[R-sig-Geo] spatial interaction models

[Roger Bivand]

On Fri, 1 Oct 2010, Carson Farmer wrote:

> 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.

Maybe just do it in the usual way, repeating the i and j specific 
variables? Unless you want to constrain anything, it shouldn't be more 
than reshaping to long format and rep()'ing the origin and destination 
variables, should it? Maybe provide a link to data and output using other 
approaches?

Roger

>
> 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/
>
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-- 
Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, Helleveien 30, N-5045 Bergen,
Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no