Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:33 AM

INPUT INSTRUCTIONS

  TITLE:      this is an example of two-level univariate first-order
              autoregressive AR(1) model with a random intercept,
              random AR(1), and random residual variance

              Step 1: although we are interested in a twolevel model
              we generate data using cross-classified analysis
              with an empty Between time model to be able to
              save data with subject and time variables.
              Missing data on y is created by Model Missing

   MONTECARLO:  NAMES ARE y w z u;
                 NOBS = 20000;
                 NREPS = 1;
                 CSIZES = 200[100(1)];
                  NCSIZES = 1[1];
                 lagged = y(1);
                 between = (level2b) w z;
                 missing = y;
                 ! u is needed if there are several y's to make all of them
                 ! have missing at the same time
                 generate = u(1);
                 categorical = u;
                 within = u;
              save = ex9.30step1.dat;

  MODEL MISSING:
              [y@-15]; ! no MCAR missing
              y on u@30; ! missing 50% on y;

  ANALYSIS:   TYPE = CROSSCLASSIFIED RANDOM;
        		estimator=bayes;
              proc=2;
              fbiter=(200); ! full convergence not needed to save the right data

  MODEL POPULATION:

      %WITHIN%
      s | y on y&1;
      logv | y;
      [u$1*0];

      %BETWEEN level2a%  ! empty
      y@0; s@0;

      %BETWEEN level2b%
      w*1;
      y on w*.3;
      y*0.09;
      s on w*.1;
      s*.01; [s*.3];
      logv on w*.3;
      logv*0; [logv*0];
      z on y*.5 s*.7 logv*.3;
      z*0.05;


  MODEL:

      %WITHIN%
      s | y on y&1;
      logv | y;
      [u$1*0];

      %BETWEEN level2a%  ! empty
      y@0; s@0;

      %BETWEEN level2b%

      y on w*.3;
      y*0.09;
      s on w*.1;
      s*.01; [s*.3];
      logv on w*.3;
      logv*0; [logv*0];
      z on y*.5 s*.7 logv*.3;
      z*0.05;

  OUTPUT:
        tech8;



*** WARNING in MODEL command
  Variable is uncorrelated with all other variables: U
*** WARNING in MODEL command
  At least one variable is uncorrelated with all other variables in the model.
  Check that this is what is intended.
   2 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS



this is an example of two-level univariate first-order
autoregressive AR(1) model with a random intercept,
random AR(1), and random residual variance

Step 1: although we are interested in a twolevel model
we generate data using cross-classified analysis
with an empty Between time model to be able to
save data with subject and time variables.
Missing data on y is created by Model Missing

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                                  2
Number of continuous latent variables                            2

Observed dependent variables

  Continuous
   Z           Y

  Binary and ordered categorical (ordinal)
   U

Observed independent variables
   W           Y&1

Continuous latent variables
   S           LOGV

Variables with special functions

  Within variables
   U           Y&1

  Level 2b between variables
   W           Z


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)
  Fixed number of iterations                                   200
  K-th iteration used for thinning                               1
Link                                                        PROBIT


SUMMARY OF DATA FOR THE FIRST REPLICATION

     Cluster information

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



SUMMARY OF MISSING DATA PATTERNS FOR THE FIRST REPLICATION

     Number of missing data patterns             4


     MISSING DATA PATTERNS (x = not missing)

           1  2  3  4
 U         x  x  x  x
 Z         x  x  x  x
 Y         x     x
 Y&1       x  x
 W         x  x  x  x


     MISSING DATA PATTERN FREQUENCIES

    Pattern   Frequency     Pattern   Frequency     Pattern   Frequency
          1        9936           3          58
          2        9963           4          43


COVARIANCE COVERAGE OF DATA FOR THE FIRST REPLICATION

Minimum covariance coverage value   0.100


     PROPORTION OF DATA PRESENT


           Covariance Coverage
              U             Z             Y             W
              ________      ________      ________      ________
 U              1.000
 Z              1.000         1.000
 Y              0.500         0.500         0.500
 W              1.000         1.000         0.500         1.000





