A Two-Stage Cox Process Model with Spatial and Nonspatial Covariates

TL;DR

This paper introduces a two-stage log Gaussian Cox process model that integrates spatial and nonspatial covariates to analyze complex marked point process data, demonstrated through police use of force and forest fire studies.

Contribution

The paper develops a flexible, interpretable two-stage Cox process model capable of incorporating diverse spatial and nonspatial covariates, addressing limitations of existing methods.

Findings

Model effectively incorporates multiple covariate types.

Allows analysis of community and event-level factors.

Demonstrates utility with simulated and real data examples.

Abstract

Rich new marked point process data allow researchers to consider disparate problems such as the factors affecting the location and type of police use of force incidents, and the characteristics that impact the location and size of forest fires. We develop a two-stage log Gaussian Cox process that models these data in terms of both spatial (community-level) and nonspatial (individual or event-level) characteristics; both types of covariates are present in the examples we consider and are not easy to incorporate via existing methods. Via simulated and real data examples we find that our model is easy to interpret and flexible, accommodating multiple types of marks and multiple types of spatial covariates. In the first example we consider, our approach allows us to study the impact of community-level socioeconomic features such as unemployment as well as event-level features such as officer tenure on force used by police, illustrated through simulated examples. In our second example we consider factors that impact the locations and severity of forest fires from the Castilla-La Mancha region of Spain between 2004-2007.