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 = ex9.40.dat;

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

      model population:

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

              %between level2a%
              ! across time variation of measurement intercepts and factor
              ftime by y1-y3*1.3 (1-3);
      		ftime*0.5;	
              y1-y3*.3;


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

              %between level2a%
              ! across time variation of measurement intercepts and factor
              ftime by y1-y3*1.3 (1-3);
      		ftime*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                            4

Observed dependent variables

  Continuous
   Y1          Y2          Y3

Continuous latent variables
   F           F&1         FTIME       FSUBJ


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                       18

Information Criteria

    Deviance (DIC)

        Mean                            197712.860
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000       197712.860     197712.860
           0.980       0.000       197712.860     197712.860
           0.950       0.000       197712.860     197712.860
           0.900       0.000       197712.860     197712.860
           0.800       0.000       197712.860     197712.860
           0.700       0.000       197712.860     197712.860
           0.500       0.000       197712.860     197712.860
           0.300       0.000       197712.860     197712.860
           0.200       0.000       197712.860     197712.860
           0.100       0.000       197712.860     197712.860
           0.050       0.000       197712.860     197712.860
           0.020       0.000       197712.860     197712.860
           0.010       0.000       197712.860     197712.860

    Estimated Number of Parameters (pD)

        Mean                             16481.857
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        16481.857      16481.857
           0.980       0.000        16481.857      16481.857
           0.950       0.000        16481.857      16481.857
           0.900       0.000        16481.857      16481.857
           0.800       0.000        16481.857      16481.857
           0.700       0.000        16481.857      16481.857
           0.500       0.000        16481.857      16481.857
           0.300       0.000        16481.857      16481.857
           0.200       0.000        16481.857      16481.857
           0.100       0.000        16481.857      16481.857
           0.050       0.000        16481.857      16481.857
           0.020       0.000        16481.857      16481.857
           0.010       0.000        16481.857      16481.857



MODEL RESULTS

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

 F        BY
  Y1                  1.300     1.2797     0.0000     0.0111     0.0004 1.000 1.000
  Y2                  1.300     1.2967     0.0000     0.0109     0.0000 1.000 1.000
  Y3                  1.300     1.2678     0.0000     0.0111     0.0010 0.000 1.000

 F          ON
  F&1                 0.300     0.2988     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     1.1987     0.0000     0.0181     0.0000 1.000 1.000
  Y2                  1.200     1.1725     0.0000     0.0189     0.0008 1.000 1.000
  Y3                  1.200     1.2319     0.0000     0.0178     0.0010 1.000 1.000
  F                   1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

Between LEVEL2A Level

 FTIME    BY
  Y1                  1.300     1.2797     0.0000     0.0111     0.0004 1.000 1.000
  Y2                  1.300     1.2967     0.0000     0.0109     0.0000 1.000 1.000
  Y3                  1.300     1.2678     0.0000     0.0111     0.0010 0.000 1.000

 Variances
  FTIME               0.500     0.6191     0.0000     0.1023     0.0142 1.000 1.000

 Residual Variances
  Y1                  0.300     0.1281     0.0000     0.0480     0.0296 0.000 1.000
  Y2                  0.300     0.3705     0.0000     0.0752     0.0050 1.000 1.000
  Y3                  0.300     0.3521     0.0000     0.0713     0.0027 1.000 1.000

Between LEVEL2B Level

 FSUBJ    BY
  Y1                  1.300     1.2797     0.0000     0.0111     0.0004 1.000 1.000
  Y2                  1.300     1.2967     0.0000     0.0109     0.0000 1.000 1.000
  Y3                  1.300     1.2678     0.0000     0.0111     0.0010 0.000 1.000

 Intercepts
  Y1                  1.000     0.9852     0.0000     0.1520     0.0002 1.000 1.000
  Y2                  1.000     1.0180     0.0000     0.1372     0.0003 1.000 1.000
  Y3                  1.000     0.8339     0.0000     0.1452     0.0276 1.000 1.000

 Variances
  FSUBJ               1.000     0.8908     0.0000     0.1084     0.0119 1.000 1.000

 Residual Variances
  Y1                  0.500     0.5350     0.0000     0.0815     0.0012 1.000 1.000
  Y2                  0.500     0.5036     0.0000     0.0828     0.0000 1.000 1.000
  Y3                  0.500     0.5895     0.0000     0.0888     0.0080 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.
  B2a_Y1              0.993       0.000              0.129       0.000
  B2a_Y2              0.994       0.000              0.130       0.000
  B2a_Y3              0.995       0.000              0.184       0.000
  B2b_Y1              0.988       0.000              0.223       0.000
  B2b_Y2              0.987       0.000              0.219       0.000
  B2b_Y3              0.989       0.000              0.271       0.000


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           NU
              Y1            Y2            Y3
              ________      ________      ________
                    0             0             0


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


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1                 4
 Y2                 0             5
 Y3                 0             0             6


           ALPHA
              F             F&1
              ________      ________
                    0             0


           BETA
              F             F&1
              ________      ________
 F                  0             7
 F&1                0             0


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


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL2A


           NU
              Y1            Y2            Y3
              ________      ________      ________
                    0             0             0


