Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:42 AM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a two-level random
          first-order autoregressive AR(1) confirmatory factor
          analysis (CFA) with continuous factor indicators,
          random indicator intercepts, random residual factor variance,
          and a between-level factor

  montecarlo:
  	names are y1-y4;
      NOBS = 20000;
      NREP = 1;
      NCSIZES = 1;
      CSIZES = 200(100);
      save = ex9.34.dat;

  ANALYSIS:
      TYPE = TWOLEVEL RANDOM;
      		estimator=bayes;
              biter=(2000);
              proc=2;

  model population:
      %within%
      f by y1@1 y2-y4*1(&1);
      y1-y4*.5;
      logv | f;
      s | f on f&1;
      %between%
      fb BY y1-y4*.7;
      fb@1;
      y1-y4*.3;
      [logv*0]; logv*.01;
      [s*0.3]; s*.02;


  model:
      %within%
      f by y1@1 y2-y4*1(&1);
      y1-y4*.5;
      logv | f;
      s | f on f&1;
      %between%
      fb BY y1-y4*.7;
      fb@1;
      y1-y4*.3;
      [logv*0]; logv*.01;
      [s*0.3]; s*.02;

  output:
  	tech8 tech9;	
  	



INPUT READING TERMINATED NORMALLY



this is an example of a two-level random
first-order autoregressive AR(1) confirmatory factor
analysis (CFA) with continuous factor indicators,
random indicator intercepts, random residual factor variance,
and a between-level factor

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                                    4
Number of independent variables                                  0
Number of continuous latent variables                            5

Observed dependent variables

  Continuous
   Y1          Y2          Y3          Y4

Continuous latent variables
   F           F&1         FB          LOGV        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                       23

Information Criteria

    Deviance (DIC)

        Mean                            189916.524
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000       189916.524     189916.524
           0.980       0.000       189916.524     189916.524
           0.950       0.000       189916.524     189916.524
           0.900       0.000       189916.524     189916.524
           0.800       0.000       189916.524     189916.524
           0.700       0.000       189916.524     189916.524
           0.500       0.000       189916.524     189916.524
           0.300       0.000       189916.524     189916.524
           0.200       0.000       189916.524     189916.524
           0.100       0.000       189916.524     189916.524
           0.050       0.000       189916.524     189916.524
           0.020       0.000       189916.524     189916.524
           0.010       0.000       189916.524     189916.524

    Estimated Number of Parameters (pD)

        Mean                             18189.418
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        18189.418      18189.418
           0.980       0.000        18189.418      18189.418
           0.950       0.000        18189.418      18189.418
           0.900       0.000        18189.418      18189.418
           0.800       0.000        18189.418      18189.418
           0.700       0.000        18189.418      18189.418
           0.500       0.000        18189.418      18189.418
           0.300       0.000        18189.418      18189.418
           0.200       0.000        18189.418      18189.418
           0.100       0.000        18189.418      18189.418
           0.050       0.000        18189.418      18189.418
           0.020       0.000        18189.418      18189.418
           0.010       0.000        18189.418      18189.418



MODEL RESULTS

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

 F        BY
  Y1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2                  1.000     1.0004     0.0000     0.0074     0.0000 1.000 1.000
  Y3                  1.000     0.9980     0.0000     0.0074     0.0000 1.000 1.000
  Y4                  1.000     0.9934     0.0000     0.0075     0.0000 1.000 1.000

 Residual Variances
  Y1                  0.500     0.4946     0.0000     0.0068     0.0000 1.000 1.000
  Y2                  0.500     0.5005     0.0000     0.0068     0.0000 1.000 1.000
  Y3                  0.500     0.4989     0.0000     0.0067     0.0000 1.000 1.000
  Y4                  0.500     0.5108     0.0000     0.0069     0.0001 1.000 1.000

Between Level

 FB       BY
  Y1                  0.700     0.6040     0.0000     0.0563     0.0092 1.000 1.000
  Y2                  0.700     0.6618     0.0000     0.0589     0.0015 1.000 1.000
  Y3                  0.700     0.6563     0.0000     0.0594     0.0019 1.000 1.000
  Y4                  0.700     0.6070     0.0000     0.0591     0.0087 1.000 1.000

 Means
  LOGV                0.000     0.0060     0.0000     0.0174     0.0000 1.000 0.000
  S                   0.300     0.2976     0.0000     0.0125     0.0000 1.000 1.000

 Intercepts
  Y1                  0.000     0.0780     0.0000     0.0593     0.0061 1.000 0.000
  Y2                  0.000     0.0350     0.0000     0.0627     0.0012 1.000 0.000
  Y3                  0.000     0.0184     0.0000     0.0630     0.0003 1.000 0.000
  Y4                  0.000    -0.0418     0.0000     0.0613     0.0017 1.000 0.000

 Variances
  FB                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  LOGV                0.010     0.0110     0.0000     0.0036     0.0000 1.000 1.000
  S                   0.020     0.0180     0.0000     0.0030     0.0000 1.000 1.000

 Residual Variances
  Y1                  0.300     0.2995     0.0000     0.0399     0.0000 1.000 1.000
  Y2                  0.300     0.2917     0.0000     0.0438     0.0001 1.000 1.000
  Y3                  0.300     0.3069     0.0000     0.0449     0.0000 1.000 1.000
  Y4                  0.300     0.3175     0.0000     0.0421     0.0003 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.
  FB                  0.891       0.000              0.419       0.000
  LOGV                0.521       0.000              0.088       0.000
  S                   0.795       0.000              0.085       0.000
  Y1                  0.981       0.000              0.159       0.000
  Y2                  0.983       0.000              0.156       0.000
  Y3                  0.983       0.000              0.154       0.000
  Y4                  0.983       0.000              0.153       0.000


