Effects of scale in spatial interaction models

We study the e ects of aggregation on four di erent cases of non linear spatial gravity models. We present some theoretical results on the relationship between the mean ows at an aggregated level and the mean ow 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 arti cial data. The main aim is to test the e ects on the aggregated ows on 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 ows connatural with aggregation while negative spatial dependence exacerbates it.