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.biv...@nhh.no
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