Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   4:42 AM

INPUT INSTRUCTIONS

  TITLE:	this is an example of an N=1 time series analysis
      with a first-order autoregressive AR(1)
      IRT model with binary factor indicators
  DATA:	FILE = ex6.27.dat;
  VARIABLE:	NAMES = u1-u4;
  	CATEGORICAL = u1-u4;
  ANALYSIS:	ESTIMATOR = BAYES;
  	PROCESSORS = 2;
  	BITERATIONS = (2000);
  MODEL:	f BY u1-u4*(&1);
  	f@1;
  	f ON f&1;
  OUTPUT:	TECH1 TECH8;
  PLOT:	TYPE = PLOT3;



INPUT READING TERMINATED NORMALLY



this is an example of an N=1 time series analysis
with a first-order autoregressive AR(1)
IRT model with binary factor indicators

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         200

Number of dependent variables                                    4
Number of independent variables                                  0
Number of continuous latent variables                            2

Observed dependent variables

  Binary and ordered categorical (ordinal)
   U1          U2          U3          U4

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
Link                                                        PROBIT

Input data file(s)
  ex6.27.dat
Input data format  FREE


UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

    U1
      Category 1    0.445           89.000
      Category 2    0.555          111.000
    U2
      Category 1    0.445           89.000
      Category 2    0.555          111.000
    U3
      Category 1    0.485           97.000
      Category 2    0.515          103.000
    U4
      Category 1    0.410           82.000
      Category 2    0.590          118.000



THE MODEL ESTIMATION TERMINATED NORMALLY

     USE THE FBITERATIONS OPTION TO INCREASE THE NUMBER OF ITERATIONS BY A FACTOR
     OF AT LEAST TWO TO CHECK CONVERGENCE AND THAT THE PSR VALUE DOES NOT INCREASE.



MODEL FIT INFORMATION

Number of Free Parameters                               9



MODEL RESULTS

                                Posterior  One-Tailed         95% C.I.
                    Estimate       S.D.      P-Value   Lower 2.5%  Upper 2.5%  Significance

 F        BY
    U1                 0.973       0.227      0.000       0.605       1.489      *
    U2                 1.018       0.224      0.000       0.685       1.536      *
    U3                 1.429       0.326      0.000       0.864       2.162      *
    U4                 1.076       0.230      0.000       0.687       1.591      *

 F          ON
    F&1                0.249       0.098      0.007       0.054       0.437      *

 Thresholds
    U1$1              -0.197       0.145      0.083      -0.494       0.077
    U2$1              -0.192       0.140      0.082      -0.478       0.063
    U3$1              -0.059       0.191      0.367      -0.466       0.274
    U4$1              -0.339       0.157      0.004      -0.668      -0.057      *

 Residual Variances
    F                  1.000       0.000      0.000       1.000       1.000


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
                    6             7             8             9


           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             5
 F&1                0             0


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


     STARTING VALUES


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
               -0.123        -0.123        -0.033        -0.202


           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              1.000
 F&1            0.000         1.000



     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~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 6~N(0.000,5.000)              0.0000              5.0000              2.2361
     Parameter 7~N(0.000,5.000)              0.0000              5.0000              2.2361
     Parameter 8~N(0.000,5.000)              0.0000              5.0000              2.2361
     Parameter 9~N(0.000,5.000)              0.0000              5.0000              2.2361


TECHNICAL 8 OUTPUT



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





     Parameter   KS Statistic P-value
     Parameter 3    0.2200    0.0131
     Parameter 2    0.1600    0.1400
     Parameter 1    0.1600    0.1400
     Parameter 4    0.1400    0.2606
     Parameter 5    0.1000    0.6766
     Parameter 8    0.0800    0.8938
     Parameter 6    0.0800    0.8938
     Parameter 9    0.0400    1.0000
     Parameter 7    0.0400    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         0.0316          4.9704          2.2294
     Parameter 7        -0.1059          4.9900          2.2338
     Parameter 8         0.0194          5.0519          2.2476
     Parameter 9        -0.0873          4.7525          2.1800


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.723               9
     200              1.371               2
     300              1.679               3
     400              2.170               3
     500              1.389               1
     600              1.131               1
     700              1.069               1
     800              1.011               2
     900              1.058               3
     1000             1.068               3
     1100             1.125               3
     1200             1.119               4
     1300             1.050               1
     1400             1.054               1
     1500             1.072               3
     1600             1.115               3
     1700             1.083               3
     1800             1.093               3
     1900             1.066               2
     2000             1.054               2


PLOT INFORMATION

The following plots are available:

  Histograms (sample values)
  Scatterplots (sample values)
  Time series plots (sample values, ACF, PACF)
  Sample proportions and estimated probabilities
  Bayesian posterior parameter distributions
  Bayesian posterior parameter trace plots
  Bayesian autocorrelation plots
  Bayesian prior parameter distributions

     Beginning Time:  04:42:51
        Ending Time:  04:42:51
       Elapsed Time:  00:00:00



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