[R] Correlated random effects in lme

[Adelchi Azzalini]

On Sat, Mar 17, 2007 at 08:12:35PM +0100, Guillermo Villa wrote:
> Hello,
> 
> I am interested in estimating this type of random effects panel:
> 
> y_it = x'_it * beta + u_it + e_it
> 
> u_it = rho * u_it-1 + d_it        rho belongs to (-1, 1)
> 
> where:
> 
> u and e are independently normally zero-mean distributed.
> 
> d is also independently normally zero-mean distributed.
> 
> So, I want random effects for group i to be correlated in t, following an
> AR(1) process.
> 
> Any idea of how to estimate this kind of models using the lme function?
> 
> (Now, I know the corAR1 option is not the way...)
> 
> G

If you add an AR(1) process, the {u_t} process process in this
case (here I drop the index "i"), and a pure noise effect, the {e_t}
process in you notation, their sum is an ARMA(1,1) process with
certain restrictions on the parameters. Given this, I do not
know lme() well enough to insert this constraint on the parameters.
As an approximate solution, you could fit a plain ARMA(1,1) model.

However, is it not the case that the e_{it} is actually constant
over t, so we have just an e_i term? (a much frequent case in 
practice). This is a much easier problem.


Adelchi Azzalini  <azzalini at stat.unipd.it>
Dipart.Scienze Statistiche, Università di Padova, Italia
tel. +39 049 8274147,  http://azzalini.stat.unipd.it/