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Abstract:
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Identifying clusters of spatial units in a regression coefficient is a useful tool to discern distinctive relationship between a response and covariates relative to the background. Here, we consider detecting a potential cluster in the regression setting based on hypothesis testing. Most of the existing methods assume independent spatial units. However, in many environmental applications, the response variables are spatially correlated. We propose a mixed effect model for spatial cluster detection, taking spatial correlation into account. Compared to a fixed effect model, the introduced random effect explains the extra variability among the spatial responses beyond the cluster effect, and thus reduces the false discovery rate. The developed method can detect multiple clusters as well with a sequential searching scheme. The performance of our proposed methods is evaluated by simulation studies in terms of true and false positive rates of a potential cluster. For applications, our methodology is applied to particular matter (PM2.5) concentration data in the U.S. with relevant weather variables and the identified spatial clusters are useful in facilitating air quality management.
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