JOURNAL OF REGIONAL SCIENCE, VOL. 22, NO. 2, 1982 zy A METHOD OF FITTING THE GRAVITY MODEL BASED ON THE POISSON DISTRIBUTION* zyxw Robin Flowerdew and Murray Aitkint 1. INTRODUCTION It is frequently important to find a concise way of summarizing and describing large sets of data on interaction. Many such sets that are treated in geography demonstrate a clear relationship between the extent of interaction and the size of the objects, or places, which are interacting. It is common also to find an inverse relationship between interaction and the distance between objects or places. Models of interaction incorporating both relationships are referred to as gravity models, and such models, in many diverse forms, have been applied to many different kinds of data. In this paper, we suggest an alternative method for fitting the gravity model. In this method, the interaction variable is treated as the outcome of a discrete probability process, whose mean is a function of the size and distance variables. This treatment seems appropriate when the dependent variable represents a count of the number of items (people, vehicles, shipments) moving from one place to another. It would seem to have special advantages where there are some pairs of places between which few items move. The argument will be illustrated with reference to data on the numbers of migrants moving in 1970-1971 between pairs of the 126 labor market areas defined for Great Britain [Flowerdew and Salt (1979) present some results from the analysis of this data set]. This data set includes a large number of zero and very small flows. The discussion is restricted to Newtonian gravity models rather than the origin- and destination-constrained forms developed by Wilson (1970). 2. THE DATA The data set used here consists of observations on one-year migration flows between the 126 SMLA’s (Standard Metropolitan Labor Areas) defined by Drewett et al. (1974) for Great Britain. The data were made available to us by Nigel Spence and Stephen Kennett of the Urban Change Study at the Depart- ment of Geography, London School of Economics. The SMLA’s are intended to *The authors would like to thank John Salt, John Nelder, and Peter Vincent for their comments and help, and to clear them of responsibility for any remaining errors. The first author would also like to thank the faculty and staff of the Department of Geography, Rutgers University, where the final version of the paper was produced. ?Lecturer in Geography, University of Lancaster and Professor of Statistics at the Centre for Applied Statistics, University of Lancaster, England, respectively. Date received June, 1980; revised, May, 1981 and September, 1981. 191