Simulation and characterization of multi-class spatial patterns from stochastic point processes of randomness,clustering and regularity

Spatial pattern analysis of data from multiple classes (i.e., multi-class data) has important implications. We investigate the resulting patterns when classes are generated from various spatial point processes. Our null pattern is that the nearest neighbor probabilities being proportional to class frequencies in the multi-class setting. In the two-class case, the deviations are mainly in two opposite directions, namely, segregation and association of the classes. But for three or more classes, the classes might exhibit mixed patterns, in which one pair exhibiting segregation, while another pair exhibiting association or complete spatial randomness independence. To detect deviations from the null case, we employ tests based on nearest neighbor contingency tables (NNCTs), as NNCT methods can provide an omnibus test and post-hoc tests after a significant omnibus test in a multi-class setting. In particular, for analyzing these multi-class patterns (mixed or not), we use an omnibus overall test based on NNCTs. After the overall test, the pairwise interactions are analyzed by the post-hoc cell-specific tests based on NNCTs. We propose various parameterizations of the segregation and association alternatives, list some appealing properties of these patterns, and propose three processes for the two-class association pattern. We also consider various clustering and regularity patterns to determine which one(s) cause segregation from or association with a class from a homogeneous Poisson process and from other processes as well. We perform an extensive Monte Carlo simulation study to investigate the newly proposed association patterns and to understand which stochastic processes might result in segregation or association. The methodology is illustrated on two real life data sets from plant ecology.