If you want to do ZIP GLMM with spatial auto-correlation, then you can 
do a couple of things:

1. Add a random effect that captures some of the spatial correlation 
(e.g. a random effect transect or area).
2. Apply a CAR ZIP GLMM in WinBUGS/OpenBUGS and get a very fast 
computer! However...my experience is that the CAR and the ZI will 
compete with each other. This is related to your second paragraph 
below...and also discussed in some of the chapters in Zuur et al (2012).

There is a nice paper from VerHoef and Janssen in which a 
spatio-temporal ZIP GLM is applied. You can easily extend their code 
with a random effect for your GLMM. You can also find example code and 
examples in our 2012 book.

But I am afraid that this is all WinBUGS stuff.

There are various papers out there in which the CAR is applied on the 
random effect itself. So something along the lines of:

y_ij ~ Poisson(mu_ij)
log(mu_ij) = alpha + beta * X_ij + a_i
a_i ~ CAR(rho,tau)


But I have also seen examples of the form:

y_ij ~ Poisson(mu_ij)
log(mu_ij) = alpha + beta * X_ij + a_i + eps_ij
a_i ~ N(0,sigma^2)
eps_ij ~ CAR(rho,tau)

This can easily be extended to a ZIP.

However...sample size is an issue. I recently tried to run a ZIP GLMM 
with CAR on a data set with 15,000 observations...but had to go for the 
first approach described above due to all kinds of vague WinBUGS error 
messages (though this may be a data specific problem).


Alain







Thank you Ben for your quick response!

I did some more homework, based on what you said below. Two remaining
questions:

- If I detect spatial autocorrelation post ZIP GLMM modeling, which I have
a feeling I might after conversations this week with someone doing a
similar analysis on another shorebird dataset, how would I incorporate the
spatial autocorrelation in the above model? I have searched extensively for
an example of a spatial zero-inflated GLMM, but have not found anything -
leading me to believe that perhaps this is not possible? I know that the
only GLMM package that allows for spatial correlation structures is
glmmPQL, which is not an option here. I've come across a couple of threads
that mention the sir() function in MCMCglmm; however, the conclusion seems
to be that it was not created for this purpose. Do you know of any examples
in the literature of a model that accounted for zero-inflation, repeated
measures, and spatial autocorrelation (oh - and crossed random effects -
see below)? Sounds too complex to me...but perhaps in WinBUGS?

- As a side note, I did come across several articles that found that
zero-inflation was accounted for by including a spatial process in a GLM
(e.g.,Flores et al. 2009,  Carroll et al. 2008 ). Likewise Thogmartin et
al. 2004 and 2006 used a spatial GLMM (overdispersed Poisson with fixed and
random effects, and a CAR term), and while there was a high number of zeros
(90%) in the dataset, overdispersion was reduced from 1.4 to 0.4 post
modeling. So perhaps this is a route to try and to compare to the results
from a ZIP GLMM in MCMCglmm? I'd love to hear if anyone else has experience
with the type of model described above applied to a zero-inflated dataset
(or a similar model such as that described by Nielson et al. 2008).

- Finally, I've realized that I have partially crossed random effects:
since sites were not necessarily sampled in the same month (i.e.,
unbalanced dataset; recall: each site is sampled monthly between Oct-Mar,
but counts are missing in many months at many sites), I should probably
include a random effect for month as well. I'm assuming that MCMCglmm can
handle partially crossed random effects, and that this would be specified
as ~random1+random2 in the model?

Thanks once again.

Cheers,
Jenn


-- 

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


4. Zero Inflated Models and Generalized Linear Mixed Models with R. (2012) Zuur, Saveliev, Ieno.
http://www.highstat.com/book4.htm

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@highstat.com
URL: www.highstat.com
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