Effects of scale in spatial interaction models

We study the effects of aggregation on four different cases of nonlinear spatial gravity models. We present some theoretical results on the relationship between the mean flows at an aggregated level and the mean flow at the disaggregated level. We then focus on the case of perfect aggregation (scale problem) showing some results based on the theoretical expressions previously derived and on some artificial data. The main aim is to test the effects on the aggregated flows of the spatial dependence observed in the origin and in the destination variables. We show that positive spatial dependence in the origin and destination variables moderate the increase of the mean flows connatural with aggregation while negative spatial dependence exacerbates it.