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 univariate first-order autoregressive AR(1) model
      for a continuous dependent variable with a covariate
  DATA:	FILE = ex6.24.dat;
  VARIABLE:	NAMES ARE y x;
  	LAGGED = y(1) x(1);
  ANALYSIS:	ESTIMATOR = BAYES;
  	PROCESSORS = 2;
  	BITERATIONS = (1000);
  MODEL:	y ON y&1 x x&1;
  OUTPUT:	TECH1 TECH8;
  PLOT:	TYPE = PLOT3;



INPUT READING TERMINATED NORMALLY



this is an example of an N=1 time series analysis
with a univariate first-order autoregressive AR(1) model
for a continuous dependent variable with a covariate

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         100

Number of dependent variables                                    1
Number of independent variables                                  3
Number of continuous latent variables                            0

Observed dependent variables

  Continuous
   Y

Observed independent variables
   X           Y&1         X&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

Input data file(s)
  ex6.24.dat
Input data format  FREE


SUMMARY OF DATA



COVARIANCE COVERAGE OF DATA

Minimum covariance coverage value   0.100

     Number of missing data patterns             2


     PROPORTION OF DATA PRESENT


           Covariance Coverage
              Y             X
              ________      ________
 Y              1.000
 X              1.000         1.000



UNIVARIATE SAMPLE STATISTICS


     UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS

         Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
        Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median

     Y                     0.109      -0.162      -3.387    1.00%      -1.605     -0.196      0.386
             100.000       2.697      -0.916       3.235    1.00%       0.610      1.651
     X                     0.139      -0.455      -2.584    1.00%      -0.885     -0.057      0.286
             100.000       1.239      -0.383       2.024    1.00%       0.522      1.154


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                               5

Information Criteria

          Deviance (DIC)                          296.229
          Estimated Number of Parameters (pD)       5.182



MODEL RESULTS

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

 Y          ON
    Y&1               -0.022       0.087      0.398      -0.193       0.147
    X                  0.797       0.106      0.000       0.575       0.980      *
    X&1                0.603       0.142      0.000       0.327       0.869      *

 Intercepts
    Y                 -0.082       0.101      0.213      -0.259       0.124

 Residual Variances
    Y                  1.083       0.159      0.000       0.827       1.445      *


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION


           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
              ________      ________      ________      ________
                    1             0             0             0


           BETA
              Y             X             Y&1           X&1
              ________      ________      ________      ________
 Y                  0             2             3             4
 X                  0             0             0             0
 Y&1                0             0             0             0
 X&1                0             0             0             0


           PSI
              Y             X             Y&1           X&1
              ________      ________      ________      ________
 Y                  5
 X                  0             0
 Y&1                0             0             0
 X&1                0             0             0             0


     STARTING VALUES


           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
              ________      ________      ________      ________
                0.109         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         0.000
 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              1.349
 X              0.000         0.619
 Y&1            0.000         0.000         1.362
 X&1            0.000         0.000         0.000         0.625



     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~IG(-1.000,0.000)          infinity            infinity            infinity


TECHNICAL 8 OUTPUT



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





     Parameter   KS Statistic P-value
     Parameter 5    0.1800    0.0691
     Parameter 4    0.1000    0.6766
     Parameter 3    0.0900    0.7942
     Parameter 1    0.0800    0.8938
     Parameter 2    0.0800    0.8938



     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


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.080               2
     200              1.007               4
     300              1.004               4
     400              1.007               5
     500              1.007               5
     600              1.000               3
     700              1.002               1
     800              1.001               1
     900              1.003               1
     1000             1.003               1


PLOT INFORMATION

The following plots are available:

  Histograms (sample values)
  Scatterplots (sample values)
  Time series plots (sample values, ACF, PACF)
  Bayesian posterior parameter distributions
  Bayesian posterior parameter trace plots
  Bayesian autocorrelation plots

     Beginning Time:  04:42:49
        Ending Time:  04:42:49
       Elapsed Time:  00:00:00



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