
Dear list,

Please
 consider the following example from a recent field experiment.  I'm in 
over my head when it comes to coding the model in lme4.

Fruits 
are counted over time (14 occasions; every 3-5 days) to evaluate 
consumption by migratory birds.  The fruits are clustered within one of 
two subplots (a treatment and a control) assigned randomly within a 
larger plot (12 plots in total).  Individual fruits were not marked, but
 rather the number of fruits consumed during a given interval was 
noted.  Thus, the number of fruits present at the start of a time 
interval varies among subplots and over time.  I'm interested in how 
consumption varies with treatment (at the subplot level), plot geography
 (e.g., north v south), and count interval on the hazard/likelihood of 
consumption.  Modeling time as a categorical variable makes more sense 
biologically (i.e., modelling consumption separately for each count 
period), as consumption over time is not likely to change linearly or 
quadratically.

I can envision two possible specifications for the
 response variable:  (1) model consumption using a time-to-event type 
binary response in which each individual fruit provides up to 14 rows of
 data, with consumption equaling 0 for each count period until 
consumption (1) occurs (fruits can not contribute in count periods after
 they have been consumed); this equates to what Singer and Willet 
(Applied Longitudinal Data Analysis, 2003) call a discrete-time hazard 
model, if that's at all familiar; or (2) ignore individual consumption 
histories and aggregate fruits within subplots and model the proportion 
of fruits consumed in each count interval.

I lack the expertise 
to decide which is most appropriate.  Moreover, I'm stumped as to how to
 specify the clustering and nesting in glmer, regardless of the approach
 taken.

For (1), the following comes to mind:

consumption.survival
 <- glmer (consumption ~ treatment + geography + count + (1|plot) + 
(1|treatment:plot), family = binomial, ...)

For (2):

consumption.binomial
 <- glmer (cbind(consumed, total) ~ treatment + geography + count + 
(1|plot) + (1|treatment:plot), family = binomial, ...)

However, 
my gut tells me neither accounts satisfactorily for the lack of 
independence among fruits grouped within a subplot, or between subplots 
within a plot, although I can't articulate why this is...

Any guidance is most appreciated.

Regards,

Adam Smith
Dept. Natural 
Resources Science
University of 
Rhode Island
 		 	   		  
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