           LAMBDA
              FTIME
              ________
 Y1                 1
 Y2                 2
 Y3                 3


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


           ALPHA
              FTIME
              ________
                    0


           BETA
              FTIME
              ________
 FTIME              0


           PSI
              FTIME
              ________
 FTIME             11


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B


           NU
              Y1            Y2            Y3
              ________      ________      ________
                   12            13            14


           LAMBDA
              FSUBJ
              ________
 Y1                 1
 Y2                 2
 Y3                 3


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1                15
 Y2                 0            16
 Y3                 0             0            17


           ALPHA
              FSUBJ
              ________
                    0


           BETA
              FSUBJ
              ________
 FSUBJ              0


           PSI
              FSUBJ
              ________
 FSUBJ             18


     STARTING VALUES FOR WITHIN


           NU
              Y1            Y2            Y3
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              F             F&1
              ________      ________
 Y1             1.300         0.000
 Y2             1.300         0.000
 Y3             1.300         0.000


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


           ALPHA
              F             F&1
              ________      ________
                0.000         0.000


           BETA
              F             F&1
              ________      ________
 F              0.000         0.300
 F&1            0.000         0.000


           PSI
              F             F&1
              ________      ________
 F              1.000
 F&1            0.000         1.000


     STARTING VALUES FOR BETWEEN LEVEL2A


           NU
              Y1            Y2            Y3
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              FTIME
              ________
 Y1             1.300
 Y2             1.300
 Y3             1.300


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


           ALPHA
              FTIME
              ________
                0.000


           BETA
              FTIME
              ________
 FTIME          0.000


           PSI
              FTIME
              ________
 FTIME          0.500


     STARTING VALUES FOR BETWEEN LEVEL2B


           NU
              Y1            Y2            Y3
              ________      ________      ________
                1.000         1.000         1.000


           LAMBDA
              FSUBJ
              ________
 Y1             1.300
 Y2             1.300
 Y3             1.300


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


           ALPHA
              FSUBJ
              ________
                0.000


           BETA
              FSUBJ
              ________
 FSUBJ          0.000


           PSI
              FSUBJ
              ________
 FSUBJ          1.000


     POPULATION VALUES FOR WITHIN


           NU
              Y1            Y2            Y3
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              F             F&1
              ________      ________
 Y1             1.300         0.000
 Y2             1.300         0.000
 Y3             1.300         0.000


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


           ALPHA
              F             F&1
              ________      ________
                0.000         0.000


           BETA
              F             F&1
              ________      ________
 F              0.000         0.300
 F&1            0.000         0.000


           PSI
              F             F&1
              ________      ________
 F              1.000
 F&1            0.000         1.000


     POPULATION VALUES FOR BETWEEN LEVEL2A


           NU
              Y1            Y2            Y3
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              FTIME
              ________
 Y1             1.300
 Y2             1.300
 Y3             1.300


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


           ALPHA
              FTIME
              ________
                0.000


           BETA
              FTIME
              ________
 FTIME          0.000


           PSI
              FTIME
              ________
 FTIME          0.500


     POPULATION VALUES FOR BETWEEN LEVEL2B


           NU
              Y1            Y2            Y3
              ________      ________      ________
                1.000         1.000         1.000


           LAMBDA
              FSUBJ
              ________
 Y1             1.300
 Y2             1.300
 Y3             1.300


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


           ALPHA
              FSUBJ
              ________
                0.000


           BETA
              FSUBJ
              ________
 FSUBJ          0.000


           PSI
              FSUBJ
              ________
 FSUBJ          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~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 5~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 6~IG(-1.000,0.000)          infinity            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~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


TECHNICAL 8 OUTPUT

     REPLICATION 1:



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





     Parameter   KS Statistic P-value
     Parameter 12    0.1600    0.1400
     Parameter 14    0.1600    0.1400
     Parameter 13    0.1500    0.1930
     Parameter 10    0.1200    0.4431
     Parameter 8    0.1000    0.6766
     Parameter 17    0.0700    0.9610
     Parameter 16    0.0600    0.9921
     Parameter 11    0.0500    0.9995
     Parameter 18    0.0400    1.0000
     Parameter 9    0.0300    1.0000
     Parameter 5    0.0200    1.0000
     Parameter 15    0.0200    1.0000
     Parameter 6    0.0100    1.0000
     Parameter 1    0.0100    1.0000
     Parameter 3    0.0100    1.0000
     Parameter 4    0.0100    1.0000
     Parameter 2    0.0000    1.0000
     Parameter 7    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


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

     REPLICATION 1:


                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.178               16
     200              1.178               8
     300              1.276               13
     400              1.441               13
     500              1.450               14
     600              1.533               14
     700              1.786               14
     800              1.669               14
     900              1.843               14
     1000             2.033               14
     1100             2.331               12
     1200             2.297               12
     1300             2.065               12
     1400             1.692               12
     1500             1.400               12
     1600             1.215               12
     1700             1.069               13
     1800             1.024               12
     1900             1.008               12
     2000             1.013               14


SAVEDATA INFORMATION

  Order of variables

    Y1
    Y2
    Y3
    LEVEL2A
    LEVEL2B

  Save file
    ex9.40.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  04:03:07
        Ending Time:  04:03:23
       Elapsed Time:  00:00:16



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