[R] lme parameterization question

[Spencer Graves]

Have you looked at Pinheiro and Bates (2000) Mixed Effects Models in S 
and s-Plus?  "lme" is great, but I couldn't make it work until I spent 
some time with that book.

Hope this helps.
Spencer Graves

John Fieberg wrote:
> Hi,
> 
> I am trying to parameterize the following mixed model (following Piepho
> and Ogutu 2002), to test for a trend over time, using multiple sites:
> 
> y[ij]=mu+b[j]+a[i]+w[j]*(beta +t[i])+c[ij]
> 
> where:
> y[ij]= a response variable at site i and year j
> mu = fixed intercept
> Beta=fixed slope
> w[j]=constant representing the jth year (covariate) 
> b[j]=random effect of jth year, iid N(0,sigma2[b])
> a[i]=random effect of the ith site, iid N(0, sigma2[a])
> t[i]=random effect of ith site, iid N(0, sigma2[t])
> c[ij]=random error associated with ith site and jth year
> 
> I would like to assume that an unstructured relationship applies to
> a[i] and t[i] (i.e., I would like to assume that the random effects a[i]
> and t[i] are drawn from a multivariate normal distribution with non-zero
> covariance parameter).  These random effects are assumed to be
> independent from the b[j]'s and from the c[ij]'s.  I have tried several
> approaches, but cannot seem to duplicate the results presented in Piepho
> and Ogutu using R's lme function (but I can reproduce the results using
> SAS proc mixed).
> 
> In SAS, the model is fit using:
> 
> proc mixed method=REML nobound;
>    class year site;
>    model y=w site/ddfm=satterth s;
>    random int/sub=year;
>    random int w/sub=site type=un;
> run;
> 
> Any help would be greatly appreciated!
> 
> Reference:
> Piepho, H-P. and J.O.Ogutu. 2002.  A simple mixed model for trend
> analysis in wildlife populations.  Journal of Agricultural, Biological,
> and Environmental Statistics, 7(3):350-360.
> 
> 
> Thanks,
> 
> John
> 
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