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

INPUT INSTRUCTIONS

  TITLE:      this is an example of path analysis with cross-
              classified data
  DATA:       FILE =   ex9.25.dat;
  VARIABLE:   NAMES = y1 y2 x w z level2a level2b;
              CLUSTER = level2b level2a;
              WITHIN = x;
              BETWEEN = (level2a) w (level2b) z;
  ANALYSIS:   TYPE = CROSSCLASSIFIED;
              ESTIMATOR = BAYES;
              PROCESSORS = 2;
  MODEL:      %WITHIN%
              y2 ON y1 x;
              y1 ON x;
              %BETWEEN level2a%
              y1-y2 ON w;
              y1 WITH y2;
              %BETWEEN level2b%
              y1-y2 ON z;
              y1 WITH y2;
  OUTPUT:     TECH1 TECH8;



INPUT READING TERMINATED NORMALLY



this is an example of path analysis with cross-
classified data

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        2000

Number of dependent variables                                    2
Number of independent variables                                  3
Number of continuous latent variables                            0

Observed dependent variables

  Continuous
   Y1          Y2

Observed independent variables
   X           W           Z

Variables with special functions

  Cluster variables     LEVEL2B   LEVEL2A

  Within variables
   X

  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)
  ex9.25.dat
Input data format  FREE


SUMMARY OF DATA

     Cluster information for LEVEL2A

       Number of clusters                       20

       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

     Cluster information for LEVEL2B

       Number of clusters                      100

       Size (s)    Cluster ID with Size s

         20        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




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                              17

Bayesian Posterior Predictive Checking using Chi-Square

          95% Confidence Interval for the Difference Between
          the Observed and the Replicated Chi-Square Values

                                -13.833            22.183

          Posterior Predictive P-Value              0.439



MODEL RESULTS

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

Within Level

 Y2         ON
    Y1                 0.509       0.023      0.000       0.467       0.554      *
    X                 -0.016       0.029      0.305      -0.074       0.038

 Y1         ON
    X                  0.722       0.024      0.000       0.675       0.770      *

 Residual Variances
    Y1                 1.038       0.034      0.000       0.973       1.105      *
    Y2                 1.063       0.035      0.000       1.000       1.137      *

Between LEVEL2A Level

 Y1         ON
    W                  0.635       0.181      0.001       0.281       0.991      *

 Y2         ON
    W                  0.469       0.192      0.010       0.087       0.874      *

 Y1       WITH
    Y2                 0.091       0.301      0.331      -0.414       0.765

 Residual Variances
    Y1                 0.933       0.427      0.000       0.449       2.067      *
    Y2                 1.048       0.460      0.000       0.513       2.328      *

Between LEVEL2B Level

 Y1         ON
    Z                  0.334       0.080      0.000       0.165       0.488      *

 Y2         ON
    Z                  0.651       0.087      0.000       0.465       0.813      *

 Y1       WITH
    Y2                 0.006       0.070      0.460      -0.132       0.140

 Intercepts
    Y1                 1.379       0.175      0.000       0.965       1.675      *
    Y2                 1.496       0.211      0.000       1.154       2.019      *

 Residual Variances
    Y1                 0.533       0.090      0.000       0.389       0.747      *
    Y2                 0.662       0.112      0.000       0.488       0.915      *


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           NU
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           LAMBDA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1                 0             0             0             0             0
 Y2                 0             0             0             0             0
 X                  0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           THETA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1                 0
 Y2                 0             0
 X                  0             0             0
 W                  0             0             0             0
 Z                  0             0             0             0             0


           ALPHA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           BETA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1                 0             0             1             0             0
 Y2                 2             0             3             0             0
 X                  0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           PSI
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1                 4
 Y2                 0             5
 X                  0             0             0
 W                  0             0             0             0
 Z                  0             0             0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL2A


           NU
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           LAMBDA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1                 0             0             0             0             0
 Y2                 0             0             0             0             0
 X                  0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           THETA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1                 0
 Y2                 0             0
 X                  0             0             0
 W                  0             0             0             0
 Z                  0             0             0             0             0


           ALPHA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           BETA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1                 0             0             0             6             0
 Y2                 0             0             0             7             0
 X                  0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           PSI
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1                 8
 Y2                 9            10
 X                  0             0             0
 W                  0             0             0             0
 Z                  0             0             0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B


