The autologistic model is a flexible model for predicting presence or absence of disease in an agricultural field, based on soil variables, while taking spatial correlation into account. In the autologistic model, the log odds of disease in a particular quadrat are modeled as a linear combination of disease presence or absence in neighboring quadrats and the soil variables. Neighboring quadrats can be defined as adjacent quadrats within a row, quadrats in adjacent rows, quadrats two rows away, and so forth. The regression coefficients give estimates of the increase in odds of disease if neighbors within a row or in adjacent rows show disease symptoms; thus, we obtain information about the degree of spread in different directions. The coefficients for the soil variables give estimates of the increase in odds of disease as soil water content or pathogen population density increase. In this problem, the soil variables may also be highly correlated over quadrats, and disease incidence in within-row neighbors may be highly correlated with disease incidence in adjacent-row neighbors. This collinearity makes estimation and interpretation of the parameters of the autologistic model more difficult. We discuss fitting the autologistic model and tools for evaluating the aptness of the model.

Key Words
Binary response variable; Disease incidence; Markov random field; Pseudolikelihood estimation; Spatial correlation.

Marcia L. Gumpertz is Associate Professor, Department of Statistics, and Jean B. Ristaino is Associate Professor, Department of Plant Pathology, North Carolina State University, Raleigh, NC 27695-8203 and 27695-7616, respectively. Jonathan M. Graham is Assistant Professor, Department of Mathematical Sciences, University of Montana, Missoula, MT 59812.