[R-sig-ME] random slope by treatment interaction: specification

[Ramon Diaz-Uriarte]

Dear All,

I want to fit a model with a specification not unlike that given in Ben Bolker's
http://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#model-specification
the entry that says

x*site + (x | site:block)

"fixed effect variation of slope and intercept varying among sites and
random variation of slope and intercept among blocks within sites".


In my case, however, I have a fixed-effects treatment, not a
(random-effect) site and blocks are not nested within treatment (they are
crossed). And I am not sure what is the way to model this.


I think a model like

x*trt + (x | trt:block)

is not really what I want: here, all the random slopes (intercepts) are
modelled as coming from the same distribution, regardless of treatment.


I think a specification like

x*trt + (x*trt | block)

is closer to what I want: for each block (not trt by block combination) I
get distributions of slopes (intercepts) that might have a different
variance for each trt.

In addition, it seems (to me) to make some sort of sense to specify the
same interaction in the fixed and random effects part (yes, a fixed by
random interaction ought to be a random effect, but I care about the
interactions between the fixed treatment and the x continuous covariate).


Is the second specification sensible?


Thanks,


R.


P.S. The actual models, with both specifications, sometimes run into
convergence problems and I might be overfitting the data (e.g., huge
correlations in the random effects estimates). But I think that is
something I'd need to deal with once I really figure out the model to use.



--
Ramon Diaz-Uriarte
Department of Biochemistry, Lab B-25
Facultad de Medicina
Universidad Autónoma de Madrid
Arzobispo Morcillo, 4
28029 Madrid
Spain

Phone: +34-91-497-2412

Email: rdiaz02 at gmail.com
       ramon.diaz at iib.uam.es

http://ligarto.org/rdiaz