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 (IPR) and deviance residuals (IDR) 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 IPR and IDR are effective to account for heterogeneous population sizes. The tests based on IPR and IDR 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.