Quasi-likelihood Estimation and Diagnostic Statistics for Spatial Interaction Models

Abstract

In calibrating many spatial interaction models it is well known that the entropy-maximising solution and estimates obtained by maximum likelihood, with the assumption that the flows are independent Poisson random variables, are the same. This assumption often underestimates the variation in the data. It is shown how estimation can be approached through the idea of quasi-likelihood, retaining many of the advantages of maximum likelihood, but allowing a more realistic assessment of model performance. In assessing model performance it is usually better to look at individual components of a fit, rather than global measures of performance. Some recent statistical work on diagnostic statistics for certain generalised linear models is introduced and illustrated using migration data given by Dorigo and Tobler.