Point-to-Point Migration Functions and Gravity Model Renormalization: Approaches to Aggregation in Spatial Interaction Modeling

Abstract

Two distinct approaches to assessing the effect of geographic scale on spatial interactions are pursued. In the first, the question of whether a distance ( d) deterrence function, which explains interactions for one system of zones, can also succeed on a more aggregate scale, is examined. Only the two-parameter function, B0+ B1 d, ( B1 < 0, B0 > |B1|, 0 < d ≤ - B0 /B1) for which it is found that distances between macrozones are weighted averages of distances between component zones, is satisfactory in this regard. Estimation of continuous (point-to-point) functions—in the form of quadrivariate cubic polynomials—for US interstate migration streams, is then undertaken. Upon numerical integration, these (higher order) trend surfaces yield predictions of interzonal and intrazonal movements at any scale of interest. Tests of spatial stationarity, isotropy, and symmetry of interstate migration are conducted in this framework.