Modelling a large, sparse spatial interaction matrix using data relating to a subset of possible flows

Spatial interaction or gravity models provide a fruitful basis from which to study the relationship between demand for a service and the attractiveness of various possible locations at which that service might be provided. This paper is concerned with their specific application within a large UK financial organisation to assist in planning branch locations in relation to those of competitors. In particular the paper addresses two methodological problems felt to be typical of such an application. Firstly, that of computationally efficient algorithms for maximum likelihood parameter estimation in constrained gravity models which assume Poisson distributed flows and involve large, sparse flow matrices. Secondly, how to formulate an interaction model of this type which has the potential to predict business flows (including those of competitors) from any postcode sector to any major UK shopping centre, but which can be calibrated using flow data relating to only a single client institution represented in a subset of shopping centres and without access to corresponding data for competitors.