Spatial Data Analysis of Regional Counts

Abstract Counts data from spatially continguous regions offer a challenge to the statistician both from the data analytic and the statistical modeling point of view. Important applications include epidemiological studies (e. g., cancer mortality over the counties of the USA) and Census surveys (e. g., undercount over the Census blocks of an urban area). It has long been recognized by time‐series analysts that data close together in time usually exhibit higher dependence than those far apart. Time‐series data analysis relies on methods of data transformation, detrending, and autocorrelation plotting. It is our intention in this article to generalize this approach to a spatial setting. To do this we consider a small spatial data set of 100 observations. Through the use of a square‐root transformation, a weighted median polish and a variogram analysis of the median‐polish residuals, we represent the transformed data as a trend plus stationary error. Thus we show how standard data‐analytic techniques can be modified both to mitigate and to exploit the spatial relationships.