Abstract
We present a method to compare spatial interaction models against data based on well known statistical measures that are appropriate for such models and data. We illustrate our approach using a widely used example: commuting data, specifically from the US Census 2000. We find that the radiation model performs significantly worse than an appropriately chosen simple gravity model. Various conclusions are made regarding the development and use of spatial interaction models, including: that spatial interaction models fit badly to data in an absolute sense, that therefore the risk of over-fitting is small and adding additional fitted parameters improves the predictive power of models, and that appropriate choices of input data can improve model fit.
Highlights
We present a method to compare spatial interaction models against data based on well known statistical measures that are appropriate for such models and data
Our primary goal is to improve upon the statistical analysis commonly carried out in the literature and apply this improved analysis to determine the relative effectiveness of key examples from two popular families of models: gravity models and radiation models
This is unsurprising since this model has assumed that mi and ni can be used analogously with ti and ni in the gravity model, without any theoretical justification for why this might be the case; an asymmetry is naïvely introduced into the model where the quantities governing site inflow and outflow are disentangled without a derivation matching this to the real world
Summary
We present a method to compare spatial interaction models against data based on well known statistical measures that are appropriate for such models and data. The ability to predict the number of vehicles, the amount of goods, or the spread of disease between two locations, using only limited data about each location, is important in a variety of academic disciplines Problems of this nature can be studied using ‘spatial interaction models’. In this paper we wish to focus on the features of spatial models and on the features of different analysis methods used to study spatial data and models To do this we sought a dataset which acts as a standard to be used when comparing different models and different analysis techniques. We have chosen to work with the US Census 2000: the county-to-county worker flow data from the US Census 20001 It is both an open source dataset and widely used
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