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 = (20000);	
  MODEL:	    f BY y1-y4 (&1);
  	        y1-y4 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                              16

Information Criteria

          Deviance (DIC)                         2444.508
          Estimated Number of Parameters (pD)     169.802



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                 1.134       0.148      0.000       0.891       1.476      *
    Y3                 1.210       0.172      0.000       0.936       1.615      *
    Y4                 1.125       0.156      0.000       0.866       1.479      *

 Y1         ON
    F&1                0.299       0.137      0.008       0.056       0.589      *

 Y2         ON
    F&1                0.299       0.130      0.006       0.062       0.575      *

 Y3         ON
    F&1                0.401       0.139      0.001       0.149       0.696      *

 Y4         ON
    F&1                0.359       0.132      0.001       0.118       0.641      *

 Intercepts
    Y1                 0.094       0.112      0.206      -0.127       0.314
    Y2                 0.177       0.117      0.065      -0.055       0.403
    Y3                 0.158       0.129      0.112      -0.100       0.404
    Y4                 0.127       0.123      0.152      -0.118       0.368

 Variances
    F                  0.878       0.197      0.000       0.527       1.300      *

 Residual Variances
    Y1                 1.020       0.137      0.000       0.786       1.320      *
    Y2                 0.883       0.133      0.000       0.646       1.171      *
    Y3                 1.052       0.156      0.000       0.774       1.388      *
    Y4                 1.136       0.155      0.000       0.870       1.473      *


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION


           NU
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
                    0             0             0             0


           LAMBDA
              F             F&1           Y1            Y2            Y3
              ________      ________      ________      ________      ________
 Y1                 0             0             0             0             0
 Y2                 0             0             0             0             0
 Y3                 0             0             0             0             0
 Y4                 0             0             0             0             0


           LAMBDA
              Y4
              ________
 Y1                 0
 Y2                 0
 Y3                 0
 Y4                 0


           THETA
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1                 0
 Y2                 0             0
 Y3                 0             0             0
 Y4                 0             0             0             0


           ALPHA
              F             F&1           Y1            Y2            Y3
              ________      ________      ________      ________      ________
                    0             0             1             2             3


           ALPHA
              Y4
              ________
                    4


           BETA
              F             F&1           Y1            Y2            Y3
              ________      ________      ________      ________      ________
 F                  0             0             0             0             0
 F&1                0             0             0             0             0
 Y1                 0             5             0             0             0
 Y2                 6             7             0             0             0
 Y3                 8             9             0             0             0
 Y4                10            11             0             0             0


           BETA
              Y4
              ________
 F                  0
 F&1                0
 Y1                 0
 Y2                 0
 Y3                 0
 Y4                 0


           PSI
              F             F&1           Y1            Y2            Y3
              ________      ________      ________      ________      ________
 F                 12
 F&1                0             0
 Y1                 0             0            13
 Y2                 0             0             0            14
 Y3                 0             0             0             0            15
 Y4                 0             0             0             0             0


           PSI
              Y4
              ________
 Y4                16


     STARTING VALUES


           NU
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


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


           LAMBDA
              Y4
              ________
 Y1             0.000
 Y2             0.000
 Y3             0.000
 Y4             1.000


           THETA
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1             0.000
 Y2             0.000         0.000
 Y3             0.000         0.000         0.000
 Y4             0.000         0.000         0.000         0.000


           ALPHA
              F             F&1           Y1            Y2            Y3
              ________      ________      ________      ________      ________
                0.000         0.000         0.096         0.179         0.160


           ALPHA
              Y4
              ________
                0.130


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


           BETA
              Y4
              ________
 F              0.000
 F&1            0.000
 Y1             0.000
 Y2             0.000
 Y3             0.000
 Y4             0.000


           PSI
              F             F&1           Y1            Y2            Y3
              ________      ________      ________      ________      ________
 F              1.000
 F&1            0.000         1.000
 Y1             0.000         0.000         1.000
 Y2             0.000         0.000         0.000         1.023
 Y3             0.000         0.000         0.000         0.000         1.212
 Y4             0.000         0.000         0.000         0.000         0.000


           PSI
              Y4
              ________
 Y4             1.156



     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~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 13~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 14~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 15~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 16~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 12    0.1500    0.1930
     Parameter 1    0.1200    0.4431
     Parameter 9    0.1200    0.4431
     Parameter 3    0.1200    0.4431
     Parameter 5    0.1000    0.6766
     Parameter 13    0.1000    0.6766
     Parameter 8    0.0900    0.7942
     Parameter 16    0.0900    0.7942
     Parameter 6    0.0900    0.7942
     Parameter 14    0.0900    0.7942
     Parameter 11    0.0800    0.8938
     Parameter 4    0.0800    0.8938
     Parameter 10    0.0700    0.9610
     Parameter 15    0.0600    0.9921
     Parameter 2    0.0600    0.9921
     Parameter 7    0.0600    0.9921



