Mplus VERSION 7
MUTHEN & MUTHEN
09/22/2012  11:20 PM

INPUT INSTRUCTIONS

  TITLE:      this is an example of regression with cross-
              classified data
  DATA:       FILE = ex9.24.dat;
  VARIABLE:   NAMES = y x1 x2 w z level2a level2b;
              CLUSTER = level2b level2a;
              WITHIN = x1 x2;
              BETWEEN = (level2a) w (level2b) z;
  ANALYSIS:   TYPE = CROSSCLASSIFIED RANDOM;
              ESTIMATOR = BAYES;
              PROCESSORS = 2;
              BITER = (2000);
  MODEL:      %WITHIN%
              y ON x1;
              s | y ON x2;
              %BETWEEN level2a%
              y ON w;
              s ON w;
              y WITH s;
              %BETWEEN level2b%
              y ON z;
              s ON Z;
              y WITH s;
  OUTPUT:     TECH1 TECH8;



INPUT READING TERMINATED NORMALLY



this is an example of regression with cross-
classified data

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        3000

Number of dependent variables                                    1
Number of independent variables                                  4
Number of continuous latent variables                            1

Observed dependent variables

  Continuous
   Y

Observed independent variables
   X1          X2          W           Z

Continuous latent variables
   S

Variables with special functions

  Cluster variables     LEVEL2B   LEVEL2A

  Within variables
   X1          X2

  Level 2a between variables
   W

  Level 2b between variables
   Z


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)
  ex9.24.dat
Input data format  FREE


SUMMARY OF DATA

     Cluster information for LEVEL2A


       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

     Cluster information for LEVEL2B


       Size (s)    Cluster ID with Size s

         60        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




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.



Number of Free Parameters                              14



MODEL RESULTS

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

Within Level

 Y          ON
    X1                 0.998       0.026      0.000       0.947       1.047      *

 Residual Variances
    Y                  1.968       0.053      0.000       1.867       2.075      *

Between LEVEL2A Level

 S          ON
    W                  0.512       0.139      0.000       0.233       0.784      *

 Y          ON
    W                  0.630       0.214      0.002       0.202       1.049      *

 Y        WITH
    S                  0.014       0.225      0.468      -0.471       0.456

 Residual Variances
    Y                  1.511       0.524      0.000       0.891       2.828      *
    S                  0.599       0.215      0.000       0.348       1.157      *

Between LEVEL2B Level

 S          ON
    Z                  0.335       0.064      0.000       0.209       0.468      *

 Y          ON
    Z                  0.674       0.121      0.000       0.424       0.901      *

 Y        WITH
    S                  0.008       0.061      0.449      -0.113       0.130

 Intercepts
    Y                  1.569       0.292      0.000       0.970       2.074      *
    S                  0.908       0.161      0.000       0.546       1.195      *

 Residual Variances
    Y                  0.686       0.163      0.000       0.452       1.092      *
    S                  0.162       0.046      0.000       0.100       0.280      *


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           NU
              Y             X1            X2            W             Z
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           LAMBDA
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 Y                  0             0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           LAMBDA
              W             Z
              ________      ________
 Y                  0             0
 X1                 0             0
 X2                 0             0
 W                  0             0
 Z                  0             0


           THETA
              Y             X1            X2            W             Z
              ________      ________      ________      ________      ________
 Y                  0
 X1                 0             0
 X2                 0             0             0
 W                  0             0             0             0
 Z                  0             0             0             0             0


           ALPHA
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           ALPHA
              W             Z
              ________      ________
 1                  0             0


           BETA
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 S%2a               0             0             0             0             0
 S%2b               0             0             0             0             0
 Y                  0             0             0             1             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           BETA
              W             Z
              ________      ________
 S%2a               0             0
 S%2b               0             0
 Y                  0             0
 X1                 0             0
 X2                 0             0
 W                  0             0
 Z                  0             0


           PSI
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 S%2a               0
 S%2b               0             0
 Y                  0             0             2
 X1                 0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           PSI
              W             Z
              ________      ________
 W                  0
 Z                  0             0


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL2A


           NU
              Y             X1            X2            W             Z
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           LAMBDA
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 Y                  0             0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           LAMBDA
              W             Z
              ________      ________
 Y                  0             0
 X1                 0             0
 X2                 0             0
 W                  0             0
 Z                  0             0