           NU
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           LAMBDA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1                 0             0             0             0             0
 Y2                 0             0             0             0             0
 X                  0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           THETA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1                 0
 Y2                 0             0
 X                  0             0             0
 W                  0             0             0             0
 Z                  0             0             0             0             0


           ALPHA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 1                 11            12             0             0             0


           BETA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1                 0             0             0             0            13
 Y2                 0             0             0             0            14
 X                  0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           PSI
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1                15
 Y2                16            17
 X                  0             0             0
 W                  0             0             0             0
 Z                  0             0             0             0             0


     STARTING VALUES FOR WITHIN


           NU
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1             1.000         0.000         0.000         0.000         0.000
 Y2             0.000         1.000         0.000         0.000         0.000
 X              0.000         0.000         1.000         0.000         0.000
 W              0.000         0.000         0.000         1.000         0.000
 Z              0.000         0.000         0.000         0.000         1.000


           THETA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1             0.000
 Y2             0.000         0.000
 X              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
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           BETA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1             0.000         0.000         0.000         0.000         0.000
 Y2             0.000         0.000         0.000         0.000         0.000
 X              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
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1             1.747
 Y2             0.000         1.743
 X              0.000         0.000         0.506
 W              0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


     STARTING VALUES FOR BETWEEN LEVEL2A


           NU
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1             1.000         0.000         0.000         0.000         0.000
 Y2             0.000         1.000         0.000         0.000         0.000
 X              0.000         0.000         1.000         0.000         0.000
 W              0.000         0.000         0.000         1.000         0.000
 Z              0.000         0.000         0.000         0.000         1.000


           THETA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1             0.000
 Y2             0.000         0.000
 X              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
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           BETA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1             0.000         0.000         0.000         0.000         0.000
 Y2             0.000         0.000         0.000         0.000         0.000
 X              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
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1             1.747
 Y2             0.000         1.743
 X              0.000         0.000         0.000
 W              0.000         0.000         0.000         0.718
 Z              0.000         0.000         0.000         0.000         0.000


     STARTING VALUES FOR BETWEEN LEVEL2B


           NU
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1             1.000         0.000         0.000         0.000         0.000
 Y2             0.000         1.000         0.000         0.000         0.000
 X              0.000         0.000         1.000         0.000         0.000
 W              0.000         0.000         0.000         1.000         0.000
 Z              0.000         0.000         0.000         0.000         1.000


           THETA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1             0.000
 Y2             0.000         0.000
 X              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
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 1              1.421         1.623         0.000         0.000         0.000


           BETA
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1             0.000         0.000         0.000         0.000         0.000
 Y2             0.000         0.000         0.000         0.000         0.000
 X              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
              Y1            Y2            X             W             Z
              ________      ________      ________      ________      ________
 Y1             1.747
 Y2             0.000         1.743
 X              0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.475



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

     Parameter 1~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 2~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 3~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 4~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 5~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 6~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 7~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 8~IW(0.000,-3)              infinity            infinity            infinity
     Parameter 9~IW(0.000,-3)              infinity            infinity            infinity
     Parameter 10~IW(0.000,-3)             infinity            infinity            infinity
     Parameter 11~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 12~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 13~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 14~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 15~IW(0.000,-3)             infinity            infinity            infinity
     Parameter 16~IW(0.000,-3)             infinity            infinity            infinity
     Parameter 17~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 6    0.2200    0.0131
     Parameter 12    0.2200    0.0131
     Parameter 11    0.2000    0.0314
     Parameter 8    0.1800    0.0691
     Parameter 10    0.1200    0.4431
     Parameter 7    0.1100    0.5560
     Parameter 15    0.0800    0.8938
     Parameter 9    0.0800    0.8938
     Parameter 13    0.0700    0.9610
     Parameter 16    0.0600    0.9921
     Parameter 17    0.0600    0.9921
     Parameter 4    0.0500    0.9995
     Parameter 14    0.0400    1.0000
     Parameter 3    0.0200    1.0000
     Parameter 2    0.0100    1.0000
     Parameter 5    0.0100    1.0000
     Parameter 1    0.0000    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
     Parameter 15 Improper Prior
     Parameter 16 Improper Prior
     Parameter 17 Improper Prior


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              2.080               11
     200              1.145               12
     300              1.189               12
     400              1.598               12
     500              2.121               12
     600              1.744               12
     700              1.232               12
     800              1.023               12


     Beginning Time:  18:01:45
        Ending Time:  18:01:46
       Elapsed Time:  00:00:01



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