Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:40 AM

INPUT INSTRUCTIONS

  Title: two-level reg of y on x with random AR(1),
      random intercept, random slope, and random variance

  MONTECARLO:  NAMES ARE y x w xm;
               NOBS = 5000;
               NREP = 1;
               NCSIZES = 1;
               CSIZES = 100(50);
               lagged = y(1) x(1);
               within = x;
               between = w xm;
               save = ex9.31.dat;

  ANALYSIS:   TYPE = TWOLEVEL RANDOM;
      		estimator=bayes;
                 proc=2;
              biter=(1000);

  MODEL POPULATION:

    %WITHIN%
    x*1;
    sx | y on x;
    sy | y on y&1;
    logv | y;
    x on x&1*.5;

    %BETWEEN%
    w-xm*1;
    [sx*.7]; [sy*.2]; [logv*0];
    y*0.3; sx*0.5; sy*.01; logv*.1;
    y on w*.5 xm*.3;
    sy on w*.1 xm*.05;
    sx on w*.3 xm*.4;
    logv on w*.3 xm*.1;


  MODEL:

    %WITHIN%
    x*1;
    sx | y on x;
    sy | y on y&1;
    logv | y;
    x on x&1*.5;

    %BETWEEN%

    [sx*.7]; [sy*.2]; [logv*0];
    y*0.3; sx*0.5; sy*.01; logv*.1;
    y on w*.5 xm*.3;
    sy on w*.1 xm*.05;
    sx on w*.3 xm*.4;
    logv on w*.3 xm*.1;

  output:
      tech8;



INPUT READING TERMINATED NORMALLY



two-level reg of y on x with random AR(1),
random intercept, random slope, and random variance

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                                    2
Number of independent variables                                  4
Number of continuous latent variables                            3

Observed dependent variables

  Continuous
   Y           X

Observed independent variables
   W           XM          Y&1         X&1

Continuous latent variables
   SX          SY          LOGV

Variables with special functions

  Within variables
   X           Y&1         X&1

  Between variables
   W           XM


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

         50           100





MODEL FIT INFORMATION

Number of Free Parameters                       19

Information Criteria

    Deviance (DIC)

        Mean                             28942.243
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        28942.243      28942.243
           0.980       0.000        28942.243      28942.243
           0.950       0.000        28942.243      28942.243
           0.900       0.000        28942.243      28942.243
           0.800       0.000        28942.243      28942.243
           0.700       0.000        28942.243      28942.243
           0.500       0.000        28942.243      28942.243
           0.300       0.000        28942.243      28942.243
           0.200       0.000        28942.243      28942.243
           0.100       0.000        28942.243      28942.243
           0.050       0.000        28942.243      28942.243
           0.020       0.000        28942.243      28942.243
           0.010       0.000        28942.243      28942.243

    Estimated Number of Parameters (pD)

        Mean                               332.607
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000          332.607        332.607
           0.980       0.000          332.607        332.607
           0.950       0.000          332.607        332.607
           0.900       0.000          332.607        332.607
           0.800       0.000          332.607        332.607
           0.700       0.000          332.607        332.607
           0.500       0.000          332.607        332.607
           0.300       0.000          332.607        332.607
           0.200       0.000          332.607        332.607
           0.100       0.000          332.607        332.607
           0.050       0.000          332.607        332.607
           0.020       0.000          332.607        332.607
           0.010       0.000          332.607        332.607



MODEL RESULTS

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

 X          ON
  X&1                 0.500     0.4885     0.0000     0.0123     0.0001 1.000 1.000

 Intercepts
  X                   0.000     0.0135     0.0000     0.0144     0.0002 1.000 0.000

 Residual Variances
  X                   1.000     1.0014     0.0000     0.0206     0.0000 1.000 1.000

Between Level

 SY         ON
  W                   0.100     0.1189     0.0000     0.0151     0.0004 1.000 1.000
  XM                  0.050     0.0522     0.0000     0.0137     0.0000 1.000 1.000

 SX         ON
  W                   0.300     0.2939     0.0000     0.0942     0.0000 1.000 1.000
  XM                  0.400     0.3489     0.0000     0.0829     0.0026 1.000 1.000

 LOGV       ON
  W                   0.300     0.3266     0.0000     0.0445     0.0007 1.000 1.000
  XM                  0.100     0.0539     0.0000     0.0382     0.0021 1.000 0.000

 Y          ON
  W                   0.500     0.4848     0.0000     0.0787     0.0002 1.000 1.000
  XM                  0.300     0.2931     0.0000     0.0662     0.0000 1.000 1.000

 Intercepts
  Y                   0.000    -0.0216     0.0000     0.0661     0.0005 1.000 0.000
  SX                  0.700     0.7716     0.0000     0.0827     0.0051 1.000 1.000
  SY                  0.200     0.1884     0.0000     0.0131     0.0001 1.000 1.000
  LOGV                0.000     0.0566     0.0000     0.0400     0.0032 1.000 0.000

