Intransitivity, the Spatial Interaction Model, and US Migration Streams

Abstract

The flows predicted by a large class of spatial interaction models are transitive, yet US migration tables have been shown to contain large numbers of intransitivities. This paper investigates a number of possible conditions under which flows regulated by the spatial interaction model might be observed to be intransitive. A singly constrained gravity model is calibrated for a number of flow tables, and distorted by sampling error, by aggregation over strata, and by an independently distributed error term. Only the last distortion gives the correct bias in the relative abundance of intransitivities in numerical flows and flow probabilities. This conclusion is supported by further simulations using random spatial interaction models. The results of the calibrations of the spatial interaction model using US interstate migration flows, 1935–1970, are given and compared with others previously published.