[Paper Review] New Cell-Specific and Overall Tests of Spatial Interaction Based on Nearest Neighbor Contingency Tables

Elvan Ceyhan|arXiv (Cornell University)|Jun 8, 2012

Spatial and Panel Data Analysis20 references3 citations

TL;DR

This paper introduces new cell-specific and overall statistical tests for spatial interaction—segregation and association—using nearest neighbor contingency tables (NNCTs). The tests are based on asymptotic distributions: cell-specific tests are asymptotically normal, while overall tests follow a chi-square distribution. The key contribution is improved power and robustness, especially under unbalanced class sizes, with type I and III tests outperforming existing methods under segregation, and Dixon’s test excelling under association.

ABSTRACT

Spatial interaction patterns such as segregation and association can be tested using nearest neighbor contingency tables (NNCTs). We introduce new cell-specific (or pairwise) and overall segregation tests and determine their asymptotic distributions. In particular, we demonstrate that cell-specific tests enjoy asymptotic normality, while overall tests have chi-square distributions asymptotically. We also perform an extensive Monte Carlo simulation study to compare the finite sample performance of the tests in terms of empirical size and power. In addition to the cell-specific tests as post-hoc tests for overall tests, we discuss one-class-versus-rest type of NNCT-tests after an overall test yields significant interaction. We also introduce the concepts of total, strong, and partial segregation/association to label levels of these patterns. We compare these new tests with the existing NNCT-tests in literature with simulations as well and illustrate the NNCT-tests on an ecological data set.

Motivation & Objective

• To develop new cell-specific and overall tests for spatial interaction using nearest neighbor contingency tables (NNCTs).
• To establish the asymptotic distributions of these tests: normal for cell-specific, chi-square for overall.
• To evaluate finite-sample performance via Monte Carlo simulations in terms of empirical size and power.
• To provide post-hoc testing strategies—cell-specific and one-class-vs-rest—after significant overall tests.
• To recommend optimal tests based on class size balance and interaction type (segregation vs. association).

Proposed method

• Proposes new cell-specific tests based on NNCT cell probabilities, with asymptotic normality proven under the null.
• Develops overall tests by combining cell-specific test statistics, with asymptotic chi-square distribution.
• Uses Monte Carlo simulations to assess empirical size and power under various class size combinations and interaction patterns.
• Introduces one-class-vs-rest NNCT-tests as an alternative post-hoc approach to detect interactions between one class and all others.
• Applies the tests to a real ecological dataset to demonstrate practical utility.
• Compares the new tests with existing NNCT-tests (e.g., Dixon’s) in terms of size and power performance.

Experimental results

Research questions

• RQ1 How do the new cell-specific and overall NNCT-tests perform in terms of empirical size and power compared to existing methods?
• RQ2 Which test type (type I, III, or Dixon’s) is most robust to differences in relative class abundances?
• RQ3 Under what conditions do the new tests outperform existing NNCT-tests in detecting segregation or association?
• RQ4 How effective are the one-class-vs-rest NNCT-tests as post-hoc tools after a significant overall test?
• RQ5 What are the asymptotic distributions of the proposed cell-specific and overall test statistics?

Key findings

• Type I and III cell-specific tests exhibit higher empirical power than existing methods under segregation, especially when the smaller class is involved.
• Under association, types I and III cell-specific tests outperform others when the smaller class is in the off-diagonal cell, while Dixon’s tests are superior when the larger class is in the off-diagonal cell.
• For overall tests, type I and III overall tests are recommended for segregation, while Dixon’s overall test has the highest power for association.
• The one-class-vs-rest type tests show similar empirical size performance across all methods but are more robust to class size imbalances when using type I and III tests.
• The cell-specific tests are asymptotically normal, and overall tests are asymptotically chi-square distributed with appropriate degrees of freedom.
• The NNCT-tests provide complementary information to pair correlation and K-functions, particularly by capturing multi-class interactions at the mean nearest-neighbor distance.