Class-Specific Tests of Spatial Segregation Based on Nearest Neighbor Contingency Tables

TL;DR

This paper introduces and evaluates new class-specific statistical tests for detecting spatial segregation or association between classes using nearest neighbor contingency tables, improving understanding of spatial patterns in multivariate data.

Contribution

The paper develops a new class-specific test based on Dixon's chi-square statistic, offering a novel decomposition and comparison with existing tests for spatial interaction analysis.

Findings

New class-specific test performs comparably to existing tests in Type I error and power.

The tests provide different insights into spatial interaction patterns.

Guidelines for applying these tests are provided.

Abstract

The spatial interaction between two or more classes (or species) has important consequences in many fields and might cause multivariate clustering patterns such as segregation or association. The spatial pattern of segregation occurs when members of a class tend to be found near members of the same class (i.e., conspecifics), while association occurs when members of a class tend to be found near members of the other class or classes. These patterns can be tested using a nearest neighbor contingency table (NNCT). The null hypothesis is randomness in the nearest neighbor (NN) structure, which may result from -- among other patterns -- random labeling (RL) or complete spatial randomness (CSR) of points from two or more classes (which is called the CSR independence, henceforth). In this article, we consider Dixon's class-specific tests of segregation and introduce a new class-specific test, which is a new decomposition of Dixon's overall chi-square segregation statistic. We demonstrate that the tests we consider provide information on different aspects of the spatial interaction between the classes and they are conditional under the CSR independence pattern, but not under the RL pattern. We analyze the distributional properties and prove the consistency of these tests; compare the empirical significant levels (Type I error rates) and empirical power estimates of the tests using Monte Carlo simulations. We demonstrate that the new class-specific tests also have comparable performance with the currently available tests based on NNCTs in terms of Type I error and power estimates. For illustrative purposes, we use three example data sets. We also provide guidelines for using these tests.