The theory of generalized linear models and quasi-likelihood provides a flexible framework for analyzing non-normal data. In this article, we demonstrate how this theory can be extended to include the analysis of discrete and categorical spatial data. This theory can be used to estimate parameters and test treatment effects in a designed experiment involving discrete or categorical spatial responses. It also provides a flexible method for spatial prediction using non-normal data and includes universal kriging and indicator kriging as special cases. Examples are given, including one where the focus is on comparing treatments in a designed experiment in which spatial correlation is present, and two others where spatial prediction or mapping is the desired goal. The methods presented here provide an additional set of tools for the analysis of spatial data that will be useful to researchers in a variety of disciplines, including hydrology, soil science, entomology, agronomy, and ecology.

Key Words
Generalized Linear Models; Geostatistics; Kriging; Quasi-likelihood; Spatial Modeling; Spatial Prediction.

C. A. Gotway is Mathematical Statistican, Centers for Disease Control and Prevention, MS F62, 1600 Clifton Road NE, Atlanta, GA 30333. W. W. Stroup is Professor, Department of Biometry, University of Nebraska, Lincoln, NE 68583-0712.