Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:32 AM

INPUT INSTRUCTIONS

    montecarlo:
    		names are u;
    		nobservations = 5000;
    		nreps = 1;
    		CSIZES = 50[100(1)]; ! 50 items and 100 subjects
    		ncsize = 1[1];
  		generate=u(1);
  		categorical=u;
          save = ex9.26.dat;

    ANALYSIS:  TYPE = cross random;
    		estimator=bayes; proc=2;

    model population:
    		%within%

  		! across subject variation
    		%between level2a%
  		s | f BY u;
  		f@1;
  		u@0;

  		! across item variation
    		%between level2b%
    		u*1.5; [u$1*0];
    		s*0.2; [s*1];

    model:
    		%within%

  		! across subject variation
    		%between level2a%
  		s | f BY u;
  		f@1;
  		u@0;

  		! across item variation
    		%between level2b%
    		u*1.5; [u$1*0];
    		s*0.2; [s*1];

    output:
    		tech8 tech9;




*** 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




SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        5000

Number of replications
    Requested                                                    1
    Completed                                                    1
Value of seed                                                    0

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


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
Link                                                        PROBIT


SUMMARY OF DATA FOR THE FIRST REPLICATION

     Cluster information

     Number of level 2a clusters          100
     Number of level 2b clusters           50






MODEL FIT INFORMATION

Number of Free Parameters                        4



MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff
Within Level

Between LEVEL2A Level

 Variances
  F                   1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

 Residual Variances
  U                   0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

Between LEVEL2B Level

 Means
  S                   1.000     1.1365     0.0000     0.1026     0.0186 1.000 1.000

 Thresholds
  U$1                 0.000    -0.3055     0.0000     0.2180     0.0933 1.000 0.000

 Variances
  U                   1.500     1.8296     0.0000     0.4404     0.1086 1.000 1.000
  S                   0.200     0.2553     0.0000     0.0867     0.0031 1.000 1.000


CORRELATIONS AND MEAN SQUARE ERROR OF THE TRUE FACTOR VALUES AND THE FACTOR SCORES

                        CORRELATIONS                MEAN SQUARE ERROR
                    Average    Std. Dev.           Average    Std. Dev.
  S                   0.894       0.000              0.421       0.000
  B2a_U               0.068       0.000              0.032       0.000
  B2b_U               0.984       0.000              0.244       0.000


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           TAU
              U$1
              ________
                    0


           NU
              U
              ________
                    0


           THETA
              U
              ________
 U                  0


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL2A


           TAU
              U$1
              ________
                    0


           NU
              U
              ________
                    0


           LAMBDA
              F
              ________
 U                  0


           THETA
              U
              ________
 U                  0


           ALPHA
              F
              ________
                    0


           BETA
              F
              ________
 F                  0


           PSI
              F
              ________
 F                  0


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B


           TAU
              U$1
              ________
                    4


           NU
              U
              ________
                    0


           LAMBDA
              S
              ________
 U                  0


           THETA
              U
              ________
 U                  1


           ALPHA
              S
              ________
                    2


           BETA
              S
              ________
 S                  0


           PSI
              S
              ________
 S                  3


     STARTING VALUES FOR WITHIN


           TAU
              U$1
              ________
                0.000


           NU
              U
              ________
                0.000


           THETA
              U
              ________
 U              1.000


     STARTING VALUES FOR BETWEEN LEVEL2A


           TAU
              U$1
              ________
                0.000


           NU
              U
              ________
                0.000


           LAMBDA
              F
              ________
 U              0.000


           THETA
              U
              ________
 U              0.000


           ALPHA
              F
              ________
                0.000


           BETA
              F
              ________
 F              0.000


           PSI
              F
              ________
 F              1.000


     STARTING VALUES FOR BETWEEN LEVEL2B


           TAU
              U$1
              ________
                0.000


           NU
              U
              ________
                0.000


           LAMBDA
              S
              ________
 U              0.000


           THETA
              U
              ________
 U              1.500


           ALPHA
              S
              ________
                1.000


           BETA
              S
              ________
 S              0.000


           PSI
              S
              ________
 S              0.200


     POPULATION VALUES FOR WITHIN


           TAU
              U$1
              ________
                0.000


           NU
              U
              ________
                0.000


           THETA
              U
              ________
 U              0.000


     POPULATION VALUES FOR BETWEEN LEVEL2A


           TAU
              U$1
              ________
                0.000


           NU
              U
              ________
                0.000


           LAMBDA
              F
              ________
 U              0.000


           THETA
              U
              ________
 U              0.000


           ALPHA
              F
              ________
                0.000


           BETA
              F
              ________
 F              0.000


           PSI
              F
              ________
 F              1.000


     POPULATION VALUES FOR BETWEEN LEVEL2B


           TAU
              U$1
              ________
                0.000


           NU
              U
              ________
                0.000


           LAMBDA
              S
              ________
 U              0.000


           THETA
              U
              ________
 U              1.500


           ALPHA
              S
              ________
                1.000


           BETA
              S
              ________
 S              0.000


           PSI
              S
              ________
 S              0.200



     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

     REPLICATION 1:



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





     Parameter   KS Statistic P-value
     Parameter 3    0.2100    0.0205
     Parameter 1    0.1500    0.1930
     Parameter 4    0.1200    0.4431
     Parameter 2    0.1200    0.4431



     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

     REPLICATION 1:


                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.725               2
     200              1.319               4
     300              1.112               4
     400              1.134               2
     500              1.034               3


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    U
    LEVEL2A
    LEVEL2B

  Save file
    ex9.26.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  03:32:11
        Ending Time:  03:32:14
       Elapsed Time:  00:00:03



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