Nearest neighbor methods for testing reflexivity

Abstract

Nearest neighbor (NN) methods are widely employed for drawing inferences about spatial point patterns of two or more classes. We introduce a method for testing reflexivity in the NN structure (i.e., NN reflexivity) based on a contingency table which will be called reflexivity contingency table (RCT) henceforth. The RCT is based on the NN relationships among the data points and was used for testing niche specificity in literature, but we demonstrate that it is actually more appropriate for testing the NN reflexivity pattern. We derive the asymptotic distribution of the entries of the RCT under random labeling and introduce tests of reflexivity based on these entries. We also consider Pielou's approach on RCT and show that it is not appropriate for completely mapped spatial data. We determine the appropriate null hypotheses and the underlying conditions/assumptions required for all tests considered. We investigate the finite sample performance of the tests in terms of empirical size and power by extensive Monte Carlo simulations and illustrate the methods on two real-life ecological data sets.