[R] random interactions in lme

[Douglas Bates]

Jacob Michaelson wrote:
> Hi All,
> 
> I'm taking an Experimental Design course this semester, and have spent 
> many long hours trying to coax the professor's SAS examples into 
> something that will work in R (I'd prefer that the things I learn not be 
> tied to a license).  It's been a long semester in that regard.
> 
> One thing that has really frustrated me is that lme has an extremely 
> counterintuitive way for specifying random terms.  I can usually figure 
> out how to express a single random term, but if there are multiple terms 
> or random interactions, the documentation available just doesn't hold up.
> 
> Here's an example: a split block (strip plot) design evaluated in SAS 
> with PROC MIXED (an excerpt of the model and random statements):
> 
> model DryMatter = Compacting|Variety / outp = residuals ddfm = 
> satterthwaite;
> random Rep Rep*Compacting Rep*Variety;
> 
> Now the fixed part of that model is easy enough in lme: 
> "DryMatter~Compacting*Variety"
> But I can't find anything that adequately explains how to simply add the 
> random terms to the model, ie "rep + rep:compacting + rep:variety"; 
> anything to do with random terms in lme seems to go off about grouping 
> factors, which just isn't intuitive for me.

The grouping factor is rep because the random effects are associated 
with the levels of rep.

I don't always understand the SAS notation so you may need to help me 
out here.  Do you expect to get a single variance component estimate for 
Rep*Compacting and a single variance component for Rep*Variety?  If so, 
you would specify the model in lmer by first creating factors for the 
interaction of Rep and Compacting and the interaction of Rep and Variety.

dat$RepC <- with(dat, Rep:Compacting)[drop=TRUE]
dat$RepV <- with(dat, Rep:Variety)[drop=TRUE]
fm <- lmer(DryMatter ~ Compacting*Variety+(1|Rep)+(1|RepC)+(1|RepV), dat)