## Comparing Models of Spatial Networks

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Talk given at Complenet 2013, on 14th March 2013 in Berlin.

Given a set of sites in space, how can we model their possible interactions? This is a problem encountered in many fields including geography, economics, transport, communications, town planning, and archaeology. The interactions can be of many types: direct links, traffic flows, or ancient trade routes. Models which produce such spatial networks may be matched to available data and then used to make predictions about the response of a complex system to proposed changes. Alternatively, such models can be used to fill in missing data, as is often needed in archaeology. The classic models in the field are the gravity models and the Intervening Opportunities Model, both of which date back to the 40's and 50's, but there are many, many variations on the original forms of these models and many alternatives.

The question we address in this talk is how can we compare different models of spatial networks to available data. In particular, given a set of data, how can we assess which models give the best fits. Due to the large number and heterogeneity of observations in modern applications, the best parameter values to use in spatial network models and their statistical significance are difficult to

estimate. We use the framework of generalised linear regression to estimate and then assess the models. We use both the Poisson distribution and the Negative Binomial Regression with a three parameter Tanner's deterrence function as our statistical model.

We will focus on gravity models and the Radiation model, a type of Intervening Opportunities model. We compare these models to each other and will also look at how variations of these models, where additional constraints are imposed, can improve results.