     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


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              2.761               12
     200              1.117               9
     300              1.375               7
     400              1.056               7
     500              1.036               13
     600              1.041               4
     700              1.027               4
     800              1.008               11
     900              1.010               12
     1000             1.004               12
     1100             1.018               8
     1200             1.042               8
     1300             1.016               8
     1400             1.013               11
     1500             1.016               11
     1600             1.017               11
     1700             1.012               11
     1800             1.011               11
     1900             1.017               11
     2000             1.014               12
     2100             1.031               12
     2200             1.029               12
     2300             1.020               12
     2400             1.010               7
     2500             1.015               12
     2600             1.032               12
     2700             1.043               12
     2800             1.053               12
     2900             1.045               12
     3000             1.032               12
     3100             1.031               12
     3200             1.030               12
     3300             1.027               12
     3400             1.039               8
     3500             1.041               8
     3600             1.039               8
     3700             1.034               6
     3800             1.027               6
     3900             1.025               8
     4000             1.024               8
     4100             1.021               8
     4200             1.023               8
     4300             1.024               8
     4400             1.033               8
     4500             1.032               8
     4600             1.032               8
     4700             1.034               8
     4800             1.026               12
     4900             1.026               12
     5000             1.019               12
     5100             1.017               12
     5200             1.016               12
     5300             1.021               12
     5400             1.019               12
     5500             1.019               12
     5600             1.018               12
     5700             1.021               12
     5800             1.021               12
     5900             1.024               12
     6000             1.024               12
     6100             1.022               12
     6200             1.020               12
     6300             1.019               12
     6400             1.020               12
     6500             1.013               12
     6600             1.016               12
     6700             1.014               12
     6800             1.007               12
     6900             1.007               12
     7000             1.004               12
     7100             1.003               12
     7200             1.004               12
     7300             1.004               12
     7400             1.003               4
     7500             1.005               12
     7600             1.006               12
     7700             1.007               12
     7800             1.006               12
     7900             1.006               12
     8000             1.005               12
     8100             1.005               12
     8200             1.004               12
     8300             1.005               12
     8400             1.006               12
     8500             1.005               12
     8600             1.007               12
     8700             1.006               12
     8800             1.003               12
     8900             1.002               12
     9000             1.002               12
     9100             1.002               12
     9200             1.002               12
     9300             1.001               5
     9400             1.001               5
     9500             1.001               5
     9600             1.001               5
     9700             1.001               12
     9800             1.001               7
     9900             1.001               5
     10000            1.001               12
     10100            1.001               12
     10200            1.001               12
     10300            1.002               12
     10400            1.002               12
     10500            1.001               12
     10600            1.001               12
     10700            1.001               12
     10800            1.001               12
     10900            1.002               12
     11000            1.001               12
     11100            1.001               12
     11200            1.001               12
     11300            1.001               12
     11400            1.000               5
     11500            1.000               5
     11600            1.001               5
     11700            1.001               5
     11800            1.001               5
     11900            1.001               5
     12000            1.001               5
     12100            1.001               15
     12200            1.000               15
     12300            1.000               5
     12400            1.001               5
     12500            1.000               14
     12600            1.000               5
     12700            1.000               5
     12800            1.001               4
     12900            1.001               12
     13000            1.001               4
     13100            1.002               4
     13200            1.001               4
     13300            1.001               4
     13400            1.001               12
     13500            1.001               4
     13600            1.001               4
     13700            1.001               4
     13800            1.001               4
     13900            1.002               4
     14000            1.002               4
     14100            1.002               12
     14200            1.002               4
     14300            1.003               4
     14400            1.003               4
     14500            1.003               4
     14600            1.003               4
     14700            1.004               4
     14800            1.004               4
     14900            1.003               4
     15000            1.003               4
     15100            1.004               4
     15200            1.003               4
     15300            1.004               4
     15400            1.004               4
     15500            1.004               4
     15600            1.005               4
     15700            1.005               4
     15800            1.004               4
     15900            1.004               4
     16000            1.004               4
     16100            1.004               4
     16200            1.003               4
     16300            1.003               4
     16400            1.003               4
     16500            1.003               4
     16600            1.003               4
     16700            1.003               4
     16800            1.003               4
     16900            1.003               4
     17000            1.003               4
     17100            1.003               4
     17200            1.003               4
     17300            1.004               4
     17400            1.004               4
     17500            1.004               4
     17600            1.004               4
     17700            1.005               4
     17800            1.005               3
     17900            1.006               3
     18000            1.005               3
     18100            1.005               3
     18200            1.005               3
     18300            1.005               3
     18400            1.004               3
     18500            1.004               3
     18600            1.005               3
     18700            1.004               3
     18800            1.004               3
     18900            1.004               3
     19000            1.004               3
     19100            1.004               3
     19200            1.004               3
     19300            1.004               3
     19400            1.003               3
     19500            1.003               3
     19600            1.003               3
     19700            1.003               3
     19800            1.003               3
     19900            1.003               3
     20000            1.003               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:  04:42:50
        Ending Time:  04:42:51
       Elapsed Time:  00:00:01



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