Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:29 AM

INPUT INSTRUCTIONS

  TITLE:	this is an example of an N=1
          first-order autoregressive AR(1) CFA model
  	with continuous factor indicators

  montecarlo:
  	names are y1-y4;
  	nobservations = 200;
  	nreps = 1;
      save = ex6.26.dat;

  ANALYSIS:	

      estimator = bayes;
      proc = 2;
      biter = (2000);

  MODEL POPULATION:

  	f BY y1@1
  	y2*1
  	y3*1
  	y4*1 (&1);
  	y1-y4*1;
      f on f&1*.3;
      f*1;

  MODEL:
  	
  f BY y1@1
  	y2*1
  	y3*1
  	y4*1 (&1);
  	y1-y4*1;
      f on f&1*.3;
      f*1;

  output:
  	tech8;



INPUT READING TERMINATED NORMALLY



this is an example of an N=1
first-order autoregressive AR(1) CFA model
with continuous factor indicators

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         200

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                            2

Observed dependent variables

  Continuous
   Y1          Y2          Y3          Y4

Continuous latent variables
   F           F&1


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





MODEL FIT INFORMATION

Number of Free Parameters                       13

Information Criteria

    Deviance (DIC)

        Mean                              2435.864
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         2435.864       2435.864
           0.980       0.000         2435.864       2435.864
           0.950       0.000         2435.864       2435.864
           0.900       0.000         2435.864       2435.864
           0.800       0.000         2435.864       2435.864
           0.700       0.000         2435.864       2435.864
           0.500       0.000         2435.864       2435.864
           0.300       0.000         2435.864       2435.864
           0.200       0.000         2435.864       2435.864
           0.100       0.000         2435.864       2435.864
           0.050       0.000         2435.864       2435.864
           0.020       0.000         2435.864       2435.864
           0.010       0.000         2435.864       2435.864

    Estimated Number of Parameters (pD)

        Mean                               167.726
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000          167.726        167.726
           0.980       0.000          167.726        167.726
           0.950       0.000          167.726        167.726
           0.900       0.000          167.726        167.726
           0.800       0.000          167.726        167.726
           0.700       0.000          167.726        167.726
           0.500       0.000          167.726        167.726
           0.300       0.000          167.726        167.726
           0.200       0.000          167.726        167.726
           0.100       0.000          167.726        167.726
           0.050       0.000          167.726        167.726
           0.020       0.000          167.726        167.726
           0.010       0.000          167.726        167.726



MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff
 F        BY
  Y1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2                  1.000     1.0973     0.0000     0.1248     0.0095 1.000 1.000
  Y3                  1.000     1.1996     0.0000     0.1431     0.0398 1.000 1.000
  Y4                  1.000     1.1179     0.0000     0.1390     0.0139 1.000 1.000

 F          ON
  F&1                 0.300     0.3100     0.0000     0.0835     0.0001 1.000 1.000

 Intercepts
  Y1                  0.000     0.0827     0.0000     0.1185     0.0068 1.000 0.000
  Y2                  0.000     0.1665     0.0000     0.1246     0.0277 1.000 0.000
  Y3                  0.000     0.1409     0.0000     0.1406     0.0199 1.000 0.000
  Y4                  0.000     0.1139     0.0000     0.1333     0.0130 1.000 0.000

 Residual Variances
  Y1                  1.000     1.0035     0.0000     0.1273     0.0000 1.000 1.000
  Y2                  1.000     0.8897     0.0000     0.1216     0.0122 1.000 1.000
  Y3                  1.000     1.0377     0.0000     0.1487     0.0014 1.000 1.000
  Y4                  1.000     1.1196     0.0000     0.1524     0.0143 1.000 1.000
  F                   1.000     0.9106     0.0000     0.1819     0.0080 1.000 1.000


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION


           NU
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
                    1             2             3             4


           LAMBDA
              F             F&1
              ________      ________
 Y1                 0             0
 Y2                 5             0
 Y3                 6             0
 Y4                 7             0


           THETA
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1                 8
 Y2                 0             9
 Y3                 0             0            10
 Y4                 0             0             0            11


           ALPHA
              F             F&1
              ________      ________
                    0             0


           BETA
              F             F&1
              ________      ________
 F                  0            12
 F&1                0             0


           PSI
              F             F&1
              ________      ________
 F                 13
 F&1                0             0


     STARTING VALUES


           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             1.000
 Y2             0.000         1.000
 Y3             0.000         0.000         1.000
 Y4             0.000         0.000         0.000         1.000


           ALPHA
              F             F&1
              ________      ________
                0.000         0.000


           BETA
              F             F&1
              ________      ________
 F              0.000         0.300
 F&1            0.000         0.000


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


     POPULATION VALUES


           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             1.000
 Y2             0.000         1.000
 Y3             0.000         0.000         1.000
 Y4             0.000         0.000         0.000         1.000


           ALPHA
              F             F&1
              ________      ________
                0.000         0.000


           BETA
              F             F&1
              ________      ________
 F              0.000         0.300
 F&1            0.000         0.000


           PSI
              F             F&1
              ________      ________
 F              1.000
 F&1            0.000         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~N(0.000,infinity)           0.0000            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~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 9~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 10~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 11~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 12~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 13~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    0.1600    0.1400
     Parameter 13    0.1200    0.4431
     Parameter 5    0.1100    0.5560
     Parameter 11    0.1000    0.6766
     Parameter 9    0.1000    0.6766
     Parameter 7    0.0800    0.8938
     Parameter 12    0.0700    0.9610
     Parameter 3    0.0700    0.9610
     Parameter 2    0.0700    0.9610
     Parameter 6    0.0700    0.9610
     Parameter 8    0.0600    0.9921
     Parameter 10    0.0600    0.9921
     Parameter 1    0.0500    0.9995



     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


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

     REPLICATION 1:


                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.280               6
     200              1.313               13
     300              1.071               13
     400              1.014               10
     500              1.031               5
     600              1.032               5
     700              1.052               6
     800              1.012               6
     900              1.015               4
     1000             1.007               4
     1100             1.005               4
     1200             1.014               7
     1300             1.005               2
     1400             1.014               7
     1500             1.003               12
     1600             1.004               8
     1700             1.015               7
     1800             1.007               7
     1900             1.005               8
     2000             1.006               5


SAVEDATA INFORMATION

  Order of variables

    Y1
    Y2
    Y3
    Y4

  Save file
    ex6.26.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  03:29:16
        Ending Time:  03:29:16
       Elapsed Time:  00:00:00



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