[R-sig-ME] Including by-item random intercepts for generalizability. Also to model (potential) heteroscedasticity?

[Jonathan Baron]

An attempt at an answer to part of ONE of your questions:

On 11/10/09 09:58, Antoine Tremblay wrote:
> It is our understanding that including participants and items in the random
> effect structure (in a mixed-effect regression) not only deals with issues
> of generalizability ...

I think that if you are after generalizability in Clark's ("Language
as fixed-effect fallacy") sense, you need more than this.  I think you
need random slopes as well as the random intercepts that you get from
simply including "+ (1|Subject) + (1|Item)".  That is, you need to ask
whether the variance across subjects or items in the size of the
effect is too big.  Thus, for a variable X, you need something like

(1+X|Subject) + (1+X|Item)

If you use pvals.fnc() in languageR, this won't work, because it won't
deal with correlated random effects.  So you have to do something
like:

(1|Subject) + (0+X|Subject) + (1|Item) + (0+X|Item)

which assumes that the random effects are independent.  I think you
can make them independent by centering (subtracting the mean from each
value) X and Y (the dependent variable) before including them.

On the other hand, I have argued that, if one-tailed tests are
appropriate, as they usually are in this sort of work, then

(1|Subject)+(1|Item)

is perfectly fine.  If it is "significant", it tells you that some
subject and some item show the effect of interest, even if other
subjects and other items go the other way (but less).  Arguably, this
is all you can ever know.

I'm saying this in part because I'd like to hear what others have to
say.

Jon
-- 
Jonathan Baron, Professor of Psychology, University of Pennsylvania
Home page: http://www.sas.upenn.edu/~baron