MODEL FIT INFORMATION

Number of Free Parameters                       15



MODEL RESULTS

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

 Thresholds
  U$1                 0.000    -0.0009     0.0000     0.0086     0.0000 1.000 0.000

Between LEVEL2A Level

 Variances
  Y                   0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  S                   0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

Between LEVEL2B Level

 S          ON
  W                   0.100     0.1254     0.0000     0.0134     0.0006 1.000 1.000

 LOGV       ON
  W                   0.300     0.2968     0.0000     0.0125     0.0000 1.000 1.000

 Z          ON
  S                   0.700     0.6285     0.0000     0.2694     0.0051 1.000 1.000
  LOGV                0.300     0.3233     0.0000     0.1333     0.0005 1.000 1.000

 Y          ON
  W                   0.300     0.2859     0.0000     0.0245     0.0002 1.000 1.000

 Z          ON
  Y                   0.500     0.4899     0.0000     0.0587     0.0001 1.000 1.000

 Intercepts
  Z                   0.000     0.0264     0.0000     0.0815     0.0007 1.000 0.000
  Y                   0.000    -0.0216     0.0000     0.0303     0.0005 1.000 0.000
  S                   0.300     0.2937     0.0000     0.0162     0.0000 1.000 1.000
  LOGV                0.000    -0.0261     0.0000     0.0128     0.0007 1.000 0.000

 Residual Variances
  Z                   0.050     0.0470     0.0000     0.0068     0.0000 1.000 1.000
  Y                   0.090     0.1032     0.0000     0.0122     0.0002 1.000 1.000
  S                   0.010     0.0128     0.0000     0.0029     0.0000 1.000 1.000
  LOGV                0.000     0.0058     0.0000     0.0020     0.0000 0.000 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.
  S%2a                0.000       0.000              0.029       0.000
  LOGV%2a             0.000       0.000              0.034       0.000
  S%2b                0.821       0.000              0.091       0.000
  LOGV%2b             0.991       0.000              0.055       0.000
  B2a_Y               0.356       0.000              0.028       0.000
  B2b_Y               0.940       0.000              0.150       0.000


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           TAU
              U$1
              ________
                   15


           NU
              U             Y             Y&1
              ________      ________      ________
                    0             0             0


           LAMBDA
              Y             Y&1
              ________      ________
 U                  0             0
 Y                  0             0
 Y&1                0             0


           THETA
              U             Y             Y&1
              ________      ________      ________
 U                  0
 Y                  0             0
 Y&1                0             0             0


           ALPHA
              Y             Y&1
              ________      ________
                    0             0


           BETA
              Y             Y&1
              ________      ________
 Y                  0             0
 Y&1                0             0


           PSI
              Y             Y&1
              ________      ________
 Y                  0
 Y&1                0             0


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL2A


           NU
              Y
              ________
                    0


           LAMBDA
              S%2a          LOGV%2a       Y
              ________      ________      ________
 Y                  0             0             0


           THETA
              Y
              ________
 Y                  0


           ALPHA
              S%2a          LOGV%2a       Y
              ________      ________      ________
                    0             0             0


           BETA
              S%2a          LOGV%2a       Y
              ________      ________      ________
 S%2a               0             0             0
 LOGV%2a            0             0             0
 Y                  0             0             0


           PSI
              S%2a          LOGV%2a       Y
              ________      ________      ________
 S%2a               0
 LOGV%2a            0             0
 Y                  0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B


           NU
              Z             Y             W
              ________      ________      ________
                    0             0             0


           LAMBDA
              S%2b          LOGV%2b       Z             Y             W
              ________      ________      ________      ________      ________
 Z                  0             0             0             0             0
 Y                  0             0             0             0             0
 W                  0             0             0             0             0


           THETA
              Z             Y             W
              ________      ________      ________
 Z                  0
 Y                  0             0
 W                  0             0             0


