On spatial unit aggregation problems in the spatial interaction model

This paper is concerned with relations between aggregate distance and biases of the distance-decay-parameter in the Huff model, which is typical of spatial interaction models. For the sake of simplicity the type of distance-decay-function of the Huff model is limited to the power function. Theoretical investigations are performed in the following steps: postulate trip patterns described perfectly by the Huff model at the basic spatial unit (BSU) level; aggregate BSUs to make up ASUs (aggregated spatial units) and define the utility of each ASU based on size and distance; predict ratio of probabilities to choose an ASU nearer the origin and one farther from it, using the ASU data and the same parameter values as those at the BSU level; consider whether such predictions leads to over-estimation or underestimation for the nearer ASU, by use of the non-bias distance. The theoretical expected directions of aggregate biases of distance-decay-parameters are shown. These findings are verified by sensitivity analysis of spatial aggregation effects like the previous studies. Using hypothetical trip data relations are investigated between aggregated biases of distance-decay-parameters and strength of distance-decay trends at the 23 zones scale. Scale changes in distance-decay-parameters certainly accorded with the theoretical expectations for the Huff model. Mean trip distance was better than mean distance in respect to goodness-of-fit, weak bias of distance-decay-parameters, and low variance of estimated parameter values at each scale. The criterion of zone compactness adopted by nearest-neighbor zoning weakened aggregation biases of distance-decay-parameters, and it could also be explained theoretically. -from English summary