I am analyzing bird count data from surveys conducted each week (from Nov-April, when bird foraging most active near breeding cycle) for 6 years in 9 large experimental plots that are split amongst 3 regions in the landscape (6 yrs x 3 regions x 3 plots/region). We are interested in comparing counts for a few common species (& the total # of birds) as a function of position in the landscape (region) & time (years), & potential interactions of these factors (region x time). The ecosystem dries down over this period each year, & water depth itself is a known important driver of bird foraging patterns & will vary over time (gets shallower through season at given plot) & space (ground surface elevation favors dry out in a north → south gradient across the landscape). I have estimated water depth at each plot for each survey date. An interesting observation we have made is that peak numbers of birds occur at different depths amongst the 3 regions – this is an important result (region x depth response).
The count data themselves are obviously non-negative, & due in part to large numbers of 0s, are highly overdispersed (variance >> mean), so was leaning towards using negative binomial (NB) GLM, or perhaps zero-inflated/adjusted (hurdle) approach. Because the depth parameter itself varies as function of space & time (my other factors of interest), I’m having some difficulty understanding how to incorporate it into a model. Can I use depth as a continuous variable or should I aggregate into categories, & in either case, how to deal w/ the fact that amongst other categorical factors of interest, years (some years wetter/drier than others, etc.) & regions (again, plots in south being deeper than north) the distribution of depths vary so much, providing weak overlap?
Then there is the issue of non-independence in the dataset that could be contributing to the overdispersion as well. As I’ve described above, the unit of interest is a given week’s survey at a given plot. This design confounds the spatial replication (n=3 plots/region ea wk) w/ the temporal replication (n=many wks of survey data for ea plot ea year). Is there a way to incorporate a “repeated measures” type of analysis for ea plot’s data in a given year into a Poisson, NB, or appropriate ZIP/ZINB, ZAP/ZANB model? While birds do move a fair amount from week to week, seems it's important to indirectly account for structural characteristics of the plots (reduced variability intra-plot vs inter-plot amongst wks of data) that such an analysis could provide.
I'll be running the models in SAS & sincerely appreciate any recommendations on these matters.