Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   4:03 AM

INPUT INSTRUCTIONS

      title: this is an example of a cross-classified time
              series analysis with a first-order
              autoregressive AR(1) confirmatory factor
              analysis (CFA) model for continuous factor
              indicators with random intercepts, random
              factor loadings, and a factor varying across
              both subjects and time

      montecarlo:
      		names are y1-y3;
      		nobservations = 20000;
      		nreps = 1;
      		CSIZES = 200[100(1)]; ! 200 subjects (2b), 100 time points (2a)
      		ncsize = 1[1];
              save = ex9.40part2.dat;

      ANALYSIS:  TYPE = cross random;
      		estimator = bayes;
              proc = 2;
              biter = (2000);

      model population:

      		%within%
      		y1-y3*1.2; [y1-y3@0];
      		s1-s3 | f by y1-y3 (&1);
              f@1;
              f on f&1*.3;
      	
      		%between level2b%
              ! across subject variation in measurement intercepts,
              ! loadings, and factor
      		f*1; 	  	
              y1-y3*.5;
              [y1-y3*1];	! estimating the intercepts on the level with most
              ! intercept variance
              s1-s3*0.1;
              [s1-s3*1.3];

              %between level2a%
              ! across time variation of measurement intercepts and factor
      		f*0.5;	
              y1-y3*.3;


      model:
      		%within%
      		y1-y3*1.2; [y1-y3@0];
      		s1-s3 | f by y1-y3 (&1);
              f@1;
              f on f&1*.3;
      	
      		%between level2b%
              ! across subject variation in measurement intercepts,
              ! loadings, and factor
      		f*1; 	  	
              y1-y3*.5;
              [y1-y3*1];	! estimating the intercepts on the level with most
              ! intercept variance
              s1-s3*0.1;
              [s1-s3*1.3];

              %between level2a%
              ! across time variation of measurement intercepts and factor
      		f*0.5;	
              y1-y3*.3;


      output:
      		tech8;




INPUT READING TERMINATED NORMALLY



this is an example of a cross-classified time
series analysis with a first-order
autoregressive AR(1) confirmatory factor
analysis (CFA) model for continuous factor
indicators with random intercepts, random
factor loadings, and a factor varying across
both subjects and time

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                       20000

Number of replications
    Requested                                                    1
    Completed                                                    1
Value of seed                                                    0

Number of dependent variables                                    3
Number of independent variables                                  0
Number of continuous latent variables                            5

Observed dependent variables

  Continuous
   Y1          Y2          Y3

Continuous latent variables
   F           F&1         S1          S2          S3


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


SUMMARY OF DATA FOR THE FIRST REPLICATION

     Cluster information

     Number of level 2a clusters          100
     Number of level 2b clusters          200






MODEL FIT INFORMATION

Number of Free Parameters                       21

Information Criteria

    Deviance (DIC)

        Mean                            198711.622
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000       198711.622     198711.622
           0.980       0.000       198711.622     198711.622
           0.950       0.000       198711.622     198711.622
           0.900       0.000       198711.622     198711.622
           0.800       0.000       198711.622     198711.622
           0.700       0.000       198711.622     198711.622
           0.500       0.000       198711.622     198711.622
           0.300       0.000       198711.622     198711.622
           0.200       0.000       198711.622     198711.622
           0.100       0.000       198711.622     198711.622
           0.050       0.000       198711.622     198711.622
           0.020       0.000       198711.622     198711.622
           0.010       0.000       198711.622     198711.622

    Estimated Number of Parameters (pD)

        Mean                             17156.030
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        17156.030      17156.030
           0.980       0.000        17156.030      17156.030
           0.950       0.000        17156.030      17156.030
           0.900       0.000        17156.030      17156.030
           0.800       0.000        17156.030      17156.030
           0.700       0.000        17156.030      17156.030
           0.500       0.000        17156.030      17156.030
           0.300       0.000        17156.030      17156.030
           0.200       0.000        17156.030      17156.030
           0.100       0.000        17156.030      17156.030
           0.050       0.000        17156.030      17156.030
           0.020       0.000        17156.030      17156.030
           0.010       0.000        17156.030      17156.030



MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff
Within Level

 F          ON
  F&1                 0.300     0.3059     0.0000     0.0085     0.0000 1.000 1.000

 Intercepts
  Y1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y3                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

 Residual Variances
  Y1                  1.200     1.2201     0.0000     0.0181     0.0004 1.000 1.000
  Y2                  1.200     1.1819     0.0000     0.0180     0.0003 1.000 1.000
  Y3                  1.200     1.2191     0.0000     0.0183     0.0004 1.000 1.000
  F                   1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

