Class‐specific tests of spatial segregation based on nearest neighbor contingency tables

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 fromamong other patterns -random labeling (RL) or complete spatial randomness (CSR) of points from two or more classes (which is called 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 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 extensive 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. For illustrative purposes, we use three example data sets. We also provide guidelines for using these tests.

Segregation indices for disease clustering

“…That is, the probability that this individual having a NN from another class is higher than the relative frequency of this other class. See Ceyhan (2010) for a more detailed discussion of the null and alternative patterns.…”

“…We provide a brief description of NNCTs below, for a more detailed description see, e.g., Ceyhan (2010). In a sample of size n, there are n NN pairs, and each NN pair consists of the point labeled as "base" point and its "NN" point.…”

“…Some of the tests like Moran's I and Whittemore's tests are shown to perform poorly in detection of some kind of clustering (Song and Kulldorff (2003)) and most of the tests require Monte Carlo simulation or randomization methods to attach significance to their results. Hence we only consider cell-specific and overall NNCT-tests due to Dixon (1994) and Ceyhan (2010) and Cuzick-Edward's k-NN tests and their combined versions (Cuzick and Edwards (1990)), and compare the segregation indices with these tests in an extensive Monte Carlo simulation study in terms of size and power performance.…”

“…Dixon's cell-specific and overall tests (Dixon (1994)) and type III cell-specific and overall tests (Ceyhan (2010)) are based on NNCTs. These tests are discussed in detail in Ceyhan (2012); here we only provide a brief description for completeness.…”

“…Furthermore, in literature, there are spatial clustering tests based on nearest neighbor contingency tables (NNCTs) due to Pielou (1961) and Dixon (1994) in a two-class setting, and due to Dixon (2002a) in a multi-class setting. Various new segregation tests were also proposed by Ceyhan (2010) based on NNCTs. These tests comprise of an overall test, a compound measure of deviation from the null pattern, and cell-specific tests for pairwise comparisons after a significant overall test.…”