[R-sig-ME] Difficulty with GLMM specification in lme4 (Adam Smith)

[Adam Smith]

Carl Von Ende <cvonende at ...> writes:

> 
> Hi Adam,
> 
> I have several questions/clarifications and some comments about your
> design: 

I am happy to clarify.

>(1) Isn't geography confounded with treatment? 

Geography is a characteristic at the plot level.  There are 9 northern plots
and 8 southern plots.  Within each plot, both levels of the treatment effect
occur.  I suppose if you stopped there, it would resemble a randomized complete
block or a split-plot design, with plot as the blocking factor. 

>(2) Subplot is
> your experimental unit for each treatment level.  Are there different
> kinds of fruits available in a subplot for each count period, or are
> they all the same kind? If the former, were all kinds always available?
> Your statement that there are 14 records for each individual fruit seems
> to suggest you are referring to repeated observations on the same fruit
> type/kind?   If only one fruit type, the number of fruits eaten or
> remaining in each subplot for each count period is your basic response
> variable; but there would actually be a cross-classified response,if
> there was more than one fruit type in each subplot (i.e. eat/not eat X
> fruit type).  

I monitored only a single type of fruit.  And, yes, the same fruits were
monitored during each of the 14 count periods to determine whether consumption
had occurred.  My concern with using the number of fruits eaten in a given count
period (relative to the number available) as the response variable is that the
consumption events may not be independent.  For example, a single bird may
consume several (or many) fruits in succession.  For what it's worth, when I
model the full (individual level) dataset using a GEE with an exchangeable
correlation structure within subplots, the working correlation is very small  
(< 0.03), perhaps suggesting that the binomial assumption of independent events
is not grossly violated.  I'm not sure if I'm interpreting this exactly
correctly though...

(3) since the same plots & subplots were monitored
> repeatedly, it certainly seems to be a repeated measures design.  In the
> Big R book, Crawley collapses time for a binary response repeated
> measures design, but it seems to be that he is assuming independence of
> repeated observations by doing that (p. 604).  

I noticed the Crawley example, but that involves a recurring event response
(i.e., a patient can test positive multiple times).  For the fruit, it's once
bitten, gone... (obviously), so I'm not sure the example is directly comparable.
And I'm not sure he's assuming independence, but rather taking a repeated
response and converting it into a single, integrated response such that each
subject contributes only a single, weighted, observation to the model.  

> 
> Carl von Ende