[R-sig-Geo] spatial interaction models

[Carson Farmer]

Hi List,

This question has come up with the past, but I have yet to find a
clear response, so I'm going to ask myself.
Has anyone had much experience with spatial interaction 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.

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 the moment?
If it helps, I can provide some sample data to those who request it.

Thanks in advance,

Carson

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