 Residual Variances
  Y                   0.300     0.3767     0.0000     0.0614     0.0059 1.000 1.000
  SX                  0.500     0.6516     0.0000     0.0998     0.0230 1.000 1.000
  SY                  0.010     0.0075     0.0000     0.0021     0.0000 1.000 1.000
  LOGV                0.100     0.0950     0.0000     0.0214     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.
  SX                  0.987       0.000              0.140       0.000
  SY                  0.824       0.000              0.080       0.000
  LOGV                0.894       0.000              0.183       0.000
  Y                   0.979       0.000              0.159       0.000


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           NU
              Y             X             Y&1           X&1
              ________      ________      ________      ________
                    0             0             0             0


           LAMBDA
              Y             X             Y&1           X&1
              ________      ________      ________      ________
 Y                  0             0             0             0
 X                  0             0             0             0
 Y&1                0             0             0             0
 X&1                0             0             0             0


           THETA
              Y             X             Y&1           X&1
              ________      ________      ________      ________
 Y                  0
 X                  0             0
 Y&1                0             0             0
 X&1                0             0             0             0


           ALPHA
              Y             X             Y&1           X&1
              ________      ________      ________      ________
                    0             1             0             0


           BETA
              Y             X             Y&1           X&1
              ________      ________      ________      ________
 Y                  0             0             0             0
 X                  0             0             0             2
 Y&1                0             0             0             0
 X&1                0             0             0             0


           PSI
              Y             X             Y&1           X&1
              ________      ________      ________      ________
 Y                  0
 X                  0             3
 Y&1                0             0             0
 X&1                0             0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN


           NU
              Y             W             XM
              ________      ________      ________
                    0             0             0


           LAMBDA
              SX            SY            LOGV          Y             W
              ________      ________      ________      ________      ________
 Y                  0             0             0             0             0
 W                  0             0             0             0             0
 XM                 0             0             0             0             0


           LAMBDA
              XM
              ________
 Y                  0
 W                  0
 XM                 0


           THETA
              Y             W             XM
              ________      ________      ________
 Y                  0
 W                  0             0
 XM                 0             0             0


           ALPHA
              SX            SY            LOGV          Y             W
              ________      ________      ________      ________      ________
                    4             5             6             7             0


           ALPHA
              XM
              ________
                    0


           BETA
              SX            SY            LOGV          Y             W
              ________      ________      ________      ________      ________
 SX                 0             0             0             0             8
 SY                 0             0             0             0            10
 LOGV               0             0             0             0            12
 Y                  0             0             0             0            14
 W                  0             0             0             0             0
 XM                 0             0             0             0             0


           BETA
              XM
              ________
 SX                 9
 SY                11
 LOGV              13
 Y                 15
 W                  0
 XM                 0


           PSI
              SX            SY            LOGV          Y             W
              ________      ________      ________      ________      ________
 SX                16
 SY                 0            17
 LOGV               0             0            18
 Y                  0             0             0            19
 W                  0             0             0             0             0
 XM                 0             0             0             0             0


           PSI
              XM
              ________
 XM                 0


     STARTING VALUES FOR WITHIN


           NU
              Y             X             Y&1           X&1
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              Y             X             Y&1           X&1
              ________      ________      ________      ________
 Y              1.000         0.000         0.000         0.000
 X              0.000         1.000         0.000         0.000
 Y&1            0.000         0.000         1.000         0.000
 X&1            0.000         0.000         0.000         1.000


           THETA
              Y             X             Y&1           X&1
              ________      ________      ________      ________
 Y              0.000
 X              0.000         0.000
 Y&1            0.000         0.000         0.000
 X&1            0.000         0.000         0.000         0.000


           ALPHA
              Y             X             Y&1           X&1
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           BETA
              Y             X             Y&1           X&1
              ________      ________      ________      ________
 Y              0.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         0.500
 Y&1            0.000         0.000         0.000         0.000
 X&1            0.000         0.000         0.000         0.000


           PSI
              Y             X             Y&1           X&1
              ________      ________      ________      ________
 Y              0.000
 X              0.000         1.000
 Y&1            0.000         0.000         0.500
 X&1            0.000         0.000         0.000         0.500


     STARTING VALUES FOR BETWEEN


           NU
              Y             W             XM
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              SX            SY            LOGV          Y             W
              ________      ________      ________      ________      ________
 Y              0.000         0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         0.000         1.000
 XM             0.000         0.000         0.000         0.000         0.000


           LAMBDA
              XM
              ________
 Y              0.000
 W              0.000
 XM             1.000


           THETA
              Y             W             XM
              ________      ________      ________
 Y              0.000
 W              0.000         0.000
 XM             0.000         0.000         0.000


           ALPHA
              SX            SY            LOGV          Y             W
              ________      ________      ________      ________      ________
                0.700         0.200         0.000         0.000         0.000


           ALPHA
              XM
              ________
                0.000


           BETA
              SX            SY            LOGV          Y             W
              ________      ________      ________      ________      ________
 SX             0.000         0.000         0.000         0.000         0.300
 SY             0.000         0.000         0.000         0.000         0.100
 LOGV           0.000         0.000         0.000         0.000         0.300
 Y              0.000         0.000         0.000         0.000         0.500
 W              0.000         0.000         0.000         0.000         0.000
 XM             0.000         0.000         0.000         0.000         0.000


