Dear all
this is a question of model specification in lme which I'd for which I'd
greatly appreciate some guidance.
Suppose I have data in long format
gene treatment rep Y
1 1 1 4.32
1 1 2 4.67
1 1 3 5.09
. . . .
. . . .
. . . .
1 4 1 3.67
1 4 2 4.64
1 4 3 4.87
. . . .
. . . .
. . . .
2000 1 1 5.12
2000 1 2 2.87
2000 1 3 7.23
. . . .
. . . .
. . . .
2000 4 1 2.48
2000 4 2 3.93
2000 4 3 5.17
that is, I have data Y_{gtr} for g (gene) =1,...,2000 t (treatment) =
1,...,4 and r (replicate) = 1,...,3
I would like to fit the following linear mixed model using lme
Y_{gtr} = \mu_{g} + W_{gt} + Z_{gtr}
where the \mu_{g}'s are fixed gene effects, W_{gt} ~ N(0, \sigma^{2})
gene-treatment interactions, and residual errors Z_{gtr} ~ N(0,\tau^{2}). (Yes,
I know I'm specifying an interaction between gene and treatment without
specifying a treatment main effect ! - there is good reason for this)
I know that specifying
model.1 <- lme(Y ~ -1 + factor(gene), data=data, random= ~1|gene/treatment)
fits Y_{gtr} = \mu_{g} + U_{g} + W_{gt} + Z_{gtr}
with \mu_{g}, W_{gt} and Z_{gtr} as previous and U_{g} ~ N(0,\gamma^{2}), but
I do NOT want to specify a random gene effect. I have scoured Bates and
Pinheiro without coming across a parallel example.
Any help would be greatly appreciated
Best
Gerwyn Green
School of Health and Medicine
Lancaster Uinversity
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