Spatial cluster detection of regression coefficients in a mixed‐effects model

Identifying spatial clusters of different regression coefficients is a useful tool for discerning the distinctive relationship between a response and covariates in space. Most of the existing cluster detection methods aim to identify the spatial similarity in responses, and the standard cluster detection algorithm assumes independent spatial units. However, the response variables are spatially correlated in many environmental applications. We propose a mixed‐effects model for spatial cluster detection that takes spatial correlation into account. Compared to a fixed‐effects model, the introduced random effects explain extra variability among the spatial responses beyond the cluster effect, thus reducing the false positive rate. The developed method exploits a sequential searching scheme and is able to identify multiple potentially overlapping clusters. We use simulation studies to evaluate the performance of our proposed method in terms of the true and false positive rates of a known cluster and the identification of multiple known clusters. We apply our proposed methodology to particulate matter (PM2.5) concentration data from the Northeastern United States in order to study the weather effect on PM2.5 and to investigate the association between the simulations from a numerical model and the satellite‐derived aerosol optical depth data. We find geographical hot spots that show distinct features, comparing to the background.