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lme parameterization question

3 messages · John Fieberg, Christian Ritz, Spencer Graves

#
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
#
Hi,

try something like:

lme(y~w,random=list(~1|year,~1+w|site))

Christian

----- Original Message ----- 
From: "John Fieberg" <John.Fieberg at dnr.state.mn.us>
To: <R-help at stat.math.ethz.ch>
Sent: Wednesday, April 02, 2003 10:36 PM
Subject: [R] lme parameterization question
#
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: