[R] lme: Specifying a formula

[Douglas Bates]

Christian Hennig <fm3a004 at math.uni-hamburg.de> writes:

> I am faced with the following model:
> 
> y=E+P+M+H+PxE+Error
> 
> y is a response, E and P are factors with fixed effects.
> M is a random effect nested in P and H is a random effect nested in M.
> PxE is interaction of P and E.
> 
> It seems that I should fit such a model with the lme function of library
> nlme, but I was not able to figure out from the help page how to specify the
> formula. In the nlme documentation, the term "nested" is always associated
> with a "grouping", and I do not know what my grouping is here.

For a complicated model like this you may find it worthwhile looking
at the examples in
@Book{pinh:bate:2000,
  author =	 {Jos\'{e} C. Pinheiro and Douglas M. Bates},
  title = 	 {Mixed-Effects Models in \textsf{S} and \textsf{S-PLUS}},
  publisher = 	 {Springer},
  year = 	 2000,
  series =	 {Statistics and Computing}
}

The grouping refers to the groups in the data with which random
effects are associated.  If the levels of the M factor are distinct
for different levels of P then you can fit your model as

 lme(y ~ E * P, data = mydata, random = ~ 1 | M/H)

The last argument indicates that there will be an additive scalar
random effect for M and for H within M.

If you do not have distinct levels for M within P you can create a new
factor with 

 getGroups(~ 1 | P/M, data = mydata, level = 2)

and assign it as the grouping factor.
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