[Paper Review] Overall and Pairwise Segregation Tests Based on Nearest Neighbor Contingency Tables

Elvan Ceyhan|ArXiv.org|May 12, 2008

Spatial and Panel Data Analysis1 references4 citations

TL;DR

This paper introduces new overall and cell-specific segregation tests based on nearest neighbor contingency tables (NNCTs) to detect small-scale spatial clustering patterns such as segregation or association among multiple classes. The proposed tests outperform Dixon’s NNCT-tests in terms of Type I error control and statistical power, particularly under segregation, and provide more nuanced pairwise interaction insights than Ripley’s K/L-functions at small scales.

ABSTRACT

Multivariate interaction between two or more classes (or species) has important consequences in many fields and causes multivariate clustering patterns such as segregation or association. The spatial segregation occurs when members of a class tend to be found near members of the same class (i.e., near conspecifics) while spatial association occurs when members of a class tend to be found near members of the other class or classes. These patterns can be studied 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 introduce new versions of overall and cell-specific tests based on NNCTs (i.e., NNCT-tests) and compare them with Dixon's overall and cell-specific tests. These NNCT-tests provide information on the spatial interaction between the classes at small scales (i.e., around the average NN distances between the points). Overall tests are used to detect any deviation from the null case, while the cell-specific tests are post hoc pairwise spatial interaction tests that are applied when the overall test yields a significant result. We analyze the distributional properties of these tests; assess the finite sample performance of the tests by an extensive Monte Carlo simulation study. Furthermore, we show that the new NNCT-tests have better performance in terms of Type I error and power. We also illustrate these NNCT-tests on two real life data sets.

Motivation & Objective

• To develop improved overall and pairwise segregation tests using nearest neighbor contingency tables (NNCTs) for multivariate spatial point patterns.
• To address limitations in existing NNCT-tests, particularly in Type I error and power, especially under segregation.
• To compare the new NNCT-tests with Ripley’s K/L-functions and other second-order methods, clarifying their complementary roles.
• To provide practical guidelines for selecting appropriate tests based on the null hypothesis (CSR independence vs. random labeling) and scale of interest.

Proposed method

• Propose new overall and cell-specific test statistics based on NNCTs, using chi-square or likelihood ratio test frameworks.
• Construct NNCTs from nearest neighbor frequencies between classes to capture local spatial interactions.
• Perform extensive Monte Carlo simulations to evaluate finite-sample performance of the new tests under various null and alternative patterns.
• Compare the new tests with Dixon’s NNCT-tests and Ripley’s K/L-functions in terms of empirical size, power, and sensitivity to spatial clustering patterns.
• Apply the tests to two real datasets to demonstrate practical utility and interpretability.
• Use the average nearest neighbor distance as a reference scale to focus on small-scale interactions.

Experimental results

Research questions

• RQ1 How do the new NNCT-based overall and cell-specific tests compare to Dixon’s tests in terms of Type I error and power under complete spatial randomness and segregation?
• RQ2 Do the new NNCT-tests detect small-scale spatial interactions more effectively than Ripley’s K/L-functions or pair correlation functions?
• RQ3 Can the new cell-specific tests distinguish between asymmetric spatial interactions (e.g., class A prefers class B, but not vice versa), unlike symmetric second-order methods?
• RQ4 Under what conditions do the new NNCT-tests maintain better empirical size and power than existing methods in finite samples?
• RQ5 How do the results of NNCT-tests compare with those of Ripley’s L-function when restricted to distances near the average nearest neighbor distance?

Key findings

• The new overall NNCT-test exhibits higher statistical power than Dixon’s overall test under segregation, particularly in small to moderate sample sizes.
• The new cell-specific tests show improved empirical size and power compared to Dixon’s cell-specific tests, especially in detecting asymmetric spatial interactions.
• The NNCT-tests are more sensitive to small-scale clustering patterns (around the mean nearest neighbor distance) than Ripley’s K/L-functions, which are more suitable for larger-scale analysis.
• The NNCT-tests provide class-specific interaction insights—such as which class drives segregation—unlike symmetric bivariate K-functions or pair correlation functions.
• Under CSR independence, the new NNCT-tests maintain better control of Type I error rates than Dixon’s tests, especially in multi-class settings.
• The proposed tests are recommended for small-scale spatial interaction analysis when CSR independence is the null, while Diggle’s D-function is preferred for higher-scale analysis under random labeling.