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 2~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 3~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 4~N(0.000,5.000)              0.0000              5.0000              2.2361


TECHNICAL 8 OUTPUT



     Kolmogorov-Smirnov comparing posterior distributions across chains 1 and 2 using 100 draws.





     Parameter   KS Statistic P-value
     Parameter 3    0.2000    0.0314
     Parameter 1    0.1500    0.1930
     Parameter 2    0.1400    0.2606
     Parameter 4    0.1300    0.3439



     Simulated prior distributions

     Parameter       Prior Mean  Prior Variance  Prior Std. Dev.


     Parameter 1 Improper Prior
     Parameter 2 Improper Prior
     Parameter 3 Improper Prior
     Parameter 4         0.0050          4.9231          2.2188


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.845               2
     200              1.334               4
     300              1.123               4
     400              1.136               2
     500              1.037               3


     Beginning Time:  18:01:46
        Ending Time:  18:01:49
       Elapsed Time:  00:00:03



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