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
              bivariate cross-lagged model for continuous outcomes
  DATA:       FILE = ex6.25.dat;
  VARIABLE:   NAMES = y1 y2;
              LAGGED = y1(1) y2(1);
  ANALYSIS:   ESTIMATOR = BAYES;
              PROCESSORS = 2;
              BITERATIONS = (500);
  MODEL:      y1 ON y1&1 y2&1;
              y2 ON y2&1 y1&1;
  OUTPUT:     TECH1 TECH8;
  PLOT:       TYPE = PLOT3;



INPUT READING TERMINATED NORMALLY



this is an example of an N=1 time series analysis with a
bivariate cross-lagged model for continuous outcomes

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         100

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

Observed dependent variables

  Continuous
   Y1          Y2

Observed independent variables
   Y1&1        Y2&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)
  ex6.25.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
              Y1            Y2
              ________      ________
 Y1             1.000
 Y2             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

     Y1                   -0.039      -0.213      -2.683    1.00%      -1.050     -0.308      0.014
             100.000       1.174      -0.511       2.230    1.00%       0.228      1.027
     Y2                    0.087       0.199      -2.566    1.00%      -0.882     -0.103      0.065
             100.000       1.083       0.774       3.635    1.00%       0.322      0.996


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

Information Criteria

          Deviance (DIC)                          590.927
          Estimated Number of Parameters (pD)       8.792



MODEL RESULTS

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

 Y1         ON
    Y1&1               0.012       0.110      0.452      -0.200       0.230
    Y2&1              -0.237       0.106      0.004      -0.457      -0.037      *

 Y2         ON
    Y2&1              -0.019       0.098      0.418      -0.216       0.167
    Y1&1               0.344       0.096      0.000       0.160       0.548      *

 Y2       WITH
    Y1                -0.006       0.119      0.482      -0.227       0.232

 Intercepts
    Y1                -0.019       0.110      0.420      -0.236       0.187
    Y2                 0.111       0.100      0.130      -0.083       0.297

 Residual Variances
    Y1                 1.201       0.198      0.000       0.902       1.653      *
    Y2                 1.018       0.158      0.000       0.758       1.373      *


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION


           NU
              Y1            Y2            Y1&1          Y2&1
              ________      ________      ________      ________
                    0             0             0             0


           LAMBDA
              Y1            Y2            Y1&1          Y2&1
              ________      ________      ________      ________
 Y1                 0             0             0             0
 Y2                 0             0             0             0
 Y1&1               0             0             0             0
 Y2&1               0             0             0             0


           THETA
              Y1            Y2            Y1&1          Y2&1
              ________      ________      ________      ________
 Y1                 0
 Y2                 0             0
 Y1&1               0             0             0
 Y2&1               0             0             0             0


           ALPHA
              Y1            Y2            Y1&1          Y2&1
              ________      ________      ________      ________
                    1             2             0             0


           BETA
              Y1            Y2            Y1&1          Y2&1
              ________      ________      ________      ________
 Y1                 0             0             3             4
 Y2                 0             0             5             6
 Y1&1               0             0             0             0
 Y2&1               0             0             0             0


           PSI
              Y1            Y2            Y1&1          Y2&1
              ________      ________      ________      ________
 Y1                 7
 Y2                 8             9
 Y1&1               0             0             0
 Y2&1               0             0             0             0


     STARTING VALUES


           NU
              Y1            Y2            Y1&1          Y2&1
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              Y1            Y2            Y1&1          Y2&1
              ________      ________      ________      ________
 Y1             1.000         0.000         0.000         0.000
 Y2             0.000         1.000         0.000         0.000
 Y1&1           0.000         0.000         1.000         0.000
 Y2&1           0.000         0.000         0.000         1.000


           THETA
              Y1            Y2            Y1&1          Y2&1
              ________      ________      ________      ________
 Y1             0.000
 Y2             0.000         0.000
 Y1&1           0.000         0.000         0.000
 Y2&1           0.000         0.000         0.000         0.000


           ALPHA
              Y1            Y2            Y1&1          Y2&1
              ________      ________      ________      ________
               -0.039         0.087         0.000         0.000


           BETA
              Y1            Y2            Y1&1          Y2&1
              ________      ________      ________      ________
 Y1             0.000         0.000         0.000         0.000
 Y2             0.000         0.000         0.000         0.000
 Y1&1           0.000         0.000         0.000         0.000
 Y2&1           0.000         0.000         0.000         0.000


           PSI
              Y1            Y2            Y1&1          Y2&1
              ________      ________      ________      ________
 Y1             0.587
 Y2             0.000         0.541
 Y1&1           0.000         0.000         0.585
 Y2&1           0.000         0.000         0.000         0.546



     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~IW(0.000,-3)              infinity            infinity            infinity
     Parameter 8~IW(0.000,-3)              infinity            infinity            infinity
     Parameter 9~IW(0.000,-3)              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 4    0.1400    0.2606
     Parameter 6    0.1200    0.4431
     Parameter 3    0.1000    0.6766
     Parameter 2    0.0800    0.8938
     Parameter 9    0.0800    0.8938
     Parameter 5    0.0700    0.9610
     Parameter 7    0.0700    0.9610
     Parameter 8    0.0600    0.9921
     Parameter 1    0.0300    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


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.031               2
     200              1.001               8
     300              1.000               1
     400              1.007               2
     500              1.001               3


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:  04:42:50
       Elapsed Time:  00:00:01



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