Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:41 AM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a two-level,
  single-indicator measurement error model

  montecarlo:
  	names are y;
      NOBS = 20000;
      NREP = 1;
      NCSIZES = 1;
      CSIZES = 200(100);
      save = ex9.33.dat;

  ANALYSIS:
      TYPE = TWOLEVEL RANDOM;
      		estimator=bayes;
              biter=(5000);
              proc=2;

  model population:
      %within%
      f by y@1(&1); y*.5;
      s | f on f&1; f*1;
      %between%
      y*.5;
      [s*0.3]; s*.02;
      [y*0];

  model:
       %within%
      f by y@1(&1); y*.5;
      s | f on f&1; f*1;
      %between%
      y*.5;
      [s*0.3]; s*.02;
      [y*0];

  output:
  	tech8 tech9;	
  	



INPUT READING TERMINATED NORMALLY



this is an example of a two-level,
single-indicator measurement error model

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                       20000

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                            3

Observed dependent variables

  Continuous
   Y

Continuous latent variables
   F           F&1         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


SUMMARY OF DATA FOR THE FIRST REPLICATION

     Cluster information

       Size (s)    Number of clusters of Size s

        100           200





MODEL FIT INFORMATION

Number of Free Parameters                        6

Information Criteria

    Deviance (DIC)

        Mean                             56414.390
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        56414.390      56414.390
           0.980       0.000        56414.390      56414.390
           0.950       0.000        56414.390      56414.390
           0.900       0.000        56414.390      56414.390
           0.800       0.000        56414.390      56414.390
           0.700       0.000        56414.390      56414.390
           0.500       0.000        56414.390      56414.390
           0.300       0.000        56414.390      56414.390
           0.200       0.000        56414.390      56414.390
           0.100       0.000        56414.390      56414.390
           0.050       0.000        56414.390      56414.390
           0.020       0.000        56414.390      56414.390
           0.010       0.000        56414.390      56414.390

    Estimated Number of Parameters (pD)

        Mean                             12592.482
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        12592.482      12592.482
           0.980       0.000        12592.482      12592.482
           0.950       0.000        12592.482      12592.482
           0.900       0.000        12592.482      12592.482
           0.800       0.000        12592.482      12592.482
           0.700       0.000        12592.482      12592.482
           0.500       0.000        12592.482      12592.482
           0.300       0.000        12592.482      12592.482
           0.200       0.000        12592.482      12592.482
           0.100       0.000        12592.482      12592.482
           0.050       0.000        12592.482      12592.482
           0.020       0.000        12592.482      12592.482
           0.010       0.000        12592.482      12592.482



MODEL RESULTS

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

 F        BY
  Y                   1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

 Residual Variances
  Y                   0.500     0.5185     0.0000     0.0657     0.0003 1.000 1.000
  F                   1.000     0.9914     0.0000     0.0722     0.0001 1.000 1.000

Between Level

 Means
  Y                   0.000     0.0206     0.0000     0.0487     0.0004 1.000 0.000
  S                   0.300     0.2977     0.0000     0.0209     0.0000 1.000 1.000

 Variances
  Y                   0.500     0.4340     0.0000     0.0472     0.0044 1.000 1.000
  S                   0.020     0.0243     0.0000     0.0044     0.0000 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                   0.748       0.000              0.097       0.000
  Y                   0.965       0.000              0.167       0.000


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           NU
              Y
              ________
                    0


           LAMBDA
              F             F&1
              ________      ________
 Y                  0             0


           THETA
              Y
              ________
 Y                  1


           ALPHA
              F             F&1
              ________      ________
                    0             0


           BETA
              F             F&1
              ________      ________
 F                  0             0
 F&1                0             0


           PSI
              F             F&1
              ________      ________
 F                  2
 F&1                0             0


     PARAMETER SPECIFICATION FOR BETWEEN


           NU
              Y
              ________
                    3


           LAMBDA
              S
              ________
 Y                  0


           THETA
              Y
              ________
 Y                  4


           ALPHA
              S
              ________
                    5


           BETA
              S
              ________
 S                  0


           PSI
              S
              ________
 S                  6


     STARTING VALUES FOR WITHIN


           NU
              Y
              ________
                0.000


           LAMBDA
              F             F&1
              ________      ________
 Y              1.000         0.000


           THETA
              Y
              ________
 Y              0.500


           ALPHA
              F             F&1
              ________      ________
                0.000         0.000


           BETA
              F             F&1
              ________      ________
 F              0.000         0.000
 F&1            0.000         0.000


