[R] spatial interaction (gravity) model as Poisson regression

[Carson Farmer]

Dear list,

I posted essentially this same question to the r-sig-geo mailing list
last week with no response :( Unfortunately I am no closer to reaching
a solution, so I now post it here (with some clarifications) in the
hope that someone following this list might have an answer for me:

Has anyone had much experience with spatial interaction (or gravity)
models, specifically in the form of Poisson regression? I'm a bit
unsure of how to operationalize this using glm(), and would appreciate
any pointers from those with more experience. I have searched the
archives extensively, and there are several mentions of this question,
but I have yet to find anything concrete that I can wrap my head
around... apologies if I have missed something.

Basically, the conventional origin constrained model would look
something like this:
T_{ij} = exp(\delta_{i} + \log{A_{j}} - \beta D_{ij}) ~ \varepsilon_{ij}
where \delta_{i} is a constant parameter specific to the ith zone,
A_{j} is the attractiveness of the jth location, and D_{ij} is the
distance between i and j. Note that \varepsilon_{ij} is just the
multiplicative error term of the flow from i to j, and \beta is the
distance decay parameter.

Similarly, the doubly constrained model follows the form:
T_{ij} = exp(\delta_{i} + \gamma_{j} - \beta D_{ij}) ~ \varepsilon_{ij}
where everything is defined as above, except exp(\gamma_{j}) is an
estimate of the attractiveness of location A_{j}.

Hopefully the above description makes things a bit clearer,
essentially my question is this:
What factors or in what form do I have to have my data in order to be
able to run such a model following the glm syntax?
I know this should be relatively straight-forward, I just can't seem
to get my head wrapped around it at all?
If it helps, I can provide some sample data to those who request it.

TIA, Carson

-- 
Carson J. Q. Farmer
ISSP Doctoral Fellow
National Centre for Geocomputation
National University of Ireland, Maynooth,
http://www.carsonfarmer.com/