[R-sig-ME] Choosing best approach for a crossover experiment

[Bradley Carlson]

Hello all,


I have data from a repeated measures, crossover experiment that goes a bit
beyond my experience. I wanted to be sure I was approaching the data in the
right way. The sample size is small as this is an independent study project
with an undergraduate student, but we see some interesting patterns and I
hope it holds up to a proper analysis. Pardon the length of the
explanation: I want to be clear about what the problems are.


I'm trying to test whether snakes respond differently to certain odor cues.
We have 5 individual snakes. The first week, each snake was tested in 3
sets of tests, with each set of tests on a different day. In each set, they
were exposed to all 4 cues in a randomized order (C B A D on day 1, then A
B D C on day 2, etc.) Don't worry about order effects - that's not where
I'm going with this. I expect the same snakes' behavior to be correlated
both across days (some snakes exhibit stronger responses reliably), and I
expect their behavior in response to the 4 different cues to be correlated
within days (e.g., if they happen to be warmer on Monday, they might have a
stronger response to all 4 cues). I don't necessarily expect this
day-to-day variation to be correlated among individuals (I doubt Monday
would be a high response day for all snakes). What I care about are the
within-subjects, within-date differences between the cues (do they reliably
respond more strongly to cue A than the other cues tested on the same day?)


***My first question is what would be the proper formatting for a repeated
measures analysis of this in lmer**.* I was torn between a few different
options:


Behavior ~ Cue + (1|Subject) + (1|Date)   <--- Seems to assume that date
effects are similar for all individuals

Behavior ~ Cue + (1|Subject/Date)

Behavior ~ Cue + (1|Subject:Date)


Any advice on which of these are more appropriate for the structure of my
data?


The second issue is that I retested these same snakes in a second battery
of tests. The structure is identical, except instead of the first 4 cues (A
B C D), two cues were switched out for new ones (A B E F). I could perform
a separate analysis of the data from this battery of tests, using the best
format from the above data. However, since it is the same individual
animals, and since the A vs. B contrast is present in both batteries of
tests, it would be nice to put all the data into a single analysis. This
would strengthen the A vs. B comparisons and seems more elegant than two
separate analyses. ***Are there any reasons I couldn't do this?*** The only
thing I could think of would be that some pairwise comparisons would have
never actually been performed on the same day (e.g., C was part of the
first battery of tests, and E was part of the second), but accounting for
date effects should control for this, I think.


Finally, I was considering bootstrap analysis to generate CIs for testing
null hypotheses, as my data are hard to normalize with
transformations. ***Would
that eliminate the ability to do pairwise, post-hoc comparisons
(using lsmeans or multcomp)?*** I'd like to know which cues are different
from which. I could do this by re-running the analysis with each cue type
as the reference level - then the effects reported would be pairwise with
respect to the reference cue, but this doesn't account for multiple
comparisons.


Thank you so much in advance for taking the time to wade through this and
offer me any thoughts. I'd also be happy to send the data and have someone
put together a script that seems reasonable to them, so I can learn the
nuances of LMM a little better.


Best,

Brad


Assistant Professor of Biology

Wabash College

Crawfordsville, IN

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