A contingency table approach based on nearest neighbour relations for testing self and mixed correspondence

Nearest neighbour methods are employed for drawing inferences about spatial patterns of points from two or more classes. We introduce a new pattern called correspondence which is motivated by (spatial) niche/habitat specificity and segregation, and define an associated contingency table called a correspondence contingency table, and examine the relation of correspondence with the motivating patterns (namely, segregation and niche specificity). We propose tests based on the correspondence contingency table for testing self and mixed correspondence and determine the appropriate null hypotheses and the underlying conditions appropriate for these tests. We compare finite sample performance of the tests in terms of empirical size and power by extensive Monte Carlo simulations and illustrate the methods on two artificial data sets and one real-life ecological data set.Peer Reviewe

Nearest Neighbor Methods for Testing Reflexivity and Species-Correspondence

Nearest neighbor (NN) methods are employed for drawing inferences about spatial patterns of points from two or more classes. We consider Pielou's test of niche specificity which is defined using a contingency table based on the NN relationships between the data points. We demonstrate that Pielou's contingency table for niche specificity is actually more appropriate for testing reflexivity in NN structure, hence we call this table as NN reflexivity contingency table (NN-RCT) henceforth. We also derive an asymptotic approximation for the distribution of the entries of the NN-RCT and consider variants of Fisher's exact test on it. Moreover, we introduce a new test of class- or species-correspondence inspired by spatial niche/habitat specificity and the associated contingency table called species-correspondence contingency table (SCCT). We also determine the appropriate null hypotheses and the underlying conditions appropriate for these tests. We investigate the finite sample performance of the tests in terms of empirical size and power by extensive Monte Carlo simulations and the methods are illustrated on a real-life ecological data set.Comment: 23 pages, 1 figur

Overall and pairwise segregation tests based on nearest neighbor contingency tables

Multivariate interaction between two or more classes (or species) has important consequences in many fields and may cause multivariate clustering patterns such as spatial 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). New versions of overall and cell-specific tests based on NNCTs (i.e.,NNCT-tests) are introduced and compared with Dixon's overall and cell-specific tests and various other spatial clustering methods. Overall segregation 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. The distributional properties of these tests are analyzed and finite sample performance of the tests are assessed by an extensive Monte Carlo simulation study. Furthermore, it is shown that the new NNCT-tests have better performance in terms of Type I error and power estimates. The methods are also applied on two real life data sets for illustrative purposes.

A contingency table approach based on nearest neighbour relations for testing self and mixed correspondence

Nearest neighbour methods are employed for drawing inferences about spatial patterns of points from two or more classes. We introduce a new pattern called correspondence which is motivated by (spatial) niche/habitat specificity and segregation, and define an associated contingency table called a correspondence contingency table, and examine the relation of correspondence with the motivating patterns (namely, segregation and niche specificity). We propose tests based on the correspondence contingency table for testing self and mixed correspondence and determine the appropriate null hypotheses and the underlying conditions appropriate for these tests. We compare finite sample performance of the tests in terms of empirical size and power by extensive Monte Carlo simulations and illustrate the methods on two artificial data sets and one real-life ecological data set