[R-sig-Geo] Question (and answer) about spdep 'autocov_dist' for use in autopoisson

[Jenn Barrett]

Hi everyone,

I recently wrote to Roger Bivand regarding the 'autocov_dist' function in spdep for use in an autopoisson, and as per his suggestion, I'm posting our conversation (below) to the list, as others may find it useful. Likewise, any thoughts/input on this matter would be more than welcome!

Cheers,
Jenn


----- Original Message -----
From: "Roger Bivand" <Roger.Bivand at nhh.no>
To: "Jenn Barrett" <jsbarret at sfu.ca>
Sent: Thursday, 24 June, 2010 00:44:51 GMT -08:00 US/Canada Pacific
Subject: Re: Question about spdep 'autocov_dist' for use in autopoisson

On Wed, 23 Jun 2010, Jenn Barrett wrote:

> Hi Dr. Bivand,
>
> My apologies for writing you directly, but I have been all over the
> internet and literature trying to find an answer to this question, and
> have had no luck.

Dear Jenn,

Please *do* write to the R-sig-geo list rather than to me directly -
others can answer your question as well, perhaps better, and in a more
timely way than I can. In addition, threads in the list can be searched in
the archives, so others can avoid the same problem later.

>
> Your R-package 'spdep' provides a function 'autocov_dist' for
> calculating a distance-weighted autocovariate for use in an
> autologistic, autopoisson or autonormal model; however, I've come across
> several papers now that suggest that autopoisson models can only account
> for negative autocorrelation. I'm confused as to why this is, as the
> approach (i.e., of including an autocovariate) is independent of the
> error distribution (as Dormann et al. 2007 point out in their Ecography
> appendix). Is it appropriate to use an autocovariate, as calculated in
> the function described above, to account for positive spatial
> autocorrelation in a poisson (or negbin) model? If not, why?

The autocov_dist function was included in connection with Dormann et al.
(2007) paper based on a workshop in 2005, where Carsten wrote the
function. It was a proof of concept idea, which I felt was rather stupid,
as shown in the examples. The main problem is that some ecology journals
never ask statisticians to referee papers, so things get done differently
in different disciplines. The underlying problem is that there is no known
way of simulating spatial autocorrelation in discrete variables to that
tests and model fitting techniques can be assessed properly.

The idea of using the spatial lag of the dependent variable in a
regression is prevalent in "spatial econometrics", but is arguably no less
wrong-headed - in the Gaussian case, it is fit with ML anyway (and with
IV methods - horror!).

A GLMM will fit with the spatial process in the error term, but its
applicability also depends on the model being well-specified. Bayesian
methods give some flexibility, but are also dependent on a "good" prior.
Spatial filtering offers some possibilities, but again, without a good way
of simulating the level of spatial autocorrelation in discrete variables
so that any tests or model fitting methods can be checked, one is
wandering around in darkness. There is no good answer to this, I'm afraid
- unless someone can show that there is a robust and workable way though,
this is a show-stopper.

Hope this helps,

Roger

>
> Many thanks in advance.
>
> Cheers,
> Jenn
>
_____________________________
Jennifer Barrett
Centre for Wildlife Ecology
Dept. of Biological Sciences
Simon Fraser University
Burnaby, B.C.


Hi Dr. Bivand,

Thanks for your timely reply. What you've written makes sense to me, and it would thus appear that I'm at a bit of a dead end in terms of how to handle the spatial autocorrelation in our count data. I suppose I could transform the counts to densities (e.g., birds/km-squared), or log or sqrt transform them, and apply Gaussian methods, as I've seen others do (e.g., Lichstein et al. 2002, Keitt et al. 2002, Tognelli and Kelt 2004) or as described in your book chapter (Chap 10: Modelling Areal Data -  Applied Spatial Data Analysis in R). That said, there are arguments against transforming count data as well (see O'Hara and Kotze 2010), so this may not be a valid approach either.

A GLMM may be an option; however, we wish to use an information theoretic approach and glmmPQL (the function suggested by Dormann et al. 2007) does not allow for calculation of AIC values. Perhaps glmmML is an option - I'll have to look into this.

I will post our conversation to R-sig-geo for the benefit of others facing the same issue.

Thanks again for your quick and informative reply.

Cheers,
Jenn