Frame independent spatial analysis

Abstract

The results of an analysis of geographical data should not depend on the spatial coordinates usedÐthe results should be frame independent. This should also apply when areal units are used as the spatial data collection entity. Previous work has shown that some analysis procedures do not yield the same results under alternate areal aggregations, but some of these studies have used measures known to be inappropriate for spatial data, e.g., Pearsonian correlation instead of cross-spectral analysis. And there are some methods of analysis which do seem to yield frame invariant results, especially under alternate partitionings of the geographic space. In other cases it is appropriate to consider aggregations as spatial filters, with response functions which can be estimated a priori. There also exist linear spatial models which allow exact calculation of the effects of a spatial aggregation, so that consistent empirical and theoretical results can be obtained at all levels of spatial resolution. It is proposed that all methods of spatial analysis be examined for the invariance of their conclusions under alternative spatial partitionings, and that only those methods be allowed which show such invariance.

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