Intransitivity, the spatial interaction model, and U.S. migration streams

"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.... The results of the calibration of the spatial interaction using US interstate migration flows, 1935-1970, are given and compared with others previously published."