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The modifiable areal unit problem and the ecological fallacy are knownproblems that occur when modeling multiscale spatial processes. We investigatehow these forms of spatial aggregation error can guide a regionalization over aspatial domain of interest. By "regionalization" we mean a specification ofgeographies that define the spatial support for areal data. This topic has beenstudied vigorously by geographers, but has been given less attention by spatialstatisticians. Thus, we propose a criterion for spatial aggregation error(CAGE), which we minimize to obtain an optimal regionalization. To define CAGEwe draw a connection between spatial aggregation error and a new multiscalerepresentation of the Karhunen-Loeve (K-L) expansion. This relationship betweenCAGE and the multiscale K-L expansion leads to illuminating theoreticaldevelopments including: connections between spatial aggregation error, squaredprediction error, spatial variance, and a novel extension of Obled-Creutineigenfunctions. The effectiveness of our approach is demonstrated through ananalysis of two datasets, one using the American Community Survey and onerelated to environmental ocean winds.

Regionalization of Multiscale Spatial Processes using a Criterion for Spatial Aggregation Error