Logistic Regression for Southern Pine Beetle Outbreaks with Spatial and Temporal Autocorrelation

Regional outbreaks of southern pine beetle (Dendroctonus frontalis Zimm.) show marked spatial and temporal patterns. While these patterns are of interest in themselves, we focus on statistical methods for estimating the effects of underlying environmental factors in the presence of spatial and temporal autocorrelation. The most comprehensive available information on outbreaks consists of binary data, specifically, annual presence or absence of outbreak for individual counties within the southern United States. We demonstrate a method for modeling spatially correlated proportions, such as the proportion of years that a county experiences outbreak, based on annual outbreak presence or absence data for counties in three states (NC, SC, and GA) over 31 yr. In this method, the proportion of years in outbreak is predicted using a marginal logistic regression model with spatial autocorrelation among counties, with adjustment of variance terms to account for temporal autocorrelation. This type of model describes the probability of outbreak as a function of explanatory variables such as host availability, physiography, climate, hurricane incidence, and management type. Explicitly including spatial autocorrelation in the model improves estimates of the probability of outbreak for a particular county and of the importance of the various explanatory variables.