Comparisons of aggregation procedures for interaction data: An illustration using a college student international flow table

Abstract

Various approaches for developing regional schemes on the basis of geographic interaction data are discussed, using a 46 × 46 international flow table of college students as an example. The hierarchical clustering procedure employed by Masser and Brown to study movement data for London and Liverpool is compared with that utilized by Slater to analyze internal migration in several nations and is found to be more successful in the sense of explained interaction, a criterion Masser and Brown maximize in a stepwise—not necessarily optimal—manner. Slater's method, however, appears to be less subject to chaining—the sequential growth of a cluster— and more productive of distinct subgroups. It can also be interpreted as the fitting of a tree structure to a dissimilarity matrix. Both techniques are shown to yield highly significant functional regions, by comparing their results with those obtained through a large number of random partitionings of the 46 nations. The substantial value of the Ford-Fulkerson network flow algorithm in optimal partitioning and hierarchical clustering is discussed. This algorithm can also be used to define nodal in- and out-migration regions—i.e. collections of nations that have fewer people entering or leaving them as a whole than their nodal nations. To determine functional regions, the flow table is first doubly-standardized to have all row and column sums equal. Nodal regions—which cannot be hierarchically ordered—are found through study of the unadjusted flows themselves. Political, linguistic and geographic influences explain many of the international groupings obtained.