Two-stage permutation tests for determining homogeneity within a spatial cluster

The discovery of spatial clusters formed by proximal spatial units with similar non-spatial attribute values plays an important role in spatial data analysis. Although several spatial contiguity-constrained clustering methods are currently available, almost all of them discover clusters in a geographical dataset, even though the dataset has no natural clustering structure. Statistically evaluating the significance of the degree of homogeneity within a single spatial cluster is difficult. To overcome this limitation, this study develops a permutation test approach Specifically, the homogeneity of a spatial cluster is measured based on the local variance and cluster member permutation, and two-stage permutation tests are developed to determine the significance of the degree of homogeneity within each spatial cluster. The proposed permutation tests can be integrated into the existing spatial clustering algorithms to detect homogeneous spatial clusters. The proposed tests are compared with four existing tests (i.e., Park’s test, the contiguity-constrained nonparametric analysis of variance (COCOPAN) method, spatial scan statistic, and <i>q</i>-statistic) using two simulated and two meteorological datasets. The comparison shows that the proposed two-stage permutation tests are more effective to identify homogeneous spatial clusters and to determine homogeneous clustering structures in practical applications.