A generalized randomization approach to local measures of spatial association

Abstract

This article establishes a unified randomization significance testing framework upon which various local measures of spatial association are commonly predicated. The generalized randomization approach presented is composed of two testing procedures, the extended Mantel test and the generalized vector randomization test. These two procedures employ different randomization assumptions, namely total and conditional randomization, according to the way in which they incorporate local measures. By properly specifying necessary matrices and vectors for a particular local measure of spatial association under a particular randomization assumption, the generalized randomization approach as a whole yields a reliable set of equations for expected values and variances, which then is confirmed by a Monte Carlo simulation utilizing random permutations.