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 with two factors
      and continuous factor indicators
  DATA:	FILE = ex6.28.dat;
  VARIABLE:	NAMES = y11-y14 y21-y24;
  ANALYSIS:	ESTIMATOR = BAYES;
  	PROCESSORS = 2;
  	BITERATIONS = (2000);
  MODEL:	f1 BY y11-y14 (&1);
  	f2 BY y21-y24 (&1);
  	f1 ON f1&1 f2&1;
  	f2 ON f2&1 f1&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 with two factors
and continuous factor indicators

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         100

Number of dependent variables                                    8
Number of independent variables                                  0
Number of continuous latent variables                            4

Observed dependent variables

  Continuous
   Y11         Y12         Y13         Y14         Y21         Y22
   Y23         Y24

Continuous latent variables
   F1          F2          F1&1        F2&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)
  ex6.28.dat
Input data format  FREE



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

     Y11                   0.021      -0.018      -3.685    1.00%      -1.103     -0.413     -0.197
             100.000       2.272      -0.225       3.860    1.00%       0.344      1.352
     Y12                   0.160      -0.169      -3.611    1.00%      -1.121     -0.272      0.302
             100.000       2.334      -0.321       3.829    1.00%       0.492      1.579
     Y13                   0.136       0.051      -3.730    1.00%      -1.264     -0.420     -0.011
             100.000       2.898      -0.349       4.298    1.00%       0.437      1.520
     Y14                   0.105      -0.019      -3.766    1.00%      -1.444     -0.267      0.256
             100.000       3.022      -0.488       3.956    1.00%       0.525      1.467
     Y21                  -0.081       0.008      -3.022    1.00%      -1.435     -0.527     -0.075
             100.000       2.129      -0.700       3.141    1.00%       0.262      1.205
     Y22                  -0.144      -0.417      -4.586    1.00%      -1.240     -0.450     -0.082
             100.000       2.368       0.006       3.045    1.00%       0.270      1.079
     Y23                   0.055      -0.050      -3.759    1.00%      -1.365     -0.256      0.058
             100.000       2.595      -0.417       3.925    1.00%       0.317      1.321
     Y24                  -0.133      -0.109      -3.628    1.00%      -1.648     -0.335      0.076
             100.000       2.233      -0.638       3.133    1.00%       0.350      1.064


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                              29

Information Criteria

          Deviance (DIC)                         2403.245
          Estimated Number of Parameters (pD)     168.227



MODEL RESULTS

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

 F1       BY
    Y11                1.000       0.000      0.000       1.000       1.000
    Y12                1.070       0.135      0.000       0.849       1.390      *
    Y13                1.199       0.148      0.000       0.945       1.543      *
    Y14                1.163       0.151      0.000       0.898       1.496      *

 F2       BY
    Y21                1.000       0.000      0.000       1.000       1.000
    Y22                1.118       0.162      0.000       0.858       1.508      *
    Y23                1.090       0.167      0.000       0.829       1.469      *
    Y24                0.900       0.146      0.000       0.659       1.232      *

 F1         ON
    F1&1               0.441       0.128      0.001       0.177       0.683      *
    F2&1               0.197       0.137      0.060      -0.047       0.489

 F2         ON
    F2&1               0.414       0.146      0.002       0.133       0.707      *
    F1&1               0.141       0.140      0.162      -0.142       0.398

 F2       WITH
    F1                 0.491       0.159      0.000       0.238       0.874      *

 Intercepts
    Y11               -0.054       0.252      0.405      -0.633       0.396
    Y12                0.072       0.263      0.393      -0.505       0.569
    Y13                0.042       0.296      0.435      -0.612       0.567
    Y14                0.013       0.294      0.481      -0.622       0.533
    Y21               -0.168       0.228      0.228      -0.604       0.292
    Y22               -0.238       0.250      0.181      -0.739       0.252
    Y23               -0.036       0.254      0.442      -0.537       0.441
    Y24               -0.215       0.216      0.167      -0.639       0.217

 Residual Variances
    Y11                0.910       0.166      0.000       0.650       1.308      *
    Y12                0.789       0.160      0.000       0.519       1.148      *
    Y13                0.980       0.189      0.000       0.667       1.411      *
    Y14                1.226       0.233      0.000       0.843       1.735      *
    Y21                0.842       0.174      0.000       0.562       1.233      *
    Y22                0.807       0.187      0.000       0.502       1.207      *
    Y23                1.137       0.219      0.000       0.783       1.650      *
    Y24                1.260       0.218      0.000       0.911       1.755      *
    F1                 1.009       0.248      0.000       0.627       1.609      *
    F2                 1.039       0.275      0.000       0.596       1.658      *


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION


           NU
              Y11           Y12           Y13           Y14           Y21
              ________      ________      ________      ________      ________
                    1             2             3             4             5


           NU
              Y22           Y23           Y24
              ________      ________      ________
                    6             7             8


           LAMBDA
              F1            F2            F1&1          F2&1
              ________      ________      ________      ________
 Y11                0             0             0             0
 Y12                9             0             0             0
 Y13               10             0             0             0
 Y14               11             0             0             0
 Y21                0             0             0             0
 Y22                0            12             0             0
 Y23                0            13             0             0
 Y24                0            14             0             0


           THETA
              Y11           Y12           Y13           Y14           Y21
              ________      ________      ________      ________      ________
 Y11               15
 Y12                0            16
 Y13                0             0            17
 Y14                0             0             0            18
 Y21                0             0             0             0            19
 Y22                0             0             0             0             0
 Y23                0             0             0             0             0
 Y24                0             0             0             0             0


