Delineating Heterogeneous Planning Regions: a Technique for Clustering Spatial Units Applied to Michigan Health Service Areas (Central Place Theory, Compactness, Regionalization, Contiguity, Care).

Abstract

An algorithm for delineating maximally heterogeneous planning regions is formulated, tested, and applied to the problem of designating Health Service Areas in Michigan. Substantial similarities are shown to exist between the spatial aspects of the health care system and central place theory. On the basis of these similarities and a review of efforts to regionalize health care, homogeneity between Health Service Areas and heterogeneity with each Area are maximized. The objective is to design a system in which each health service area contains services that are comparable to the services available in every other health service area and that these services represent the widest possible variation commensurate with efficient use of resources. Concepts employed in the analysis of variance are used to quantify the notion of heterogeneity. The algorithm's objective function maximizes the variation within each cluster of spatial units and the compactness of each cluster. Its formulation and implementation allows the analyst to emphasize the maximization of variation or the maximization of compactness. The objective function is subject to contiguity and size constraints. The algorithm is designed to cluster spatial units in n-dimensional space. The algorithm's computational performance is tested using two fixed K central place networks. It is found to cluster elementary hexagonal spatial units into the expected hexagonal regions successfully. Then, the algorithm is used to delineate Health Service Areas in Michigan. Clustering schemes are generated based on different assumptions about the relative importance of internal variation versus compactness and /or the number of desired clusters. These schemes are found to exceed the heterogeneity and compactness exhibited by the existing Health Service Areas. Given its satisfactory performance, the algorithm is considered to be sufficiently general to be applied to a variety of regional delineation problems.