           THETA
              Y             X1            X2            W             Z
              ________      ________      ________      ________      ________
 Y                  0
 X1                 0             0
 X2                 0             0             0
 W                  0             0             0             0
 Z                  0             0             0             0             0


           ALPHA
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           ALPHA
              W             Z
              ________      ________
 1                  0             0


           BETA
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 S%2a               0             0             0             0             0
 S%2b               0             0             0             0             0
 Y                  0             0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           BETA
              W             Z
              ________      ________
 S%2a               3             0
 S%2b               0             0
 Y                  4             0
 X1                 0             0
 X2                 0             0
 W                  0             0
 Z                  0             0


           PSI
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 S%2a               5
 S%2b               0             0
 Y                  6             0             7
 X1                 0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           PSI
              W             Z
              ________      ________
 W                  0
 Z                  0             0


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B


           NU
              Y             X1            X2            W             Z
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           LAMBDA
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 Y                  0             0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           LAMBDA
              W             Z
              ________      ________
 Y                  0             0
 X1                 0             0
 X2                 0             0
 W                  0             0
 Z                  0             0


           THETA
              Y             X1            X2            W             Z
              ________      ________      ________      ________      ________
 Y                  0
 X1                 0             0
 X2                 0             0             0
 W                  0             0             0             0
 Z                  0             0             0             0             0


           ALPHA
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 1                  0             8             9             0             0


           ALPHA
              W             Z
              ________      ________
 1                  0             0


           BETA
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 S%2a               0             0             0             0             0
 S%2b               0             0             0             0             0
 Y                  0             0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           BETA
              W             Z
              ________      ________
 S%2a               0             0
 S%2b               0            10
 Y                  0            11
 X1                 0             0
 X2                 0             0
 W                  0             0
 Z                  0             0


           PSI
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 S%2a               0
 S%2b               0            12
 Y                  0            13            14
 X1                 0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           PSI
              W             Z
              ________      ________
 W                  0
 Z                  0             0


     STARTING VALUES FOR WITHIN


           NU
              Y             X1            X2            W             Z
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 Y              0.000         0.000         1.000         0.000         0.000
 X1             0.000         0.000         0.000         1.000         0.000
 X2             0.000         0.000         0.000         0.000         1.000
 W              0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              W             Z
              ________      ________
 Y              0.000         0.000
 X1             0.000         0.000
 X2             0.000         0.000
 W              1.000         0.000
 Z              0.000         1.000


           THETA
              Y             X1            X2            W             Z
              ________      ________      ________      ________      ________
 Y              0.000
 X1             0.000         0.000
 X2             0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           ALPHA
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           ALPHA
              W             Z
              ________      ________
 1              0.000         0.000


           BETA
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 S%2a           0.000         0.000         0.000         0.000         0.000
 S%2b           0.000         0.000         0.000         0.000         0.000
 Y              0.000         0.000         0.000         0.000         0.000
 X1             0.000         0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           BETA
              W             Z
              ________      ________
 S%2a           0.000         0.000
 S%2b           0.000         0.000
 Y              0.000         0.000
 X1             0.000         0.000
 X2             0.000         0.000
 W              0.000         0.000
 Z              0.000         0.000


           PSI
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 S%2a           0.000
 S%2b           0.000         0.000
 Y              0.000         0.000         3.802
 X1             0.000         0.000         0.000         0.492
 X2             0.000         0.000         0.000         0.000         0.514
 W              0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           PSI
              W             Z
              ________      ________
 W              0.000
 Z              0.000         0.000


     STARTING VALUES FOR BETWEEN LEVEL2A


           NU
              Y             X1            X2            W             Z
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 Y              0.000         0.000         1.000         0.000         0.000
 X1             0.000         0.000         0.000         1.000         0.000
 X2             0.000         0.000         0.000         0.000         1.000
 W              0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              W             Z
              ________      ________
 Y              0.000         0.000
 X1             0.000         0.000
 X2             0.000         0.000
 W              1.000         0.000
 Z              0.000         1.000


           THETA
              Y             X1            X2            W             Z
              ________      ________      ________      ________      ________
 Y              0.000
 X1             0.000         0.000
 X2             0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           ALPHA
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           ALPHA
              W             Z
              ________      ________
 1              0.000         0.000


