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spatial interaction models

3 messages · Roger Bivand, 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 speci?c 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 ?ow 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
3 days later
#
On Fri, 1 Oct 2010, Carson Farmer wrote:

            
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

  
    
1 day later