[R-sig-ME] Help on example from Baayen, Davidson & Bates, 2008

[Margaret Wardle]

Hi, I'm trying to apply lmer to a data set structured as follows:  In
a fully within-subject design, all subjects receive 0, 10mg and 20mg
of a stimulant drug (Drug - a factor with three levels, with two
contrasts representing the linear effect of drug, and the quadratic
effect of drug).  On each dose they view the same 40 videos consisting
of 10 actors, each of whom produces one happy, angry, fearful and sad
expression.  The main DV is the intensity of expression (from 0-100%)
at which participants are able to identify the emotions.  The thought
is that stimulant drugs will reduce the intensity of expression needed
to identify happy emotions.  Emotion is thus a factor with 4 levels,
and 3 Helmert contrasts (happy vs. all negative, angry vs. other
negative, fearful vs. sad, with our primary interest being contrast
1).

This would appear to me to be a good use of the crossed random effects
set-up illustrated in Baayen et al.
(http://www.ualberta.ca/~baayen/publications/baayenDavidsonBates.pdf),
as actors may vary in their overall ability at producing expressions,
or alternately in their ability at producing a particular expression
(for example, there's one guy whose face just looks angry).

There is heteroskedasticity in the data, in the sense that everyone
reacts pretty similarly to the placebo, but they vary a lot more in
their reactions to the drug doses (as is pretty normal in drug
studies).

Thus, I think my model would be the following:

intensity ~ Drug*Emotion + (1+Drug|Subject) + (1+Emotion|Actor)

If I understand correctly, this allows for Subject and Actor random
intercepts, random slopes for drugs by subjects (varying responses to
drug), and random slopes for emotions by actor (varying abilities at
producing emotions).  Which is great.  However, I won't lie to you, I
was hoping to use mcmcsamp for p-values, and mcmcsamp does not like
these correlated slopes and intercepts.  I have been reading and
reading and reading about the p-values thing, and I think I get it,
but I'm a post-doc, and I answer to an advisor, and if I bring her
something without p-values, she will make me do an RMANOVA instead.

However, reading further in the Baayen article, it seems there may be
some simplifications to the model that I could potentially make that
would allow me to use mcmcsamp and thus avoid the problem with my
advisor while still maintaining some statistical integrity.
Specifically, at one point, they reduce their model from

RT ~ SOA + (1|Item) + (1+SOA|Subject)

to

RT ~ SOA + (1|Item) + (1|Subject) + (1|SOA:Subject)

And say this is "removing the correlation parameter and assuming
homoskedasticity for the subjects with respect to the SOA conditions."
 I have been trying to understand this for a few days now, but I can't
figure out what (1|SOA:Subject) is still allowing to vary randomly, or
if the homoskedasticity they're talking about is the same kind that
I'm worried about in my study.  I'd love to be able to reduce my model
in the same fashion, but I'm not going to do it without understanding
what I'm doing.  Could anyone help me out?  If I did indeed drop down
to:

intensity ~ Drug*Emotion + (1|Subject) + (1|Drug:Subject) + (1|Actor)
+ (1|Emotion:Actor)

What exactly would be still allowed to vary randomly?

I should note that I've considered the alternate intensity ~
Drug*Emotion + (1|Subject) + (0+Drug|Subject), and although that
removes the correlation between intercept and slopes, it does not
remove the correlation between the levels of Drug, and thus does not
solve my mcmcsamp problem.  I've also considered just abandoning the
factor and making two new variables representing for the linear and
quadratic effect of drug, and then having those vary independently,
i.e. (Drug_lin|Subject) + (Drug_quad|Subject), but I've been told by
my one other lmer using friend that would be wrong and evil (Hi,
Adam!).

Thanks so much for the help in advance.  Sorry to be bringing this up
for the sake of p-values, I know that's annoying and everyone's
thoroughly sick of it, but I can't help it. You probably all had
advisors once, right?

-Megin Wardle