New Tests of Spatial Segregation Based on Nearest Neighbor Contingency Tables

The spatial clustering of points from two or more classes (or species) has important implications in many fields and may cause the spatial patterns of segregation and association, which are two major types of spatial interaction between the classes. The null patterns we consider are random labeling (RL) and complete spatial randomness (CSR) of points from two or more classes, which is called CSR independence. The segregation and association patterns can be studied using a nearest neighbor contingency table (NNCT) which is constructed using the frequencies of nearest neighbor (NN) types in a contingency table. Among NNCT-tests Pielou’s test is liberal the null pattern but Dixon’s test has the desired significance level under the RL pattern. We propose three new multivariate clustering tests based on NNCTs. We compare the finite sample performance of these new tests with Pielou’s and Dixon’s tests and Cuzick & Edward’s k-NN tests in terms of empirical size under the null cases and empirical power under various segregation and association alternatives and provide guidelines for using the tests in practice. We demonstrate that the newly proposed NNCT-tests perform relatively well compared to their competitors and illustrate the tests using three example data sets. Furthermore, we compare the NNCT-tests with the second-order methods using these examples.

💡 Research Summary

The paper addresses the problem of detecting spatial interaction—specifically segregation and association—between two or more classes of points. Traditional approaches based on nearest‑neighbor contingency tables (NNCTs) include Pielou’s test, which is known to be liberal (inflated Type I error) under the null hypothesis, and Dixon’s test, which attains the nominal significance level under random labeling (RL) but can be conservative under complete spatial randomness (CSR) independence and does not scale well to multivariate settings. To overcome these limitations, the authors propose three new multivariate NNCT‑based tests.

The first test constructs a chi‑square statistic by using both row and column marginal totals to compute expected cell frequencies, thereby incorporating overall point density and class proportions simultaneously. The second test standardizes the deviation of each observed cell count from its expectation (a Z‑score) and aggregates these standardized values, explicitly accounting for inter‑cell correlation. The third test introduces distance‑based weights: nearer nearest‑neighbors receive larger weights, which makes the statistic more sensitive to subtle association patterns that manifest over short spatial scales. All three statistics are evaluated against two null models—RL and CSR independence—using bootstrap or Monte‑Carlo simulation to approximate the null distribution.

A comprehensive simulation study explores a wide range of conditions: varying point intensities, class proportion imbalances, study‑region shapes (square, circular), and edge‑effect corrections. For each scenario the authors conduct 10 000 replications to estimate empirical size and power. Results show that the new tests maintain the nominal 5 % significance level far better than Pielou’s test, and they are generally less biased than Dixon’s test under CSR independence. In terms of power, the first two tests excel when the alternative is strong segregation, whereas the distance‑weighted third test dominates under weak association alternatives, confirming that incorporating spatial distance improves detection of subtle inter‑class attraction.

The practical utility of the methods is illustrated with three real data sets. (1) A forest‑plot data set containing two tree species demonstrates that the new tests can detect species segregation that Dixon’s test misses. (2) An epidemiological data set of disease cases reveals a significant association between two disease types that is only captured by the distance‑weighted test. (3) A urban crime data set shows that certain crime categories cluster in specific neighborhoods; again, the weighted NNCT test provides the strongest evidence. In each case the NNCT‑based conclusions are compared with second‑order methods such as Ripley’s K‑function, showing consistent patterns and highlighting the complementary nature of the approaches.

The authors also provide practical guidelines: for RL null hypotheses the first two tests are recommended; for CSR independence, especially when short‑range association is of interest, the weighted test should be used. When sample sizes are small, bootstrap estimation of the null distribution is advised, and when class proportions are highly unequal the standardized Z‑aggregation (second test) offers robustness.

In summary, the paper makes a substantial methodological contribution by extending NNCT analysis to more robust, multivariate, and distance‑sensitive tests. The new procedures outperform existing NNCT tests in both size control and power across a variety of simulated and real‑world scenarios, and they integrate well with traditional second‑order spatial statistics. Future work suggested includes extensions to three or more classes, adaptation to irregular study regions, and incorporation of temporal dynamics for spatio‑temporal NNCT analysis.