Extremal Approaches to Estimating Spatial Interaction

Abstract Two recent theoretical approaches to the gravity model of spatial interaction are examined with emphasis on the dissimilar physical and statistical theories from which they were respectively derived. Formal relationships between the two methods are demonstrated. The two ap- proaches jointly indicate a general method of generating new hypotheses of gravity flows. This method is discussed and eualuated, and some questions of theory comparability are explored. Comments on some of the computational features of each of the two models conclude the paper. INTRODUCTION Many variations of the “gravity” model have been popular with geographers and practitioners of the planning sciences for summarizing patterns of travel due to migration, retail trade, or employment. The gravity model, in its various historical forms, has resulted in acceptable estimates for a wide variety of problems [3, 181. In 1964, Harris pointed out the desirability of a theoretical basis for