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Lin, Ge, and T.L. Zhang. 2007. "Loglinear residual tests of Moran's I autocorrelation and their applications to Kentucky breast cancer data." Geographical Analysis, 39:293-310.
This article bridges the permutation test of Moran's I to the residuals of a loglinear model under the asymptotic normality assumption. It provides the versions of Moran's I based on Pearson residuals (I-PR) and deviance residuals (I-DR) so that they can be used to test for spatial clustering while at the same time account for potential covariates and heterogeneous population sizes. Our simulations showed that both I-PR and I-DR are effective to account for heterogeneous population sizes. The tests based on I-PR and I-DR are applied to a set of log-rate models for early-stage and late-stage breast cancer with socioeconomic and access-to-care data in Kentucky. The results showed that socioeconomic and access-to-care variables can sufficiently explain spatial clustering of early-stage breast carcinomas, but these factors cannot explain that for the late stage. For this reason, we used local spatial association terms and located four late-stage breast cancer clusters that could not be explained. The results also confirmed our expectation that a high screening level would be associated with a high incidence rate of early-stage disease, which in turn would reduce late-stage incidence rates.