I have posted some questions about the mixed model approach for
a repeated-measure design last week. The post was probably too
long for most people. I can summarize the previous post into
two short questions. I would greatly appreciate your comments
and I'll post a summary of the responses.
1) how to use lme() when the random effect is not statistically
significant but the interaction between the fixed and random
factors is significant?
2) how to use lme() when the residual variance depends in an
ADDITIVE manner from the levels of the fixed effect AND from
the levels of the random effect?
I give a little bit more of details and motive these questions
below. Let assume that I have a repeated measures design with
eight subjects (su factor) who perform a task in four different
conditions (plane factor). Each conditon is presented six times
to each subject in a randomized order (6 replications).
1) With respect to the first question, the most common examples
involving an interaction I have seen in books were modeled
with a two-level random effects model:
lme(response~plane,random=~1|su/plane,data)
but what if var(su)~0 and I would like to simplify
the model ? One possibility is:
data$grp<-factor(paste(data$su,data$plane)
lme(response~plane,random=~1|grp,data)
In that case, is the following correct
lme(response~plane,random=list(grp=pdDiag(form=~plane)),data)
if the variance depends on the level of plane? A LRT test
with my dataset shows marked improvement with respect to the
previous model but there are many zeros in ranefs() and the
corresponding qqnorm plots look strange because of these zeros.
2) With respect to the second questions. I know two methods
with the weights argument:
weights=varComb(varIdent(form=~1|plane),varIdent(form=~1|su))
or
weights=varIdent(form=~1|plane*su)
but the first one multiplies and not add the variances and the
second one define a parameters for each combination of levels. I
have looked at the varComb function as a guide to program a new
set of functions to implement the desired behavior but I could not
find which function actually carries out the multiplication of
the variance during the fit of the model.
Gabriel Baud-Bovy
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