Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:43 AM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a two-level random
              first-order autoregressive AR(1) IRT model
              with binary indicators, random indicator thresholds,
              random residual factor variance, and a between-level factor

  montecarlo:
  	names are u1-u4;
      NOBS = 20000;
      NREP = 1;
      NCSIZES = 1;
      CSIZES = 200(100);
       generate = u1-u4(1);
    	categorical = u1-u4;
      save = ex9.35part2.dat;

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

  model population:
      %within%
      f by u1-u4*1(&1);
  !    y1-y4*.5;
      logvf | f;
      s | f on f&1;
      %between%
      fb BY u1-u4*1;
      fb*.2;
      u1-u4*.3;
      [logvf@0]; logvf*.1;
      [s*0.3]; s*.02;

  model:
       %within%
      f by u1-u4*1(&1 1-4);
  !    y1-y4*.5;
      logvf | f;
      s | f on f&1;
      %between%
      fb BY u1-u4*1 (1-4);
      fb*.2;
      u1-u4*.3;
      [logvf@0]; logvf*.1;
      [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) IRT model
with binary indicators, random indicator thresholds,
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

  Binary and ordered categorical (ordinal)
   U1          U2          U3          U4

Continuous latent variables
   F           F&1         FB          LOGVF       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
Link                                                        PROBIT


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                       16



MODEL RESULTS

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

 F        BY
  U1                  1.000     0.9670     0.0000     0.0278     0.0011 1.000 1.000
  U2                  1.000     0.9978     0.0000     0.0265     0.0000 1.000 1.000
  U3                  1.000     1.0119     0.0000     0.0278     0.0001 1.000 1.000
  U4                  1.000     0.9791     0.0000     0.0256     0.0004 1.000 1.000

Between Level

 FB       BY
  U1                  1.000     0.9670     0.0000     0.0278     0.0011 1.000 1.000
  U2                  1.000     0.9978     0.0000     0.0265     0.0000 1.000 1.000
  U3                  1.000     1.0119     0.0000     0.0278     0.0001 1.000 1.000
  U4                  1.000     0.9791     0.0000     0.0256     0.0004 1.000 1.000

 Means
  LOGVF               0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  S                   0.300     0.2976     0.0000     0.0144     0.0000 1.000 1.000

 Thresholds
  U1$1                0.000    -0.0656     0.0000     0.0509     0.0043 1.000 0.000
  U2$1                0.000    -0.0422     0.0000     0.0515     0.0018 1.000 0.000
  U3$1                0.000    -0.0170     0.0000     0.0543     0.0003 1.000 0.000
  U4$1                0.000     0.0384     0.0000     0.0504     0.0015 1.000 0.000

 Variances
  FB                  0.200     0.1642     0.0000     0.0271     0.0013 1.000 1.000
  LOGVF               0.100     0.1098     0.0000     0.0234     0.0001 1.000 1.000
  S                   0.020     0.0177     0.0000     0.0036     0.0000 1.000 1.000

 Residual Variances
  U1                  0.300     0.2772     0.0000     0.0396     0.0005 1.000 1.000
  U2                  0.300     0.3236     0.0000     0.0440     0.0006 1.000 1.000
  U3                  0.300     0.3367     0.0000     0.0463     0.0013 1.000 1.000
  U4                  0.300     0.2877     0.0000     0.0391     0.0002 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                  0.762       0.000              0.264       0.000
  LOGVF               0.712       0.000              0.228       0.000
  S                   0.647       0.000              0.106       0.000
  U1                  0.949       0.000              0.210       0.000
  U2                  0.954       0.000              0.207       0.000
  U3                  0.954       0.000              0.205       0.000
  U4                  0.954       0.000              0.202       0.000


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
                    0             0             0             0


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
                    0             0             0             0


           LAMBDA
              F             F&1
              ________      ________
 U1                 1             0
 U2                 2             0
 U3                 3             0
 U4                 4             0


           THETA
              U1            U2            U3            U4
              ________      ________      ________      ________
 U1                 0
 U2                 0             0
 U3                 0             0             0
 U4                 0             0             0             0


           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


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
                   13            14            15            16


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
                    0             0             0             0


           LAMBDA
              FB            LOGVF         S
              ________      ________      ________
 U1                 1             0             0
 U2                 2             0             0
 U3                 3             0             0
 U4                 4             0             0


           THETA
              U1            U2            U3            U4
              ________      ________      ________      ________
 U1                 5
 U2                 0             6
 U3                 0             0             7
 U4                 0             0             0             8


           ALPHA
              FB            LOGVF         S
              ________      ________      ________
                    0             0             9


           BETA
              FB            LOGVF         S
              ________      ________      ________
 FB                 0             0             0
 LOGVF              0             0             0
 S                  0             0             0


           PSI
              FB            LOGVF         S
              ________      ________      ________
 FB                10
 LOGVF              0            11
 S                  0             0            12


     STARTING VALUES FOR WITHIN


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              F             F&1
              ________      ________
 U1             1.000         0.000
 U2             1.000         0.000
 U3             1.000         0.000
 U4             1.000         0.000


