# GLM questions for landscape experiment

#### Kayaker

##### New Member
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.

#### terzi

##### TS Contributor
Hi Kayaker,

Due to the complications of your design, I'd say that the best analysis would likely require some forms of Hierarchical Modeling. This technique will allow to consider the repeated measures in the design at the same time that allows you to incorporate the spatial information and also include interactions if you consider it necessary. Multilevel Modeling can be used with almost any form of regression, including Generalized Linear Models such as those that you are correctly assuming.

If I remember correctly, the PROC MIXED in SAS can be used to fit these type of models, yet I'm a little rusty on SAS so it may be another procedure. But I'm quiet sure that the results can be obtained in the software.

Regards,

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