Directional Clustering Tests Based on Nearest Neighbor Contingency Tables

TL;DR

This paper introduces new directional clustering tests based on nearest neighbor contingency tables to better detect segregation or association patterns in spatial data, with extensive simulations and practical examples demonstrating their effectiveness.

Contribution

The paper develops and evaluates new one-sided NNCT-based tests for spatial interaction, enhancing the ability to detect specific clustering patterns.

Findings

New directional NNCT-tests perform comparably to existing tests in size and power.

Simulations show the tests effectively distinguish segregation and association.

Guidelines provided for practical application of the tests.

Abstract

Spatial interaction between two or more classes or species has important implications in various fields and causes multivariate patterns such as segregation or association. Segregation occurs when members of a class or species are more likely to be found near members of the same class or conspecifics; while association occurs when members of a class or species are more likely to be found near members of another class or species. The null patterns considered are random labeling (RL) and complete spatial randomness (CSR) of points from two or more classes, which is called \emph{CSR independence}, henceforth. The clustering tests based on nearest neighbor contingency tables (NNCTs) that are in use in literature are two-sided tests. In this article, we consider the directional (i.e., one-sided) versions of the cell-specific NNCT-tests and introduce new directional NNCT-tests for the two-class case. We analyze the distributional properties; compare the empirical significant levels and empirical power estimates of the tests using extensive Monte Carlo simulations. We demonstrate that the new directional tests have comparable performance with the currently available NNCT-tests in terms of empirical size and power. We use four example data sets for illustrative purposes and provide guidelines for using these NNCT-tests.