  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.