           ALPHA
              S%2b          LOGV%2b       Z             Y             W
              ________      ________      ________      ________      ________
                    1             2             3             4             0


           BETA
              S%2b          LOGV%2b       Z             Y             W
              ________      ________      ________      ________      ________
 S%2b               0             0             0             0             5
 LOGV%2b            0             0             0             0             6
 Z                  7             8             0             9             0
 Y                  0             0             0             0            10
 W                  0             0             0             0             0


           PSI
              S%2b          LOGV%2b       Z             Y             W
              ________      ________      ________      ________      ________
 S%2b              11
 LOGV%2b            0            12
 Z                  0             0            13
 Y                  0             0             0            14
 W                  0             0             0             0             0


     STARTING VALUES FOR WITHIN


           TAU
              U$1
              ________
                0.000


           NU
              U             Y             Y&1
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              Y             Y&1
              ________      ________
 U              0.000         0.000
 Y              1.000         0.000
 Y&1            0.000         1.000


           THETA
              U             Y             Y&1
              ________      ________      ________
 U              1.000
 Y              0.000         0.000
 Y&1            0.000         0.000         0.000


           ALPHA
              Y             Y&1
              ________      ________
                0.000         0.000


           BETA
              Y             Y&1
              ________      ________
 Y              0.000         0.000
 Y&1            0.000         0.000


           PSI
              Y             Y&1
              ________      ________
 Y              0.000
 Y&1            0.000         0.500


     STARTING VALUES FOR BETWEEN LEVEL2A


           NU
              Y
              ________
                0.000


           LAMBDA
              S%2a          LOGV%2a       Y
              ________      ________      ________
 Y              0.000         0.000         1.000


           THETA
              Y
              ________
 Y              0.000


           ALPHA
              S%2a          LOGV%2a       Y
              ________      ________      ________
                0.000         0.000         0.000


           BETA
              S%2a          LOGV%2a       Y
              ________      ________      ________
 S%2a           0.000         0.000         0.000
 LOGV%2a        0.000         0.000         0.000
 Y              0.000         0.000         0.000


           PSI
              S%2a          LOGV%2a       Y
              ________      ________      ________
 S%2a           0.000
 LOGV%2a        0.000         0.000
 Y              0.000         0.000         0.000


     STARTING VALUES FOR BETWEEN LEVEL2B


           NU
              Z             Y             W
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              S%2b          LOGV%2b       Z             Y             W
              ________      ________      ________      ________      ________
 Z              0.000         0.000         1.000         0.000         0.000
 Y              0.000         0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         0.000         1.000


           THETA
              Z             Y             W
              ________      ________      ________
 Z              0.000
 Y              0.000         0.000
 W              0.000         0.000         0.000


           ALPHA
              S%2b          LOGV%2b       Z             Y             W
              ________      ________      ________      ________      ________
                0.300         0.000         0.000         0.000         0.000


           BETA
              S%2b          LOGV%2b       Z             Y             W
              ________      ________      ________      ________      ________
 S%2b           0.000         0.000         0.000         0.000         0.100
 LOGV%2b        0.000         0.000         0.000         0.000         0.300
 Z              0.700         0.300         0.000         0.500         0.000
 Y              0.000         0.000         0.000         0.000         0.300
 W              0.000         0.000         0.000         0.000         0.000


           PSI
              S%2b          LOGV%2b       Z             Y             W
              ________      ________      ________      ________      ________
 S%2b           0.010
 LOGV%2b        0.000         0.000
 Z              0.000         0.000         0.050
 Y              0.000         0.000         0.000         0.090
 W              0.000         0.000         0.000         0.000         0.500


     POPULATION VALUES FOR WITHIN


           TAU
              U$1
              ________
                0.000


           NU
              U             Y             Y&1
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              Y             Y&1
              ________      ________
 U              0.000         0.000
 Y              1.000         0.000
 Y&1            0.000         1.000


           THETA
              U             Y             Y&1
              ________      ________      ________
 U              0.000
 Y              0.000         0.000
 Y&1            0.000         0.000         0.000