           BETA
              XM
              ________
 SX             0.400
 SY             0.050
 LOGV           0.100
 Y              0.300
 W              0.000
 XM             0.000


           PSI
              SX            SY            LOGV          Y             W
              ________      ________      ________      ________      ________
 SX             0.500
 SY             0.000         0.010
 LOGV           0.000         0.000         0.100
 Y              0.000         0.000         0.000         0.300
 W              0.000         0.000         0.000         0.000         0.500
 XM             0.000         0.000         0.000         0.000         0.000


           PSI
              XM
              ________
 XM             0.500


     POPULATION VALUES FOR WITHIN


           NU
              Y             X             Y&1           X&1
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              Y             X             Y&1           X&1
              ________      ________      ________      ________
 Y              1.000         0.000         0.000         0.000
 X              0.000         1.000         0.000         0.000
 Y&1            0.000         0.000         1.000         0.000
 X&1            0.000         0.000         0.000         1.000


           THETA
              Y             X             Y&1           X&1
              ________      ________      ________      ________
 Y              0.000
 X              0.000         0.000
 Y&1            0.000         0.000         0.000
 X&1            0.000         0.000         0.000         0.000


           ALPHA
              Y             X             Y&1           X&1
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           BETA
              Y             X             Y&1           X&1
              ________      ________      ________      ________
 Y              0.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         0.500
 Y&1            0.000         0.000         0.000         0.000
 X&1            0.000         0.000         0.000         0.000


           PSI
              Y             X             Y&1           X&1
              ________      ________      ________      ________
 Y              0.000
 X              0.000         1.000
 Y&1            0.000         0.000         1.000
 X&1            0.000         0.000         0.000         1.000


     POPULATION VALUES FOR BETWEEN


           NU
              Y             W             XM
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              SX            SY            LOGV          Y             W
              ________      ________      ________      ________      ________
 Y              0.000         0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         0.000         1.000
 XM             0.000         0.000         0.000         0.000         0.000


           LAMBDA
              XM
              ________
 Y              0.000
 W              0.000
 XM             1.000


           THETA
              Y             W             XM
              ________      ________      ________
 Y              0.000
 W              0.000         0.000
 XM             0.000         0.000         0.000


           ALPHA
              SX            SY            LOGV          Y             W
              ________      ________      ________      ________      ________
                0.700         0.200         0.000         0.000         0.000


           ALPHA
              XM
              ________
                0.000


           BETA
              SX            SY            LOGV          Y             W
              ________      ________      ________      ________      ________
 SX             0.000         0.000         0.000         0.000         0.300
 SY             0.000         0.000         0.000         0.000         0.100
 LOGV           0.000         0.000         0.000         0.000         0.300
 Y              0.000         0.000         0.000         0.000         0.500
 W              0.000         0.000         0.000         0.000         0.000
 XM             0.000         0.000         0.000         0.000         0.000


           BETA
              XM
              ________
 SX             0.400
 SY             0.050
 LOGV           0.100
 Y              0.300
 W              0.000
 XM             0.000


           PSI
              SX            SY            LOGV          Y             W
              ________      ________      ________      ________      ________
 SX             0.500
 SY             0.000         0.010
 LOGV           0.000         0.000         0.100
 Y              0.000         0.000         0.000         0.300
 W              0.000         0.000         0.000         0.000         1.000
 XM             0.000         0.000         0.000         0.000         0.000


           PSI
              XM
              ________
 XM             1.000



     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~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 4~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 5~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 6~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 7~N(0.000,infinity)           0.0000            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~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~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 16~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 17~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 18~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 19~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 4    0.0900    0.7942
     Parameter 15    0.0900    0.7942
     Parameter 8    0.0800    0.8938
     Parameter 16    0.0700    0.9610
     Parameter 7    0.0700    0.9610
     Parameter 9    0.0500    0.9995
     Parameter 14    0.0500    0.9995
     Parameter 12    0.0500    0.9995
     Parameter 13    0.0500    0.9995
     Parameter 19    0.0500    0.9995
     Parameter 3    0.0200    1.0000
     Parameter 6    0.0200    1.0000
     Parameter 10    0.0100    1.0000
     Parameter 2    0.0000    1.0000
     Parameter 11    0.0000    1.0000
     Parameter 5    0.0000    1.0000
     Parameter 17    0.0000    1.0000
     Parameter 18    0.0000    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
     Parameter 18 Improper Prior
     Parameter 19 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              1.113               6
     200              1.037               13
     300              1.068               11
     400              1.081               11
     500              1.024               18
     600              1.021               13
     700              1.014               11
     800              1.009               12
     900              1.008               12
     1000             1.006               12


SAVEDATA INFORMATION

  Order of variables

    Y
    X
    W
    XM
    CLUSTER
    Y&1
    X&1

  Save file
    ex9.31.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  03:40:53
        Ending Time:  03:41:05
       Elapsed Time:  00:00:12



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