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

[Thierry Onkelinx]

Dear Bradley,

For your first question you could consider the combination of crossed
and interaction random effects. (1|Subject) + (1|Date) +
(1|Subject:Date) That might be overkill given that you have only 4
observations for each level of Subject:Date. Therefore I'd rather go
for (1|Subject) + (1|Date).

For the second one: though not the most efficient design to test 6
treatment, it seems reasonable to me to analyse them with a single
model.

For the last question: What is hard to normalise? The response or the
residuals? Note that only the residuals are assumed to be normal.

Best regards,


ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE
AND FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx op inbo.be
Kliniekstraat 25, B-1070 Brussel
www.inbo.be

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more than asking him to perform a post-mortem examination: he may be
able to say what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
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not ensure that a reasonable answer can be extracted from a given body
of data. ~ John Tukey
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2017-12-05 17:50 GMT+01:00 Bradley Carlson <carbrae op gmail.com>:
> 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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>
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