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