           THETA
              Y22           Y23           Y24
              ________      ________      ________
 Y22               20
 Y23                0            21
 Y24                0             0            22


           ALPHA
              F1            F2            F1&1          F2&1
              ________      ________      ________      ________
                    0             0             0             0


           BETA
              F1            F2            F1&1          F2&1
              ________      ________      ________      ________
 F1                 0             0            23            24
 F2                 0             0            25            26
 F1&1               0             0             0             0
 F2&1               0             0             0             0


           PSI
              F1            F2            F1&1          F2&1
              ________      ________      ________      ________
 F1                27
 F2                28            29
 F1&1               0             0             0
 F2&1               0             0             0             0


     STARTING VALUES


           NU
              Y11           Y12           Y13           Y14           Y21
              ________      ________      ________      ________      ________
                0.021         0.160         0.136         0.105        -0.081


           NU
              Y22           Y23           Y24
              ________      ________      ________
               -0.144         0.055        -0.133


           LAMBDA
              F1            F2            F1&1          F2&1
              ________      ________      ________      ________
 Y11            1.000         0.000         0.000         0.000
 Y12            1.000         0.000         0.000         0.000
 Y13            1.000         0.000         0.000         0.000
 Y14            1.000         0.000         0.000         0.000
 Y21            0.000         1.000         0.000         0.000
 Y22            0.000         1.000         0.000         0.000
 Y23            0.000         1.000         0.000         0.000
 Y24            0.000         1.000         0.000         0.000


           THETA
              Y11           Y12           Y13           Y14           Y21
              ________      ________      ________      ________      ________
 Y11            1.136
 Y12            0.000         1.167
 Y13            0.000         0.000         1.449
 Y14            0.000         0.000         0.000         1.511
 Y21            0.000         0.000         0.000         0.000         1.065
 Y22            0.000         0.000         0.000         0.000         0.000
 Y23            0.000         0.000         0.000         0.000         0.000
 Y24            0.000         0.000         0.000         0.000         0.000


           THETA
              Y22           Y23           Y24
              ________      ________      ________
 Y22            1.184
 Y23            0.000         1.298
 Y24            0.000         0.000         1.116


           ALPHA
              F1            F2            F1&1          F2&1
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           BETA
              F1            F2            F1&1          F2&1
              ________      ________      ________      ________
 F1             0.000         0.000         0.000         0.000
 F2             0.000         0.000         0.000         0.000
 F1&1           0.000         0.000         0.000         0.000
 F2&1           0.000         0.000         0.000         0.000


           PSI
              F1            F2            F1&1          F2&1
              ________      ________      ________      ________
 F1             1.000
 F2             0.000         1.000
 F1&1           0.000         0.000         1.000
 F2&1           0.000         0.000         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~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 9~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 10~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 11~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 12~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 13~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 14~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 15~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 16~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 17~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 18~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 19~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 20~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 21~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 22~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 23~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 24~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 25~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 26~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 27~IW(0.000,-3)             infinity            infinity            infinity
     Parameter 28~IW(0.000,-3)             infinity            infinity            infinity
     Parameter 29~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 20    0.2100    0.0205
     Parameter 12    0.1900    0.0470
     Parameter 5    0.1900    0.0470
     Parameter 4    0.1700    0.0994
     Parameter 28    0.1600    0.1400
     Parameter 7    0.1600    0.1400
     Parameter 16    0.1400    0.2606
     Parameter 6    0.1300    0.3439
     Parameter 24    0.1300    0.3439
     Parameter 26    0.1200    0.4431
     Parameter 3    0.1200    0.4431
     Parameter 2    0.1100    0.5560
     Parameter 13    0.1100    0.5560
     Parameter 22    0.1000    0.6766
     Parameter 18    0.1000    0.6766
     Parameter 11    0.1000    0.6766
     Parameter 19    0.0900    0.7942
     Parameter 23    0.0800    0.8938
     Parameter 1    0.0800    0.8938
     Parameter 27    0.0800    0.8938
     Parameter 9    0.0700    0.9610
     Parameter 10    0.0700    0.9610
     Parameter 8    0.0700    0.9610
     Parameter 17    0.0700    0.9610
     Parameter 21    0.0600    0.9921
     Parameter 25    0.0600    0.9921
     Parameter 15    0.0500    0.9995
     Parameter 29    0.0500    0.9995
     Parameter 14    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
     Parameter 14 Improper Prior
     Parameter 15 Improper Prior
     Parameter 16 Improper Prior
     Parameter 17 Improper Prior
     Parameter 18 Improper Prior
     Parameter 19 Improper Prior
     Parameter 20 Improper Prior
     Parameter 21 Improper Prior
     Parameter 22 Improper Prior
     Parameter 23 Improper Prior
     Parameter 24 Improper Prior
     Parameter 25 Improper Prior
     Parameter 26 Improper Prior
     Parameter 27 Improper Prior
     Parameter 28 Improper Prior
     Parameter 29 Improper Prior


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.190               4
     200              1.081               9
     300              1.468               6
     400              1.348               1
     500              1.134               1
     600              1.075               5
     700              1.034               23
     800              1.031               29
     900              1.054               1
     1000             1.030               7
     1100             1.101               3
     1200             1.099               3
     1300             1.070               1
     1400             1.076               1
     1500             1.054               2
     1600             1.012               20
     1700             1.011               28
     1800             1.009               20
     1900             1.016               28
     2000             1.021               20


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:  04:42:52
        Ending Time:  04:42:52
       Elapsed Time:  00:00:00



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