Directional clustering tests based on nearest neighbour contingency tables

Spatial interaction between two or more classes or species has important implications in various fields, and might cause multivariate patterns such as segregation or association. Segregation occurs when members of a class or species are more likely to be found near members of the same class or conspecifics; association occurs when members of a class or species are more likely to be found near members of another class or species. The null patterns considered are random labelling and complete spatial randomness (CSR) of points from two or more classes, which is henceforth called CSR independence. The clustering tests based on nearest neighbour contingency tables (NNCTs) that are in use in the literature are two-sided tests. In this article, we consider the directional (i.e. one-sided) versions of the cell-specific NNCT tests and introduce new directional NNCT tests for the two-class case. We analyse the distributional properties and compare the empirical significant levels and empirical power estimates of the tests using extensive Monte Carlo simulations. We demonstrate that the new directional tests have comparable performance with the currently available NNCT tests in terms of empirical size and power. We use an ecological data set for illustrative purposes and provide guidelines for using these NNCT tests.