A Multiscalar Approach for Identifying Clusters and Segregation Patterns That Avoids the Modifiable Areal Unit Problem

One problem encountered in analyses based on data aggregated into areal units is that the results can depend on the delineation of the areal units. Therefore, a particular aggregation at a specific scale can yield an arbitrary result that is valid only for that specific delineation. This problem is called the modifiable areal unit problem (MAUP), and it has previously been shown to create issues in analyses of clusters and segregation patterns. Many analyses of segregation and clustering use the ratio or difference between a value for an areal unit and the corresponding value for a larger area of reference. We argue that the results of such an analysis can also be rendered arbitrary if one does not examine the effects of varying the geographical extent of the area of reference to test whether the analysis results are valid for more than a specific areal delineation. We call this the part of the MAUP that is related to the area of reference. In this article, we present and demonstrate a multiscalar approach for studying segregation and clustering that avoids the MAUP, including the part of the problem related to the area of reference. The proposed methods rely on multiscalar aggregation of the k nearest neighbors of a location in a statistical comparison with a larger area of reference consisting of the K nearest neighbors. The methods are exemplified by identifying clusters and segregation patterns of the Hispanic population in the contiguous United States.