           THETA
              U1            U2            U3            U4
              ________      ________      ________      ________
 U1             1.000
 U2             0.000         1.000
 U3             0.000         0.000         1.000
 U4             0.000         0.000         0.000         1.000


           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


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              FB            LOGVF         S
              ________      ________      ________
 U1             1.000         0.000         0.000
 U2             1.000         0.000         0.000
 U3             1.000         0.000         0.000
 U4             1.000         0.000         0.000


           THETA
              U1            U2            U3            U4
              ________      ________      ________      ________
 U1             0.300
 U2             0.000         0.300
 U3             0.000         0.000         0.300
 U4             0.000         0.000         0.000         0.300


           ALPHA
              FB            LOGVF         S
              ________      ________      ________
                0.000         0.000         0.300


           BETA
              FB            LOGVF         S
              ________      ________      ________
 FB             0.000         0.000         0.000
 LOGVF          0.000         0.000         0.000
 S              0.000         0.000         0.000


           PSI
              FB            LOGVF         S
              ________      ________      ________
 FB             0.200
 LOGVF          0.000         0.100
 S              0.000         0.000         0.020


     POPULATION VALUES FOR WITHIN


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              F             F&1
              ________      ________
 U1             1.000         0.000
 U2             1.000         0.000
 U3             1.000         0.000
 U4             1.000         0.000


           THETA
              U1            U2            U3            U4
              ________      ________      ________      ________
 U1             0.000
 U2             0.000         0.000
 U3             0.000         0.000         0.000
 U4             0.000         0.000         0.000         0.000


           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


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              FB            LOGVF         S
              ________      ________      ________
 U1             1.000         0.000         0.000
 U2             1.000         0.000         0.000
 U3             1.000         0.000         0.000
 U4             1.000         0.000         0.000


           THETA
              U1            U2            U3            U4
              ________      ________      ________      ________
 U1             0.300
 U2             0.000         0.300
 U3             0.000         0.000         0.300
 U4             0.000         0.000         0.000         0.300


           ALPHA
              FB            LOGVF         S
              ________      ________      ________
                0.000         0.000         0.300


           BETA
              FB            LOGVF         S
              ________      ________      ________
 FB             0.000         0.000         0.000
 LOGVF          0.000         0.000         0.000
 S              0.000         0.000         0.000


           PSI
              FB            LOGVF         S
              ________      ________      ________
 FB             0.200
 LOGVF          0.000         0.100
 S              0.000         0.000         0.020



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

     Parameter 1~N(0.000,5.000)              0.0000              5.0000              2.2361
     Parameter 2~N(0.000,5.000)              0.0000              5.0000              2.2361
     Parameter 3~N(0.000,5.000)              0.0000              5.0000              2.2361
     Parameter 4~N(0.000,5.000)              0.0000              5.0000              2.2361
     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~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 9~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 10~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 11~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 12~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 13~N(0.000,5.000)             0.0000              5.0000              2.2361
     Parameter 14~N(0.000,5.000)             0.0000              5.0000              2.2361
     Parameter 15~N(0.000,5.000)             0.0000              5.0000              2.2361
     Parameter 16~N(0.000,5.000)             0.0000              5.0000              2.2361


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    0.1400    0.2606
     Parameter 16    0.1300    0.3439
     Parameter 1    0.1000    0.6766
     Parameter 15    0.1000    0.6766
     Parameter 13    0.0900    0.7942
     Parameter 5    0.0600    0.9921
     Parameter 2    0.0500    0.9995
     Parameter 14    0.0500    0.9995
     Parameter 4    0.0400    1.0000
     Parameter 8    0.0300    1.0000
     Parameter 6    0.0300    1.0000
     Parameter 7    0.0200    1.0000
     Parameter 10    0.0100    1.0000
     Parameter 9    0.0100    1.0000
     Parameter 3    0.0100    1.0000
     Parameter 12    0.0000    1.0000



     Simulated prior distributions

     Parameter       Prior Mean  Prior Variance  Prior Std. Dev.


     Parameter 1         0.0050          4.9231          2.2188
     Parameter 2         0.0037          4.9991          2.2359
     Parameter 3        -0.0395          5.2395          2.2890
     Parameter 4         0.1095          5.4076          2.3254
     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         0.0316          4.9704          2.2294
     Parameter 14        -0.1059          4.9900          2.2338
     Parameter 15         0.0194          5.0519          2.2476
     Parameter 16        -0.0873          4.7525          2.1800


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

     REPLICATION 1:


                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.263               3
     200              1.797               3
     300              1.612               3
     400              1.059               3
     500              1.062               4
     600              1.091               11
     700              1.156               11
     800              1.200               11
     900              1.127               2
     1000             1.101               2
     1100             1.056               2
     1200             1.019               2
     1300             1.036               11
     1400             1.021               8
     1500             1.066               2
     1600             1.081               2
     1700             1.069               2
     1800             1.031               2
     1900             1.057               1
     2000             1.091               1
     2100             1.101               1
     2200             1.120               1
     2300             1.061               1


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    U1
    U2
    U3
    U4
    CLUSTER

  Save file
    ex9.35part2.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  03:43:31
        Ending Time:  03:44:57
       Elapsed Time:  00:01:26



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