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           NU
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
                    0             0             0             0


           LAMBDA
              F             F&1
              ________      ________
 Y1                 0             0
 Y2                 1             0
 Y3                 2             0
 Y4                 3             0


           THETA
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1                 4
 Y2                 0             5
 Y3                 0             0             6
 Y4                 0             0             0             7


           ALPHA
              F             F&1
              ________      ________
                    0             0


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


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


     PARAMETER SPECIFICATION FOR BETWEEN


           NU
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
                    8             9            10            11


           LAMBDA
              FB            LOGV          S
              ________      ________      ________
 Y1                12             0             0
 Y2                13             0             0
 Y3                14             0             0
 Y4                15             0             0


           THETA
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1                16
 Y2                 0            17
 Y3                 0             0            18
 Y4                 0             0             0            19


           ALPHA
              FB            LOGV          S
              ________      ________      ________
                    0            20            21


           BETA
              FB            LOGV          S
              ________      ________      ________
 FB                 0             0             0
 LOGV               0             0             0
 S                  0             0             0


           PSI
              FB            LOGV          S
              ________      ________      ________
 FB                 0
 LOGV               0            22
 S                  0             0            23


     STARTING VALUES FOR WITHIN


           NU
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              F             F&1
              ________      ________
 Y1             1.000         0.000
 Y2             1.000         0.000
 Y3             1.000         0.000
 Y4             1.000         0.000


           THETA
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1             0.500
 Y2             0.000         0.500
 Y3             0.000         0.000         0.500
 Y4             0.000         0.000         0.000         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              0.000
 F&1            0.000         1.000


     STARTING VALUES FOR BETWEEN


           NU
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              FB            LOGV          S
              ________      ________      ________
 Y1             0.700         0.000         0.000
 Y2             0.700         0.000         0.000
 Y3             0.700         0.000         0.000
 Y4             0.700         0.000         0.000


           THETA
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1             0.300
 Y2             0.000         0.300
 Y3             0.000         0.000         0.300
 Y4             0.000         0.000         0.000         0.300


           ALPHA
              FB            LOGV          S
              ________      ________      ________
                0.000         0.000         0.300


           BETA
              FB            LOGV          S
              ________      ________      ________
 FB             0.000         0.000         0.000
 LOGV           0.000         0.000         0.000
 S              0.000         0.000         0.000


           PSI
              FB            LOGV          S
              ________      ________      ________
 FB             1.000
 LOGV           0.000         0.010
 S              0.000         0.000         0.020


     POPULATION VALUES FOR WITHIN


           NU
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              F             F&1
              ________      ________
 Y1             1.000         0.000
 Y2             1.000         0.000
 Y3             1.000         0.000
 Y4             1.000         0.000


           THETA
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1             0.500
 Y2             0.000         0.500
 Y3             0.000         0.000         0.500
 Y4             0.000         0.000         0.000         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              0.000
 F&1            0.000         1.000


     POPULATION VALUES FOR BETWEEN


           NU
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              FB            LOGV          S
              ________      ________      ________
 Y1             0.700         0.000         0.000
 Y2             0.700         0.000         0.000
 Y3             0.700         0.000         0.000
 Y4             0.700         0.000         0.000


           THETA
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1             0.300
 Y2             0.000         0.300
 Y3             0.000         0.000         0.300
 Y4             0.000         0.000         0.000         0.300


           ALPHA
              FB            LOGV          S
              ________      ________      ________
                0.000         0.000         0.300


           BETA
              FB            LOGV          S
              ________      ________      ________
 FB             0.000         0.000         0.000
 LOGV           0.000         0.000         0.000
 S              0.000         0.000         0.000


           PSI
              FB            LOGV          S
              ________      ________      ________
 FB             1.000
 LOGV           0.000         0.010
 S              0.000         0.000         0.020



     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~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 7~IG(-1.000,0.000)          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~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
     Parameter 20~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 21~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 22~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 23~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 11    0.1300    0.3439
     Parameter 9    0.0800    0.8938
     Parameter 12    0.0800    0.8938
     Parameter 15    0.0800    0.8938
     Parameter 17    0.0700    0.9610
     Parameter 10    0.0700    0.9610
     Parameter 13    0.0700    0.9610
     Parameter 14    0.0700    0.9610
     Parameter 16    0.0600    0.9921
     Parameter 20    0.0500    0.9995
     Parameter 8    0.0400    1.0000
     Parameter 18    0.0300    1.0000
     Parameter 19    0.0200    1.0000
     Parameter 21    0.0100    1.0000
     Parameter 3    0.0100    1.0000
     Parameter 7    0.0000    1.0000
     Parameter 22    0.0000    1.0000
     Parameter 4    0.0000    1.0000
     Parameter 5    0.0000    1.0000
     Parameter 1    0.0000    1.0000
     Parameter 23    0.0000    1.0000
     Parameter 2    0.0000    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
     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
     Parameter 20 Improper Prior
     Parameter 21 Improper Prior
     Parameter 22 Improper Prior
     Parameter 23 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              1.251               20
     200              1.112               22
     300              1.064               15
     400              1.047               13
     500              1.056               12
     600              1.028               15
     700              1.023               20
     800              1.017               19
     900              1.043               20
     1000             1.068               20
     1100             1.155               20
     1200             1.056               20
     1300             1.049               20
     1400             1.048               20
     1500             1.013               20
     1600             1.011               20
     1700             1.011               18
     1800             1.014               20
     1900             1.050               20
     2000             1.038               20


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    Y1
    Y2
    Y3
    Y4
    CLUSTER

  Save file
    ex9.34.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  03:42:42
        Ending Time:  03:43:31
       Elapsed Time:  00:00:49



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