QR-Adjustment for Clustering Tests Based on Nearest Neighbor Contingency Tables

Details QR-Adjustment for Clustering Tests Based on Nearest Neighbor Contingency Tables QR-Adjustment for Clustering Tests Based on Nearest Neighbor Contingency Tables

2008-07-26

arxiv.org/abs/0807.4231v1

Statistics

Methodology

Scientific paper

The spatial interaction between two or more classes of points may cause spatial clustering patterns such as segregation or association, which can be tested using a nearest neighbor contingency table (NNCT). A NNCT is constructed using the frequencies of class types of points in nearest neighbor (NN) pairs. For the NNCT-tests, the null pattern is either complete spatial randomness (CSR) of the points from two or more classes (called CSR independence) or random labeling (RL). The distributions of the NNCT-test statistics depend on the number of reflexive NNs (denoted by $R$) and the number of shared NNs (denoted by $Q$), both of which depend on the allocation of the points. Hence $Q$ and $R$ are fixed quantities under RL, but random variables under CSR independence. Using their observed values in NNCT analysis makes the distributions of the NNCT-test statistics conditional on $Q$ and $R$ under CSR independence. In this article, I use the empirically estimated expected values of $Q$ and $R$ under CSR independence pattern to remove the conditioning of NNCT-tests (such a correction is called the \emph{QR-adjustment}, henceforth). I present a Monte Carlo simulation study to compare the conditional NNCT-tests and QR-adjusted tests under CSR independence and segregation and association alternatives. I demonstrate that QR-adjustment does not significantly improve the empirical size estimates under CSR independence and power estimates under segregation or association alternatives. For illustrative purposes, I apply the conditional and empirically corrected tests on two example data sets.

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