Between LEVEL2A Level

 Variances
  Y1                  0.300     0.3113     0.0000     0.0524     0.0001 1.000 1.000
  Y2                  0.300     0.2700     0.0000     0.0468     0.0009 1.000 1.000
  Y3                  0.300     0.3453     0.0000     0.0573     0.0021 1.000 1.000
  F                   0.500     0.4924     0.0000     0.0786     0.0001 1.000 1.000

Between LEVEL2B Level

 Means
  Y1                  1.000     1.0436     0.0000     0.1485     0.0019 1.000 1.000
  Y2                  1.000     1.0252     0.0000     0.1556     0.0006 1.000 1.000
  Y3                  1.000     0.9718     0.0000     0.1479     0.0008 1.000 1.000
  S1                  1.300     1.3157     0.0000     0.0263     0.0002 1.000 1.000
  S2                  1.300     1.3162     0.0000     0.0258     0.0003 1.000 1.000
  S3                  1.300     1.3163     0.0000     0.0245     0.0003 1.000 1.000

 Variances
  Y1                  0.500     0.5712     0.0000     0.0843     0.0051 1.000 1.000
  Y2                  0.500     0.5807     0.0000     0.0842     0.0065 1.000 1.000
  Y3                  0.500     0.3897     0.0000     0.0699     0.0122 1.000 1.000
  F                   1.000     0.8762     0.0000     0.0975     0.0153 1.000 1.000
  S1                  0.100     0.1105     0.0000     0.0132     0.0001 1.000 1.000
  S2                  0.100     0.1036     0.0000     0.0124     0.0000 1.000 1.000
  S3                  0.100     0.0952     0.0000     0.0116     0.0000 1.000 1.000


CORRELATIONS AND MEAN SQUARE ERROR OF THE TRUE FACTOR VALUES AND THE FACTOR SCORES

                        CORRELATIONS                MEAN SQUARE ERROR
                    Average    Std. Dev.           Average    Std. Dev.
  F%2a                0.972       0.000              0.163       0.000
  S1%2a               0.000       0.000              0.029       0.000
  S2%2a               0.000       0.000              0.031       0.000
  S3%2a               0.000       0.000              0.030       0.000
  F%2b                0.972       0.000              0.234       0.000
  S1%2b               0.927       0.000              0.123       0.000
  S2%2b               0.928       0.000              0.115       0.000
  S3%2b               0.916       0.000              0.124       0.000
  B2a_Y1              0.936       0.000              0.204       0.000
  B2a_Y2              0.920       0.000              0.198       0.000
  B2a_Y3              0.928       0.000              0.217       0.000
  B2b_Y1              0.806       0.000              0.430       0.000
  B2b_Y2              0.827       0.000              0.383       0.000
  B2b_Y3              0.794       0.000              0.388       0.000


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           NU
              Y1            Y2            Y3
              ________      ________      ________
                    0             0             0


           LAMBDA
              F%W           F&1
              ________      ________
 Y1                 0             0
 Y2                 0             0
 Y3                 0             0


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1                 1
 Y2                 0             2
 Y3                 0             0             3


           ALPHA
              F%W           F&1
              ________      ________
                    0             0


           BETA
              F%W           F&1
              ________      ________
 F%W                0             4
 F&1                0             0


           PSI
              F%W           F&1
              ________      ________
 F%W                0
 F&1                0             0


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL2A


           NU
              Y1            Y2            Y3
              ________      ________      ________
                    0             0             0


           LAMBDA
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
 Y1                 0             0             0             0
 Y2                 0             0             0             0
 Y3                 0             0             0             0


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1                 5
 Y2                 0             6
 Y3                 0             0             7


           ALPHA
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
                    0             0             0             0


           BETA
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
 F%2a               0             0             0             0
 S1%2a              0             0             0             0
 S2%2a              0             0             0             0
 S3%2a              0             0             0             0


           PSI
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
 F%2a               8
 S1%2a              0             0
 S2%2a              0             0             0
 S3%2a              0             0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B


           NU
              Y1            Y2            Y3
              ________      ________      ________
                    9            10            11


           LAMBDA
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
 Y1                 0             0             0             0
 Y2                 0             0             0             0
 Y3                 0             0             0             0


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1                12
 Y2                 0            13
 Y3                 0             0            14


           ALPHA
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
                    0            15            16            17


