Inhomogeneous log-Gaussian Cox processes with piecewise constant covariates: a case study in modeling of COVID-19 transmission risk in East Java

The inhomogeneous Log-Gaussian Cox Process (LGCP) defines a flexible point process model for the analysis of spatial point patterns featuring inhomogeneity/spatial trend and aggregation patterns. To fit an LGCP model to spatial point pattern data and study the spatial trend, one could link the intensity function with continuous spatial covariates. Although non-continuous covariates are becoming more common in practice, the existing estimation methods so far only cover covariates in continuous form. As a consequence, to implement such methods, the non-continuous covariates are replaced by the continuous ones by applying some transformation techniques, which are many times problematic. In this paper, we develop a technique for inhomogeneous LGCP involving non-continuous covariates, termed piecewise constant covariates. The method does not require covariates transformation and likelihood approximation, resulting in an estimation technique equivalent to the one for generalized linear models. We apply our method for modeling COVID-19 transmission risk in East Java, Indonesia, which involves five piecewise constant covariates representing population density and sources of crowd. We outline that population density and industry density are significant covariates affecting the COVID-19 transmission risk in East Java.