[R] lme, mixed models, and nuisance parameters

Scott Rifkin scott.rifkin at yale.edu
Thu Apr 8 17:37:00 CEST 2004

I have the following dataset:

96 plots 
12 varieties 
2 time points 

The experiment is arranged as follows: 

A single plot has two varieties tested on it.

With respect to time points, plots come in 3 kinds:
(1) varietyA, timepoint#1 vs. variety B, timepoint#1 
(2) varietyA timepoint #2 vs. varietyB timepoint #2
(3) varietyA timepoint #1 vs. variety A timepoint#2   
- there are 36 of each kind of within timepoint comparison and 24 between
timepoint comparisons.  so it isn't a fully connected design.  

Plots and varieties are random samples from a population of plots and 
varieties, so they are random effects. The timepoints are fixed effects. 

I am particularly interested in the variance components for variety and
timepoint within variety, in the estimate for the fixed timepoint effect
and in the predictions (BLUP) for variety and timepoint within variety.

So the mixed model looks like:

Measurement ~ Timepoint + Plot + Variety + Variety/Timepoint

Here is the question:

I am not interested in Plot, so it would be great if I could avoid 
estimating it.

Since I take two measurements from each plot, I could remove plot by 
taking the difference between the measurements and feeding that into the 
appropriate model.  If I had only one Timepoint, this seems like it would 
be straightforward since in that case the variance of the difference would 
just be twice the variance of Variety, and from the blups of the 
differences I could reconstruct the blups of the individual varieties (or 
would that not be statistically sound?)

However, my differences come in different kinds because of the Timepoints, 
so it's a bit more complicated.

Does anyone have any suggestions for whether it is possible to extract the 
Variety and Variety/Timepont variances and blups and the Timepoint 
estimates if my measurements are differences rather than individual 
measurements?  If so, how would I go about setting the appropriate 
model using lme?

Thanks much for any help,

Scott Rifkin
scott.rifkin at yale.edu

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