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)
      confirmatory factor analysis (CFA) model
      with continuous factor indicators
  DATA:	FILE = ex6.26.dat;
  VARIABLE:	NAMES = y1-y4;
  ANALYSIS:	ESTIMATOR = BAYES;
  	PROCESSORS = 2;
  	BITERATIONS = (2000);	
  MODEL:	f BY y1-y4 (&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)
confirmatory factor analysis (CFA) model
with continuous 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

  Continuous
   Y1          Y2          Y3          Y4

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

Input data file(s)
  ex6.26.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

     Y1                    0.096      -0.218      -3.443    0.50%      -1.214     -0.218      0.115
             200.000       2.000      -0.336       3.146    0.50%       0.456      1.287
     Y2                    0.179       0.096      -3.403    0.50%      -0.965     -0.155      0.091
             200.000       2.046       0.068       5.042    0.50%       0.437      1.375
     Y3                    0.160      -0.095      -4.141    0.50%      -1.168     -0.345      0.030
             200.000       2.424      -0.447       3.793    0.50%       0.552      1.612
     Y4                    0.130      -0.186      -4.430    0.50%      -1.137     -0.125      0.301
             200.000       2.313       0.074       4.586    0.50%       0.657      1.283


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                              13

Information Criteria

          Deviance (DIC)                         2435.851
          Estimated Number of Parameters (pD)     167.713



MODEL RESULTS

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

 F        BY
    Y1                 1.000       0.000      0.000       1.000       1.000
    Y2                 1.097       0.125      0.000       0.890       1.391      *
    Y3                 1.200       0.143      0.000       0.950       1.522      *
    Y4                 1.118       0.139      0.000       0.882       1.443      *

 F          ON
    F&1                0.310       0.084      0.000       0.152       0.482      *

 Intercepts
    Y1                 0.083       0.118      0.232      -0.164       0.307
    Y2                 0.166       0.125      0.097      -0.087       0.401
    Y3                 0.141       0.141      0.154      -0.148       0.411
    Y4                 0.114       0.133      0.184      -0.162       0.374

 Residual Variances
    Y1                 1.004       0.127      0.000       0.777       1.274      *
    Y2                 0.890       0.122      0.000       0.669       1.137      *
    Y3                 1.038       0.149      0.000       0.777       1.355      *
    Y4                 1.120       0.152      0.000       0.842       1.443      *
    F                  0.911       0.182      0.000       0.575       1.283      *


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION


           NU
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
                    1             2             3             4


           LAMBDA
              F             F&1
              ________      ________
 Y1                 0             0
 Y2                 5             0
 Y3                 6             0
 Y4                 7             0


           THETA
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1                 8
 Y2                 0             9
 Y3                 0             0            10
 Y4                 0             0             0            11


           ALPHA
              F             F&1
              ________      ________
                    0             0


           BETA
              F             F&1
              ________      ________
 F                  0            12
 F&1                0             0


           PSI
              F             F&1
              ________      ________
 F                 13
 F&1                0             0


     STARTING VALUES


           NU
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
                0.096         0.179         0.160         0.130


           LAMBDA
              F             F&1
              ________      ________
 Y1             1.000         0.000
 Y2             1.000         0.000
 Y3             1.000         0.000
 Y4             1.000         0.000


           THETA
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1             1.000
 Y2             0.000         1.023
 Y3             0.000         0.000         1.212
 Y4             0.000         0.000         0.000         1.156


           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,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~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 9~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 10~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 11~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 12~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 13~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 4    0.1600    0.1400
     Parameter 13    0.1200    0.4431
     Parameter 5    0.1100    0.5560
     Parameter 11    0.1000    0.6766
     Parameter 9    0.1000    0.6766
     Parameter 7    0.0800    0.8938
     Parameter 12    0.0700    0.9610
     Parameter 3    0.0700    0.9610
     Parameter 2    0.0700    0.9610
     Parameter 6    0.0700    0.9610
     Parameter 8    0.0600    0.9921
     Parameter 10    0.0600    0.9921
     Parameter 1    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


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.279               6
     200              1.313               13
     300              1.071               13
     400              1.014               10
     500              1.031               5
     600              1.032               5
     700              1.052               6
     800              1.012               6
     900              1.015               4
     1000             1.007               4
     1100             1.005               4
     1200             1.014               7
     1300             1.005               2
     1400             1.014               7
     1500             1.003               12
     1600             1.004               8
     1700             1.015               7
     1800             1.007               7
     1900             1.005               8
     2000             1.006               5


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:  04:42:50
        Ending Time:  04:42:50
       Elapsed Time:  00:00:00



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