           ALPHA
              Y             Y&1
              ________      ________
                0.000         0.000


           BETA
              Y             Y&1
              ________      ________
 Y              0.000         0.000
 Y&1            0.000         0.000


           PSI
              Y             Y&1
              ________      ________
 Y              0.000
 Y&1            0.000         1.000


     POPULATION VALUES FOR BETWEEN LEVEL2A


           NU
              Y
              ________
                0.000


           LAMBDA
              S%2a          LOGV%2a       Y
              ________      ________      ________
 Y              0.000         0.000         1.000


           THETA
              Y
              ________
 Y              0.000


           ALPHA
              S%2a          LOGV%2a       Y
              ________      ________      ________
                0.000         0.000         0.000


           BETA
              S%2a          LOGV%2a       Y
              ________      ________      ________
 S%2a           0.000         0.000         0.000
 LOGV%2a        0.000         0.000         0.000
 Y              0.000         0.000         0.000


           PSI
              S%2a          LOGV%2a       Y
              ________      ________      ________
 S%2a           0.000
 LOGV%2a        0.000         0.000
 Y              0.000         0.000         0.000


     POPULATION VALUES FOR BETWEEN LEVEL2B


           NU
              Z             Y             W
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              S%2b          LOGV%2b       Z             Y             W
              ________      ________      ________      ________      ________
 Z              0.000         0.000         1.000         0.000         0.000
 Y              0.000         0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         0.000         1.000


           THETA
              Z             Y             W
              ________      ________      ________
 Z              0.000
 Y              0.000         0.000
 W              0.000         0.000         0.000


           ALPHA
              S%2b          LOGV%2b       Z             Y             W
              ________      ________      ________      ________      ________
                0.300         0.000         0.000         0.000         0.000


           BETA
              S%2b          LOGV%2b       Z             Y             W
              ________      ________      ________      ________      ________
 S%2b           0.000         0.000         0.000         0.000         0.100
 LOGV%2b        0.000         0.000         0.000         0.000         0.300
 Z              0.700         0.300         0.000         0.500         0.000
 Y              0.000         0.000         0.000         0.000         0.300
 W              0.000         0.000         0.000         0.000         0.000


           PSI
              S%2b          LOGV%2b       Z             Y             W
              ________      ________      ________      ________      ________
 S%2b           0.010
 LOGV%2b        0.000         0.000
 Z              0.000         0.000         0.050
 Y              0.000         0.000         0.000         0.090
 W              0.000         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~IG(-1.000,0.000)         infinity            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(0.000,5.000)             0.0000              5.0000              2.2361


TECHNICAL 8 OUTPUT

     REPLICATION 1:



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





     Parameter   KS Statistic P-value
     Parameter 6    0.1100    0.5560
     Parameter 3    0.1100    0.5560
     Parameter 7    0.1000    0.6766
     Parameter 9    0.0900    0.7942
     Parameter 2    0.0700    0.9610
     Parameter 8    0.0700    0.9610
     Parameter 5    0.0500    0.9995
     Parameter 10    0.0400    1.0000
     Parameter 1    0.0300    1.0000
     Parameter 4    0.0100    1.0000
     Parameter 14    0.0000    1.0000
     Parameter 11    0.0000    1.0000
     Parameter 12    0.0000    1.0000
     Parameter 13    0.0000    1.0000
     Parameter 15    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         0.0050          4.9231          2.2188


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

     REPLICATION 1:


                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.221               8
     200              1.113               6


SAVEDATA INFORMATION

  Order of variables

    U
    Z
    Y
    W
    LEVEL2A
    LEVEL2B
    Y&1

  Save file
    ex9.30step1.dat

  Save file format           Free
  Save file record length    10000
  Missing designated by 999


     Beginning Time:  03:33:27
        Ending Time:  03:40:51
       Elapsed Time:  00:07:24



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Los Angeles, CA  90066

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Fax: (310) 391-8971
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