Nonparametric testing of the covariate significance for spatial point patterns under the presence of nuisance covariates

TL;DR

This paper introduces a nonparametric testing method for assessing the significance of covariates in spatial point patterns, effectively handling nuisance covariates and outperforming parametric tests when models are misspecified.

Contribution

The authors develop a fully nonparametric approach using Monte Carlo testing and novel residual measures to evaluate covariate significance in spatial point processes.

Findings

Tests match nominal significance levels

Higher power when parametric models are incorrect

Comparable power to parametric tests when models are correct

Abstract

Determining the relevant spatial covariates is one of the most important problems in the analysis of point patterns. Parametric methods may lead to incorrect conclusions, especially when the model of interactions between points is wrong. Therefore, we propose a fully nonparametric approach to testing significance of a covariate, taking into account the possible effects of nuisance covariates. Our tests match the nominal significance level, and their powers are comparable with the powers of parametric tests in cases where both the model for intensity function and the model for interactions are correct. When the parametric model for the intensity function is wrong, our tests achieve higher powers. The proposed methods rely on Monte Carlo testing and take advantage of the newly introduced covariate-weighted residual measure. We also define a correlation coefficient between a point process and a covariate and a partial correlation coefficient quantifying the dependence between a point process and a covariate of interest while removing the influence of nuisance covariates.