R help - Oct 2003 - cross-classified random factors in lme without blocking

On page 165 of Mixed-Effects Models in S and S-Plus by Pinheiro and Bates 
there is an example of using lme() in the nlme package to fit a model with 
crossed random factors. The example assumes though that the data is 
grouped. Is it possible to use lme() to fit crossed random factors when the 
data is not grouped?

E.g., y <- rnorm(12); a=gl(4,1,12); b=gl(3,4,12). Can I fit an additive 
model like y~a+b but with a and b random?

Everything I've tried gives an error:

 > lme(y~1,random=~1|(a+b))
Error in switch(mode(object), name = , numeric = , call = object, character 
= as.name(object),  :
         [[ cannot be of mode (
 > lme(y~1,random=~a+b)
Error in getGroups.data.frame(dataMix, groups) :
         Invalid formula for groups

Thanks
Gordon

Gordon Smyth <smyth at wehi.edu.au> writes:
> On page 165 of Mixed-Effects Models in S and S-Plus by Pinheiro and
> Bates there is an example of using lme() in the nlme package to fit a
> model with crossed random factors. The example assumes though that the
> data is grouped. Is it possible to use lme() to fit crossed random
> factors when the data is not grouped?
> 
> E.g., y <- rnorm(12); a=gl(4,1,12); b=gl(3,4,12). Can I fit an
> additive model like y~a+b but with a and b random?
> 
> Everything I've tried gives an error:
> 
>  > lme(y~1,random=~1|(a+b))
> Error in switch(mode(object), name = , numeric = , call = object,
> character = as.name(object),  :
>          [[ cannot be of mode (
>  > lme(y~1,random=~a+b)
> Error in getGroups.data.frame(dataMix, groups) :
>          Invalid formula for groups
> 
A standard trick is to define a grouping with one level:

one <- rep(1,length(y)
lme(...., random=~pdBlocked(.....)|one)

(Sorry, I'm a little rusty on the syntax, but just follow the example
in P&B)

AFAIR, it also works with random=list(a=~1,one=~b) and vice versa.

(The model is the same but you get different DF calculations, none of
which are correct in the completely balanced case...)

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