Repeated measures data: Can MLwiN allow AR1 residual errors?

[Queena]

For the repeated measures data, the within-individual (level 1) residuals are correlated.
The autocorrelation or other types of the correlation structure of the level 1 residual have been discussed by some authors.

From the runmlwin document (manual), the "restype" is restricted to MCMC estimation.
Is there any possible way to run such model without using MCMC estimation?

[GeorgeLeckie]

Hi Queena,

The only way to fit AR1 residual errors to repeated measures data (measurement occasions at level 1, nested within individuals at level 2) is to formulate the model as a multivariate response model and to fit this model using MCMC. You cannot fit the equivilent model using IGLS (i.e. maximim likelihood). See Chapter 19 "Mixed Response Models and Correlated Residuals" of the MCMC manual. The do-file to replicate this chapter using runmlwin is at:

http://www.bristol.ac.uk/cmm/software/r ... /examples/

I have highlighted the model output from the example given in the manual below

Code: Select all

. runmlwin ///
>         (y8  cons, eq(1)) ///
>         (y15 cons, eq(2)) ///
>         (y22 cons, eq(3)) ///
>         (y29 cons, eq(4)) ///
>         (y36 cons, eq(5)), ///
>         level1(rat: ///
>                 (cons, eq(1)) ///
>                 (cons, eq(2)) ///
>                 (cons, eq(3)) ///
>                 (cons, eq(4)) ///
>                 (cons, eq(5)) ///
>         ) ///
>         mcmc(chain(50000) refresh(500) corresiduals(arindepvars)) ///
>         initsb(b) initsv(V) corr ///
>         nopause
 
MLwiN 2.24 multilevel model                     Number of obs      =        30
Multivariate response model
Estimation algorithm: MCMC

Burnin                     =        500
Chain                      =      50000
Thinning                   =          1
Run time (seconds)         =       47.9
Deviance (dbar)            =    1015.67
Deviance (thetabar)        =    1006.32
Effective no. of pars (pd) =       9.35
Bayesian DIC               =    1025.03
------------------------------------------------------------------------------
             |      Mean    Std. Dev.      z      ESS     [95% Cred. Interval]
-------------+----------------------------------------------------------------
y8           |
      cons_1 |   152.1868    2.50771    60.69   47940     147.2231    157.1141
-------------+----------------------------------------------------------------
y15          |
      cons_2 |   201.7874   2.851714    70.76   47188     196.1168    207.4404
-------------+----------------------------------------------------------------
y22          |
      cons_3 |   245.0578   3.414991    71.76   48589     238.3248    251.8354
-------------+----------------------------------------------------------------
y29          |
      cons_4 |   289.5148   4.245057    68.20   48435     281.1146    297.9683
-------------+----------------------------------------------------------------
y36          |
      cons_5 |   324.8218   4.306853    75.42   49030     316.3396    333.3538
------------------------------------------------------------------------------

------------------------------------------------------------------------------
   Random-effects Parameters |     Mean   Std. Dev.   ESS     [95% Cred. Int]
-----------------------------+------------------------------------------------
Level 1: rat                 |
                 var(cons_1) |  188.7329  62.31378    316   101.9742  344.2719
         corr(cons_1,cons_2) |  .9417586  .0181803    353   .9009867  .9711142
                 var(cons_2) |  243.7805  81.49138    266   130.3406  451.0101
         corr(cons_1,cons_3) |  .8872397  .0340243    350    .811777  .9430629
         corr(cons_2,cons_3) |  .9417586  .0181803    353   .9009867  .9711142
                 var(cons_3) |  347.1763  116.0362    258   186.6769  637.7278
         corr(cons_1,cons_4) |  .8361841   .047789    346   .7314003  .9158218
         corr(cons_2,cons_4) |  .8872397  .0340243    350    .811777  .9430629
         corr(cons_3,cons_4) |  .9417586  .0181803    353   .9009866  .9711143
                 var(cons_4) |  534.1096  176.6114    254   290.4864  977.8517
         corr(cons_1,cons_5) |   .788352  .0597024    343   .6589819  .8893676
         corr(cons_2,cons_5) |  .8361841   .047789    346   .7314003  .9158218
         corr(cons_3,cons_5) |  .8872397  .0340243    350    .811777  .9430629
         corr(cons_4,cons_5) |  .9417586  .0181803    353   .9009867  .9711143
                 var(cons_5) |  553.0598  181.8033    294   304.6109  1014.016
------------------------------------------------------------------------------

However, I believe you can fit AR1 errors now using Stata's xtmixed command.

Best wishes

George