Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   4:54 AM

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

       Number of clusters                       30

       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

       Number of clusters                       50

       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




UNIVARIATE SAMPLE STATISTICS


     UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS

         Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
        Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median

     Y                     1.938       0.148      -7.667    0.03%      -0.294      1.269      1.831
            3000.000       7.602       0.422      13.976    0.03%       2.479      4.142
     X1                   -0.021      -0.047      -3.801    0.03%      -0.853     -0.271     -0.020
            3000.000       0.983       0.070       3.610    0.03%       0.219      0.811
     X2                    0.018      -0.016      -3.558    0.03%      -0.808     -0.243      0.019
            3000.000       1.028       0.067       4.267    0.03%       0.274      0.858
     W                     0.135       0.109      -1.729    3.33%      -0.965     -0.092      0.284
              30.000       1.167      -0.281       2.816    3.33%       0.518      0.954
     Z                     0.160       0.016      -2.058    2.00%      -0.691     -0.152      0.300
              50.000       1.030      -0.040       2.716    2.00%       0.433      0.977


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                              14

Information Criteria

          Deviance (DIC)                        10690.173
          Estimated Number of Parameters (pD)     148.893



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
              ________      ________      ________
                    0             0             0


           LAMBDA
              Y             X1            X2
              ________      ________      ________
 Y                  0             0             0
 X1                 0             0             0
 X2                 0             0             0


           THETA
              Y             X1            X2
              ________      ________      ________
 Y                  0
 X1                 0             0
 X2                 0             0             0


           ALPHA
              Y             X1            X2
              ________      ________      ________
                    0             0             0


           BETA
              Y             X1            X2
              ________      ________      ________
 Y                  0             1             0
 X1                 0             0             0
 X2                 0             0             0


           PSI
              Y             X1            X2
              ________      ________      ________
 Y                  2
 X1                 0             0
 X2                 0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL2A


           NU
              Y             W
              ________      ________
                    0             0


           LAMBDA
              S%2a          Y             W
              ________      ________      ________
 Y                  0             0             0
 W                  0             0             0


           THETA
              Y             W
              ________      ________
 Y                  0
 W                  0             0


           ALPHA
              S%2a          Y             W
              ________      ________      ________
                    0             0             0


           BETA
              S%2a          Y             W
              ________      ________      ________
 S%2a               0             0             3
 Y                  0             0             4
 W                  0             0             0


           PSI
              S%2a          Y             W
              ________      ________      ________
 S%2a               5
 Y                  6             7
 W                  0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B


           NU
              Y             Z
              ________      ________
                    0             0


           LAMBDA
              S%2b          Y             Z
              ________      ________      ________
 Y                  0             0             0
 Z                  0             0             0


           THETA
              Y             Z
              ________      ________
 Y                  0
 Z                  0             0


           ALPHA
              S%2b          Y             Z
              ________      ________      ________
                    8             9             0


           BETA
              S%2b          Y             Z
              ________      ________      ________
 S%2b               0             0            10
 Y                  0             0            11
 Z                  0             0             0


           PSI
              S%2b          Y             Z
              ________      ________      ________
 S%2b              12
 Y                 13            14
 Z                  0             0             0


     STARTING VALUES FOR WITHIN


           NU
              Y             X1            X2
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              Y             X1            X2
              ________      ________      ________
 Y              1.000         0.000         0.000
 X1             0.000         1.000         0.000
 X2             0.000         0.000         1.000


           THETA
              Y             X1            X2
              ________      ________      ________
 Y              0.000
 X1             0.000         0.000
 X2             0.000         0.000         0.000


           ALPHA
              Y             X1            X2
              ________      ________      ________
                0.000         0.000         0.000


           BETA
              Y             X1            X2
              ________      ________      ________
 Y              0.000         0.000         0.000
 X1             0.000         0.000         0.000
 X2             0.000         0.000         0.000


           PSI
              Y             X1            X2
              ________      ________      ________
 Y              3.801
 X1             0.000         0.492
 X2             0.000         0.000         0.514


     STARTING VALUES FOR BETWEEN LEVEL2A


           NU
              Y             W
              ________      ________
                0.000         0.000


           LAMBDA
              S%2a          Y             W
              ________      ________      ________
 Y              0.000         1.000         0.000
 W              0.000         0.000         1.000


           THETA
              Y             W
              ________      ________
 Y              0.000
 W              0.000         0.000


           ALPHA
              S%2a          Y             W
              ________      ________      ________
                0.000         0.000         0.000


           BETA
              S%2a          Y             W
              ________      ________      ________
 S%2a           0.000         0.000         0.000
 Y              0.000         0.000         0.000
 W              0.000         0.000         0.000


           PSI
              S%2a          Y             W
              ________      ________      ________
 S%2a           1.000
 Y              0.000         3.801
 W              0.000         0.000         0.584


     STARTING VALUES FOR BETWEEN LEVEL2B


           NU
              Y             Z
              ________      ________
                0.000         0.000


           LAMBDA
              S%2b          Y             Z
              ________      ________      ________
 Y              0.000         1.000         0.000
 Z              0.000         0.000         1.000


           THETA
              Y             Z
              ________      ________
 Y              0.000
 Z              0.000         0.000


           ALPHA
              S%2b          Y             Z
              ________      ________      ________
                0.000         1.938         0.000


           BETA
              S%2b          Y             Z
              ________      ________      ________
 S%2b           0.000         0.000         0.000
 Y              0.000         0.000         0.000
 Z              0.000         0.000         0.000


           PSI
              S%2b          Y             Z
              ________      ________      ________
 S%2b           1.000
 Y              0.000         3.801
 Z              0.000         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



     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


   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


     Beginning Time:  04:54:18
        Ending Time:  04:54:20
       Elapsed Time:  00:00:02



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