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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