           PSI
              F             F&1
              ________      ________
 F              1.000
 F&1            0.000         1.000


     STARTING VALUES FOR BETWEEN


           NU
              Y
              ________
                0.000


           LAMBDA
              S
              ________
 Y              0.000


           THETA
              Y
              ________
 Y              0.500


           ALPHA
              S
              ________
                0.300


           BETA
              S
              ________
 S              0.000


           PSI
              S
              ________
 S              0.020


     POPULATION VALUES FOR WITHIN


           NU
              Y
              ________
                0.000


           LAMBDA
              F             F&1
              ________      ________
 Y              1.000         0.000


           THETA
              Y
              ________
 Y              0.500


           ALPHA
              F             F&1
              ________      ________
                0.000         0.000


           BETA
              F             F&1
              ________      ________
 F              0.000         0.000
 F&1            0.000         0.000


           PSI
              F             F&1
              ________      ________
 F              1.000
 F&1            0.000         1.000


     POPULATION VALUES FOR BETWEEN


           NU
              Y
              ________
                0.000


           LAMBDA
              S
              ________
 Y              0.000


           THETA
              Y
              ________
 Y              0.500


           ALPHA
              S
              ________
                0.300


           BETA
              S
              ________
 S              0.000


           PSI
              S
              ________
 S              0.020



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

     Parameter 1~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 2~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 3~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 4~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 5~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 6~IG(-1.000,0.000)          infinity            infinity            infinity


TECHNICAL 8 OUTPUT

     REPLICATION 1:



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





     Parameter   KS Statistic P-value
     Parameter 2    0.2900    0.0003

     REPLICATION 1:


     THE KOLMOGOROV-SMIRNOV DISTRIBUTION TEST FOR PARAMETER 2 HAS A P-VALUE 0.0003,
     INDICATING DISCREPANT POSTERIOR DISTRIBUTIONS IN THE DIFFERENT MCMC CHAINS.
     THIS MAY INDICATE NON-CONVERGENCE DUE TO AN INSUFFICIENT NUMBER OF MCMC ITERATIONS OR IT MAY
     INDICATE A NON-IDENTIFIED MODEL. SPECIFY A LARGER NUMBER OF MCMC ITERATIONS USING THE FBITER
     OPTION OF THE ANALYSIS COMMAND TO INVESTIGATE THE PROBLEM.

     Parameter 1    0.2600    0.0018
     Parameter 4    0.0600    0.9921
     Parameter 3    0.0400    1.0000
     Parameter 5    0.0100    1.0000
     Parameter 6    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


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

     REPLICATION 1:


                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.145               1
     200              4.463               1
     300              4.451               2
     400              6.580               1
     500              3.515               1
     600              1.732               1
     700              1.320               1
     800              1.215               1
     900              1.064               2
     1000             1.006               6
     1100             1.007               1
     1200             1.012               1
     1300             1.007               4
     1400             1.001               6
     1500             1.007               5
     1600             1.022               5
     1700             1.093               1
     1800             1.092               2
     1900             1.096               1
     2000             1.141               1
     2100             1.147               1
     2200             1.157               1
     2300             1.138               1
     2400             1.100               1
     2500             1.094               1
     2600             1.085               1
     2700             1.097               1
     2800             1.132               1
     2900             1.148               1
     3000             1.137               1
     3100             1.119               1
     3200             1.068               1
     3300             1.047               1
     3400             1.047               1
     3500             1.055               1
     3600             1.065               1
     3700             1.060               1
     3800             1.034               1
     3900             1.027               1
     4000             1.032               1
     4100             1.049               1
     4200             1.062               1
     4300             1.068               1
     4400             1.064               1
     4500             1.061               1
     4600             1.072               1
     4700             1.087               1
     4800             1.092               1
     4900             1.088               1
     5000             1.069               1


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    Y
    CLUSTER

  Save file
    ex9.33.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  03:41:52
        Ending Time:  03:42:42
       Elapsed Time:  00:00:50



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