           BETA
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
 F%2b               0             0             0             0
 S1%2b              0             0             0             0
 S2%2b              0             0             0             0
 S3%2b              0             0             0             0


           PSI
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
 F%2b              18
 S1%2b              0            19
 S2%2b              0             0            20
 S3%2b              0             0             0            21


     STARTING VALUES FOR WITHIN


           NU
              Y1            Y2            Y3
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              F%W           F&1
              ________      ________
 Y1             0.000         0.000
 Y2             0.000         0.000
 Y3             0.000         0.000


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1             1.200
 Y2             0.000         1.200
 Y3             0.000         0.000         1.200


           ALPHA
              F%W           F&1
              ________      ________
                0.000         0.000


           BETA
              F%W           F&1
              ________      ________
 F%W            0.000         0.300
 F&1            0.000         0.000


           PSI
              F%W           F&1
              ________      ________
 F%W            1.000
 F&1            0.000         1.000


     STARTING VALUES FOR BETWEEN LEVEL2A


           NU
              Y1            Y2            Y3
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
 Y1             0.000         0.000         0.000         0.000
 Y2             0.000         0.000         0.000         0.000
 Y3             0.000         0.000         0.000         0.000


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1             0.300
 Y2             0.000         0.300
 Y3             0.000         0.000         0.300


           ALPHA
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           BETA
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
 F%2a           0.000         0.000         0.000         0.000
 S1%2a          0.000         0.000         0.000         0.000
 S2%2a          0.000         0.000         0.000         0.000
 S3%2a          0.000         0.000         0.000         0.000


           PSI
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
 F%2a           0.500
 S1%2a          0.000         0.000
 S2%2a          0.000         0.000         0.000
 S3%2a          0.000         0.000         0.000         0.000


     STARTING VALUES FOR BETWEEN LEVEL2B


           NU
              Y1            Y2            Y3
              ________      ________      ________
                1.000         1.000         1.000


           LAMBDA
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
 Y1             0.000         0.000         0.000         0.000
 Y2             0.000         0.000         0.000         0.000
 Y3             0.000         0.000         0.000         0.000


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1             0.500
 Y2             0.000         0.500
 Y3             0.000         0.000         0.500


           ALPHA
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
                0.000         1.300         1.300         1.300


           BETA
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
 F%2b           0.000         0.000         0.000         0.000
 S1%2b          0.000         0.000         0.000         0.000
 S2%2b          0.000         0.000         0.000         0.000
 S3%2b          0.000         0.000         0.000         0.000


           PSI
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
 F%2b           1.000
 S1%2b          0.000         0.100
 S2%2b          0.000         0.000         0.100
 S3%2b          0.000         0.000         0.000         0.100


     POPULATION VALUES FOR WITHIN


           NU
              Y1            Y2            Y3
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              F%W           F&1
              ________      ________
 Y1             0.000         0.000
 Y2             0.000         0.000
 Y3             0.000         0.000


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1             1.200
 Y2             0.000         1.200
 Y3             0.000         0.000         1.200


           ALPHA
              F%W           F&1
              ________      ________
                0.000         0.000


           BETA
              F%W           F&1
              ________      ________
 F%W            0.000         0.300
 F&1            0.000         0.000


           PSI
              F%W           F&1
              ________      ________
 F%W            1.000
 F&1            0.000         1.000


     POPULATION VALUES FOR BETWEEN LEVEL2A


           NU
              Y1            Y2            Y3
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
 Y1             0.000         0.000         0.000         0.000
 Y2             0.000         0.000         0.000         0.000
 Y3             0.000         0.000         0.000         0.000


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1             0.300
 Y2             0.000         0.300
 Y3             0.000         0.000         0.300


           ALPHA
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           BETA
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
 F%2a           0.000         0.000         0.000         0.000
 S1%2a          0.000         0.000         0.000         0.000
 S2%2a          0.000         0.000         0.000         0.000
 S3%2a          0.000         0.000         0.000         0.000


           PSI
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
 F%2a           0.500
 S1%2a          0.000         0.000
 S2%2a          0.000         0.000         0.000
 S3%2a          0.000         0.000         0.000         0.000


     POPULATION VALUES FOR BETWEEN LEVEL2B


           NU
              Y1            Y2            Y3
              ________      ________      ________
                1.000         1.000         1.000


           LAMBDA
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
 Y1             0.000         0.000         0.000         0.000
 Y2             0.000         0.000         0.000         0.000
 Y3             0.000         0.000         0.000         0.000


