Hello,

I have been reading the Pinheiro and Bates book and following
the examples in R.  We have a 2-level problem.  A simplified version of it 
is:
\[
E_{ijk} = a_1 + (a_2 \times S_i^p + \alpha_i + \beta_{ij}) T_{ijk}^{n + 
\gamma_i + \theta_{ij}} + \epsilon_{ijk}
\]
where $E_{ijk}$ is the response (strain), $S_i, T_{ijk}$ are predictors 
(stress and time), $a_1, a_2, p, n$ are fixed effects, and 
$\alpha_i, \beta_{ij}, \gamma_i, \theta_{ij}, \epsilon_{ijk}$ are random 
effects.  It is not clear to me that this can be
fit by nlme.  ($i$ denotes stress level, $j$ denotes a replicate within a 
stress level, $k$ denotes a time within a replicate within a stress level)

If $a_2 \times S_i^p + \alpha_i + \beta_{ij}$ were instead $a_2 + b \times 
S_i + \alpha_i + \beta_{ij}$ then I assume that there would be no problem
as we would be modeling a fixed effect as a linear function of a covariate 
which I think that
I know how to do from the examples in the book.  However, the 
documentation for nlme in Appendix B of the book indicates
that the formula in the fixed argument must be linear.  Is it true that 
nlme cannot handle the problem as stated,
or am I misunderstanding the documentation, or am I missing a way to 
recast the problem?

                                                      Steve Verrill
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