A Stochastic Analysis of the Spatial Clustering of Retail Establishments

The tendency for particular retail establishments to cluster has been noted by several theorists on the subject of intraurban retail spatial structure. Hotelling, for example, in his classical essay on spatial competition, concludes that as “more and more sellers of the same commodity arise, the tendency is not to become distributed in the socially optimum manner but to cluster unduly.”1 Rolph and Proudfoot provide empirical evidence of this tendency,2 and Nelson supplies a rationale for it by his “principle of cumulative attraction.”3 The analysis of the spatial clustering of particular categories of retail establishments has received considerable attention in the literature on intraurban retail spatial structure. However, the efforts thus far have not provided a readily utilizable means for investigating interurban and temporal differentials. A pioneering effort in this direction is a study by Roland Artle which, though very rudimentary, is the first reference system proposed with quantitative comparisons in mind.4 Artie begins by gridding the central area of Stockholm into a net of 210 squares, 250 meters on a side, and counts the number of retail establishments in each square for each of six selected categories of merchandise groups. He then studies the deviation of the resulting distributions from that which could be expected under the assumption of a random (i.e., Poisson) distribution. The analysis of spatial clustering described below is an attempt to generalize and extend Artie's schema and indeed utilizes his data for purposes of empirical verification.