[R] Crossed random effects

[Jonathan Williams]

I would be very grateful for help with devising the correct formula 
for an analysis with crossed random effects.

The data consist of measurements of the width of a brain structure
from 145 subjects, on both the right and left. So, Side is nested
within Subject in a balanced design. 

3 raters measured the widths. One rater measured all 145 widths twice 
- so there were 2 replications. One rater measured all the widths, 
and then re-measured a random 30% of them. One measured only a random 
70% of the widths once. So, replication is nested within rater, and 
these random factors are highly unbalanced.

I want to analyse the relationship of the widths to subject variables 
such as age and gender. But, I do not know how to write the correct
formula for the random effects to specify how the Subject/Side structure 
is crossed with the Rater/Replication structure. I gather from reading
Pinheiro and Bates (p163) that "The crossed random effects structure is
represented in lme by a combination of pdBlocked and pdIdent objects".
But, I cannot see how to extend the example in the book to fit my data.

I would be very grateful for help with this.

Jonathan Williams
OPTIMA Clinical Fellow and Honorary Consultant Psychiatrist
Dept Pharmacology
Oxford University
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