[R-sig-ME] Model specification: crossed vs nested factors

[Richard Feldman]

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>
> 
>     _______________________________________________
>     R-sig-mixed-models at r-project.org
>     <mailto:R-sig-mixed-models at r-project.org> mailing list
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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