[R-sig-ME] repeated measure in partially crossed design

[Ben Bolker]

matteo dossena <m.dossena at ...> writes:

> Dear all,
 
> sorry to write again on this topic, but i feel like I haven't make
> myself clear.  I try to rephrase my question, hope I'm not annoying
> you.  So given that each level of season - e.g. April and Oct -
> occurs at each level of subject while each level of treatment
> -e.g. high or control - only occurs on a half of the the subjects
> respectively and randomly, should I specify the random effects in
> the model as

If you really want to "... assess[] the effect of treatment, season
and their interaction on the relationship between the two variables",
you may want treatment*season*V2 as fixed effect (so you can tell whether 
the V1~V2 relationship changes with treatment and season)

  Having any *factor* included as both a fixed effect and a random
effect will cause trouble, e.g. in your model (2).  (On the other
hand, it does sometimes make sense to include a _continuous_ predictor
as both fixed (which will estimate a linear trend) and random (which
will consider variation around the linear trend -- this only makes
sense if you have multiple measurements per value of the predictor,
though.  Another apparent exception to this is subject in the
(1|treatment/subject) term, which is only included as subject nested
within treatment.
 
> (1) having subject nested within treatment and crossed with date, 
>  V1 ~ treatment * season + V2 + (1|treatment/subject) + (1|season)

  Here both treatment and season are included as both fixed and random --
probably not a good idea.

> (2) subject crossed with date ignoring the nesting with treatment,
> (3) random effects on subject only ignoring the crossed and nested
> data structure V1 ~ treatment * season + V2 + (1|subject) +
> (1|season)

  Still probably don't want season and (1|season)
> 

> (3) random effects on subject only ignoring the crossed and nested
> data structure V1 ~ treatment * season + V2 + (1|subject)

   This is not unreasonable.  You could consider (season|subject),
or (1|subject)+(0+season|subject) [which fits the intercept and slope
independently], since you have both seasons assessed for each individual.

   This gets raised a lot on this list, but: I would generally only
drop a random effect from the model if it actually appears overfitted
(i.e.  estimated as zeros, or a perfect +1/-1 correlation between
random effects), and not if it is merely non-significant (Hurlbert
calls this "sacrificial pseudoreplication").  I've been very impressed
by the results from the blme package, which incorporates a weak
Bayesian prior to push underdetermined variance components away from
zero ...