Finding upper-level sets in cellular surface data using echelons and saTScan

Across a spectrum of contemporary contexts from public health to landscape ecology and natural resources, there is need for objective determination of elevated occurrence in phenomena such as disease incidence and biodiversity. Occurrences of such phenomena constitute response surfaces, but data regarding the surface is typically acquired in a cellular framework. The cells may comprise a regular grid, or may be of irregular shapes such as counties in which statistics are collected. Echelons are a topologically based approach to systematic determination of spatial structure in a step surface. Spatial scan statistics are a probability-based approach to the same issue when interest lies in a rate variable. Here we examine the use of echelons both separately and in conjunction with the SaTScan implementation of spatial scan statistics for purposes of determination and visualization of upper-level sets. Consideration is given to both conventional geographic space and to the cellular pseudo-space of contingency tables for ordered categorical variables.