Model specification: crossed vs nested factors
Ah, yes, I forgot one key piece of information. The treatments were added sequentially in time at the site. In Site #1, treatment A was applied, measurements taken, then treatment B was applied, etc. A proper control period (4 days) occurred between the application of the treatment. This is why I see my design as analogous to a growth model, though the treatment does vary in time.
Dennis Murphy wrote:
Hi:
No direct answers, but some questions...
On Tue, Aug 24, 2010 at 2:01 PM, Richard Feldman
<richard.feldman at mail.mcgill.ca <mailto:richard.feldman at mail.mcgill.ca>>
wrote:
Hello,
I am at my wit's end with regards to specifying my model, perhaps
because I am confused about nested vs. crossed grouping factors.
My dataset has 16 sites and within each site I applied 3 treatments
(A, B, C). The sites differ based on elevation. I originally thought
I had a hierarchical (nested) model and specified the full model as
such:
How did you assign treatments within site? Were they assigned to
divisions of a site (e.g., subplots) or were they assigned to the entire
site at different times, or ??? This matters in the analysis...a lot.
model.n <- glmer(Y ~ Treatment*Elevation + (Treatment|Site), data=Data)
The data also seemed analogous to a longitudinal model where instead
of subject I have site and instead of time/days I have treatment. I
am not totally clear on why this analogy breaks down.
Longitudinal models involve a time element, usually within
subject/primary unit, and constitute repeated measurements on that unit
over time with the same treatment conditions and possibly time-varying
covariates. How would such a scenario correspond to your design?
After extensive reading, it seems that because each site receives
the same three treatments, my model is crossed and not nested. Hence
the specification should be:
It's not obvious at this point whether you have crossed or nested
effects. It's entirely possible that site could be a blocking factor. Go
back to the initial question.
model.c <- glmer(Y ~ Treatment*Elevation + (1|Site) + (1|Treatment),
data=Data)
I have three questions:
1. Is model.c indeed the correct specification given my data?
2. Given model.c, does the treatment by elevation interaction
capture this cross-scale effect, even though the former is a level-1
predictor (varies within site) and the latter a level-2 predictor
(varies among sites)?
3. The output from model.c gives zero variance for the random effect
of treatment. I assume this is because there are only three levels.
Hence, treatment can only be a fixed variable. I have no problem
with that. What I am confused about is how I can discover how much
the treatment-response relationship varies among sites. I originally
thought that (Treatment|Site) made sense because the
treatment-response slope could vary based on site.
I don't think we have enough information yet to make a determination on
any of your questions.
Hope this helps somewhat,
Dennis
I appreciate all your help in getting me out of this mental
quagmire. Thank you!
--
Richard Feldman, PhD Candidate
Dept. of Biological Sciences, McGill University
W3/5 Stewart Biology Building
1205 Docteur Penfield
Montreal, QC H3A 1B1
514-212-3466
richard.feldman at mail.mcgill.ca <mailto:richard.feldman at mail.mcgill.ca>
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Richard Feldman, PhD Candidate Dept. of Biological Sciences, McGill University W3/5 Stewart Biology Building 1205 Docteur Penfield Montreal, QC H3A 1B1 514-212-3466 richard.feldman at mail.mcgill.ca