           BETA
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 S%2a           0.000         0.000         0.000         0.000         0.000
 S%2b           0.000         0.000         0.000         0.000         0.000
 Y              0.000         0.000         0.000         0.000         0.000
 X1             0.000         0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           BETA
              W             Z
              ________      ________
 S%2a           0.000         0.000
 S%2b           0.000         0.000
 Y              0.000         0.000
 X1             0.000         0.000
 X2             0.000         0.000
 W              0.000         0.000
 Z              0.000         0.000


           PSI
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 S%2a           1.000
 S%2b           0.000         0.000
 Y              0.000         0.000         3.802
 X1             0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           PSI
              W             Z
              ________      ________
 W              0.584
 Z              0.000         0.000


     STARTING VALUES FOR BETWEEN LEVEL2B


           NU
              Y             X1            X2            W             Z
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 Y              0.000         0.000         1.000         0.000         0.000
 X1             0.000         0.000         0.000         1.000         0.000
 X2             0.000         0.000         0.000         0.000         1.000
 W              0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              W             Z
              ________      ________
 Y              0.000         0.000
 X1             0.000         0.000
 X2             0.000         0.000
 W              1.000         0.000
 Z              0.000         1.000


           THETA
              Y             X1            X2            W             Z
              ________      ________      ________      ________      ________
 Y              0.000
 X1             0.000         0.000
 X2             0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           ALPHA
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 1              0.000         0.000         1.938         0.000         0.000


           ALPHA
              W             Z
              ________      ________
 1              0.000         0.000


           BETA
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 S%2a           0.000         0.000         0.000         0.000         0.000
 S%2b           0.000         0.000         0.000         0.000         0.000
 Y              0.000         0.000         0.000         0.000         0.000
 X1             0.000         0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           BETA
              W             Z
              ________      ________
 S%2a           0.000         0.000
 S%2b           0.000         0.000
 Y              0.000         0.000
 X1             0.000         0.000
 X2             0.000         0.000
 W              0.000         0.000
 Z              0.000         0.000


           PSI
              S%2a          S%2b          Y             X1            X2
              ________      ________      ________      ________      ________
 S%2a           0.000
 S%2b           0.000         1.000
 Y              0.000         0.000         3.802
 X1             0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           PSI
              W             Z
              ________      ________
 W              0.000
 Z              0.000         0.515



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

     Parameter 1~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 2~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 3~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 4~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 5~IW(0.000,-3)              infinity            infinity            infinity
     Parameter 6~IW(0.000,-3)              infinity            infinity            infinity
     Parameter 7~IW(0.000,-3)              infinity            infinity            infinity
     Parameter 8~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 9~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 10~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 11~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 12~IW(0.000,-3)             infinity            infinity            infinity
     Parameter 13~IW(0.000,-3)             infinity            infinity            infinity
     Parameter 14~IW(0.000,-3)             infinity            infinity            infinity


TECHNICAL 8 OUTPUT

   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.135               8
     200              1.259               9
     300              2.020               9
     400              2.133               9
     500              1.433               8
     600              1.372               8
     700              1.276               9
     800              1.367               9
     900              1.549               9
     1000             1.384               9
     1100             1.282               9
     1200             1.076               9
     1300             1.018               9
     1400             1.053               9
     1500             1.090               9
     1600             1.064               9
     1700             1.016               9
     1800             1.007               7
     1900             1.008               7
     2000             1.007               7



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





     Parameter   KS Statistic P-value
     Parameter 9    0.2700    0.0010
     Parameter 3    0.2000    0.0314
     Parameter 6    0.1800    0.0691
     Parameter 10    0.1500    0.1930
     Parameter 11    0.1500    0.1930
     Parameter 1    0.1200    0.4431
     Parameter 14    0.1200    0.4431
     Parameter 7    0.1100    0.5560
     Parameter 4    0.1000    0.6766
     Parameter 2    0.0800    0.8938
     Parameter 5    0.0800    0.8938
     Parameter 8    0.0600    0.9921
     Parameter 12    0.0400    1.0000
     Parameter 13    0.0300    1.0000



     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 Improper Prior
     Parameter 5 Improper Prior
     Parameter 6 Improper Prior
     Parameter 7 Improper Prior
     Parameter 8 Improper Prior
     Parameter 9 Improper Prior
     Parameter 10 Improper Prior
     Parameter 11 Improper Prior
     Parameter 12 Improper Prior
     Parameter 13 Improper Prior
     Parameter 14 Improper Prior


     Beginning Time:  23:20:03
        Ending Time:  23:20:07
       Elapsed Time:  00:00:04



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