Hierarchical second-order analysis of replicated spatial point patterns with non-spatial covariates

In this paper we propose a method for incorporating the effect of non-spatial covariates into the spatial second-order analysis of replicated point patterns. The variance stabilizing transformation of Ripley’s KK function is used to summarize the spatial arrangement of points, and the relationship between this summary function and covariates is modelled by hierarchical Gaussian process regression. In particular, we investigate how disease status and some other covariates affect the level and scale of clustering of epidermal nerve fibres. The data are point patterns with replicates extracted from skin blister samples taken from 47 subjects.