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1             0.500
 Y2             0.000         0.500
 Y3             0.000         0.000         0.500


           ALPHA
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
                0.000         1.300         1.300         1.300


           BETA
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
 F%2b           0.000         0.000         0.000         0.000
 S1%2b          0.000         0.000         0.000         0.000
 S2%2b          0.000         0.000         0.000         0.000
 S3%2b          0.000         0.000         0.000         0.000


           PSI
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
 F%2b           1.000
 S1%2b          0.000         0.100
 S2%2b          0.000         0.000         0.100
 S3%2b          0.000         0.000         0.000         0.100



     PRIORS FOR ALL PARAMETERS            PRIOR MEAN      PRIOR VARIANCE     PRIOR STD. DEV.

     Parameter 1~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 2~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 3~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 4~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 5~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 6~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 7~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 8~IG(-1.000,0.000)          infinity            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~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 16~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 17~N(0.000,infinity)          0.0000            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


TECHNICAL 8 OUTPUT

     REPLICATION 1:



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





     Parameter   KS Statistic P-value
     Parameter 10    0.2700    0.0010
     Parameter 9    0.2100    0.0205
     Parameter 11    0.1700    0.0994
     Parameter 14    0.1300    0.3439
     Parameter 13    0.1300    0.3439
     Parameter 12    0.1200    0.4431
     Parameter 8    0.0800    0.8938
     Parameter 18    0.0600    0.9921
     Parameter 15    0.0600    0.9921
     Parameter 7    0.0500    0.9995
     Parameter 16    0.0300    1.0000
     Parameter 5    0.0300    1.0000
     Parameter 6    0.0300    1.0000
     Parameter 3    0.0200    1.0000
     Parameter 2    0.0100    1.0000
     Parameter 20    0.0100    1.0000
     Parameter 17    0.0100    1.0000
     Parameter 1    0.0000    1.0000
     Parameter 21    0.0000    1.0000
     Parameter 4    0.0000    1.0000
     Parameter 19    0.0000    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
     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


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

     REPLICATION 1:


                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.744               11
     200              1.637               14
     300              1.711               14
     400              1.517               12
     500              1.462               12
     600              1.412               11
     700              1.355               11
     800              1.441               11
     900              1.220               11
     1000             1.210               11
     1100             1.195               11
     1200             1.187               14
     1300             1.169               12
     1400             1.159               12
     1500             1.123               12
     1600             1.061               12
     1700             1.077               10
     1800             1.121               11
     1900             1.171               11
     2000             1.206               11
     2100             1.253               11
     2200             1.290               11
     2300             1.303               11
     2400             1.371               11
     2500             1.436               11
     2600             1.509               11
     2700             1.664               11
     2800             1.728               11
     2900             1.569               11
     3000             1.497               11
     3100             1.493               11
     3200             1.482               11
     3300             1.410               11
     3400             1.366               11
     3500             1.339               11
     3600             1.310               11
     3700             1.252               11
     3800             1.185               11
     3900             1.169               11
     4000             1.177               11
     4100             1.177               11
     4200             1.169               11
     4300             1.194               11
     4400             1.238               11
     4500             1.275               11
     4600             1.320               11
     4700             1.353               11
     4800             1.387               11
     4900             1.414               11
     5000             1.442               11
     5100             1.484               11
     5200             1.510               11
     5300             1.521               11
     5400             1.532               11
     5500             1.573               11
     5600             1.600               9
     5700             1.630               9
     5800             1.639               9
     5900             1.598               9
     6000             1.523               9
     6100             1.446               9
     6200             1.390               9
     6300             1.344               9
     6400             1.301               10
     6500             1.265               10
     6600             1.233               10
     6700             1.216               10
     6800             1.187               9
     6900             1.176               9
     7000             1.163               9
     7100             1.151               9
     7200             1.140               9
     7300             1.126               9
     7400             1.120               9
     7500             1.119               9
     7600             1.109               9
     7700             1.105               9
     7800             1.103               9
     7900             1.103               9
     8000             1.099               9
     8100             1.094               9
     8200             1.092               9
     8300             1.094               10
     8400             1.095               10
     8500             1.089               10
     8600             1.087               10
     8700             1.087               10
     8800             1.085               10


SAVEDATA INFORMATION

  Order of variables

    Y1
    Y2
    Y3
    LEVEL2A
    LEVEL2B

  Save file
    ex9.40part2.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  04:03:23
        Ending Time:  04:17:15
       Elapsed Time:  00:13:52



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