Document Type

Working Paper

Publication Date


Document Number



Spatial regressions have been widely used, but their use with the permutation tests of residuals either in linear or loglinear models is rarely seen. In the present study, we have linked the Cliff-Ord permutation test of Moran’s I on linear regression errors to loglinear regression residuals under asymptotic normality. We devised both Pearson residual Moran’s IP R and deviance residual Moran’s IDR tests and applied them to a set of log-rate models for early stage and late-stage breast cancer together with socioeconomic and access-to-care data in Kentucky. The results showed that socioeconomic and access-to-care variables were sufficient to account for spatial clustering of early stage breast carcinomas with breast cancer screening and number of primary care providers being more persistent than county median family income. For late-stage carcinomas, in contrast, the late-stage incidence rate was negatively associated with breast cancer screening level. This result confirmed our expectation: a high screening level is associated with high incidence rate of early stage disease, which in turn reduces late-stage incidence rates. In addition, we located four late-stage breast cancer clusters that cannot be explained by socioeconomic and access-to-care variables.