A Composite Likelihood Approach to Binary Spatial Data

Abstract

Conventional geostatistics addresses the problem of estimation and prediction for continuous observations. But in many practical applications in public health, environmental remediation, or ecological research the most commonly available data are in the form of counts (e.g., number of cases) or indicator variables denoting above or below threshold values. Also, in many situations it is less expensive to obtain an imprecise categorical observation than to obtain precise measurements of the variable of interest (such as a contaminant). This article proposes a computationally simple method for estimation and prediction using binary or indicator data in space. The proposed method is based on pairwise likelihood contributions, and the large-sample properties of the estimators are obtained in a straightforward manner. We illustrate the methodology through application to indicator data related to gypsy moth defoliation in Massachusetts.