[R-sig-eco] delta poisson using residual autocovariate

[David March Morla]

Dear all,

Currently, I am considering analysing a highly skewed (zero-inflated) 
count georeferenced-data by combining two published approaches that made 
use of boosted regression trees. The first one (Leathwick et al. 2008 ), 
follows a delta-log-normal approach, whereas the second (Crase et al. 
2007) introduces the concept of residual autocovariate (RAC) on binary 
data. I would like to incorporate the RAC approach with a delta-poisson 
approach. However, although a previous paper (Dormann et al. 2007) 
suggests that autocovariate regression could also be extended to any 
type of data (eg. Poisson or Gaussian errors), the same authors alert 
about its correctness.

Then, my main thoughts are:
-    Is there any potential problem for extending the RAC approach to 
Poisson or Gaussian distributions?
-    If there is no major drawback, what should be the best way to 
implement the RAC into a delta approach that consists in a binary model 
(BM) for presence/absence and a poisson model (PM) for only positive 
counts? My first idea is to calculate the residuals from the delta 
(BMxPM), estimate the autocovariate (RAC), and include this new term to 
both the BM and PM models. However, I am not sure if I should need to 
calculate different autocovariates for the BM (ie. RAC from the BM) and 
PM (RAC from BMxPM) respectively.

Any comments or suggestion about these issues would be more than welcome.

Kind regards,
David March

References:
Crase et al 2012. A new method for dealing with residual spatial 
autocorrelation in species distribution models. Ecography, 35: 879-888
Dormann et al. 2007. Methods to account for spatial autocorrelation in 
the analysis of species distributional data:  a review. Ecography, 30: 
609-628.
Leathwick et al. 2008. Novel methods for the design and evaluation of 
marine protected in offshore waters. Conservation Letters, 1: 91-102

-- 
David March Morlà
Spatial Ecologist
Email: david at imedea.uib-csic.es

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