zero inflated and spatial autocorrelation
(sorry if the message was double posted...) Good afternoon, I currently try to estimate the relative contribution of habitat quality and a proxy of conspecific attraction for a bird species (3 years of data: 2000, 2004 and 2008) with a model of the form Abundance (year t) ~ Abundance (year t-1) + Habitat_quality + Epsi I would like being able to compare what happened between 2000-2004 to 2004-2008 and would need some advices. Problems are 1/ that the distribution of abundance (integer values) is zero inflated, with 80% of my grid cells "tagged" with 0
The negative binomial can cope with some degree of zeros....but 80% is a lot. I guess a zero inflated distribution would be better. Besides...I can't remember wether gamm in mgcv is estimating the theta, or whether it uses a fixed value. Have a look how these guys fitted their models....it is similar: http://www.unavarra.es/metma3/Papers/Invited/VerHoef.pdf The first author published a couple of similar papers. But I don't think that this is going to be a simple call to a gamm function.
2/ I need to account for spatial autocorrelation (which is detectable below 10 km, my grid being 3 x 3 km in order to account for between years short dispersal). I lack some skills in statistics to fully handle this on my own
This is not easy..:-)
Shall I run straight ahead with a gamm model which is the only one, to my knowledge, that can account for both the spatial autocorrelation structure (with for example correlation=corSpher(form=~(X+Y))) and the zero inflated distribution (with family= negbin) ? Or is there a way to relax some constraints on the distribution in order to handle overdispersion (induced by the ZI distribution) and thus trust the run of a glmmPQL with quasipoisson ?
Have a look at the VGAM package. Perhaps it can do this type of stuff by now. If I remember well it can do smoothing with zero inflation. Not sure if it can do correlation. As a quick-and-dirty approach you could include s(X,Y) and capture the spatial pattern with such a 2-d smoother. But that may be more for larger scale patterns? However....it may cause trouble if your habitat stuff is collinear with spatial positions. Have fun....this is not easy...but shit happens. Alain
>From what I read, glmm and gamm are at the edge of statistics and need
to be examined cautiously... so if I can avoid inserting irrelevant information in it... Thanks for any help or link Best regards Alex Tiebreaker: my observation window has an irregular shape, meaning that cells at the edge are truncated. If it is the correct solution to manage this, how do I properly specify weights=... with the area of cells as argument. Do I need to transform the value of areas ? Or would it also be correct to exclude those piece of cells (which are mainly zeros --> 0 would then represent "only" 68% of observations, 392/577 )?
Dr. Alain F. Zuur First author of: 1. Analysing Ecological Data (2007). Zuur, AF, Ieno, EN and Smith, GM. Springer. 680 p. URL: www.springer.com/0-387-45967-7 2. Mixed effects models and extensions in ecology with R. (2009). Zuur, AF, Ieno, EN, Walker, N, Saveliev, AA, and Smith, GM. Springer. http://www.springer.com/life+sci/ecology/book/978-0-387-87457-9 3. A Beginner's Guide to R (2009). Zuur, AF, Ieno, EN, Meesters, EHWG. Springer http://www.springer.com/statistics/computational/book/978-0-387-93836-3 Other books: http://www.highstat.com/books.htm Statistical consultancy, courses, data analysis and software Highland Statistics Ltd. 6 Laverock road UK - AB41 6FN Newburgh Tel: 0044 1358 788177 Email: highstat at highstat.com URL: www.highstat.com URL: www.brodgar.com