Bark Beetle Infestation - Preisler - Equation 1

Let Y be a random variable such that Yi=1 if an infestation is present in a km2 grid at location (utmxi,utmyi) and year yri and Yi=0 otherwise. The random variable Y is assumed to follow a Bernoulli distribution with probability of response and where the matrix X of predictors includes history of fire and insect infestation in previous years and within 1 km of infestation. The functions gk(Xk) in equation [1] are transformations of the variable Xk using linear-basis splines (Hastie and others 2001). For the spatial component, g(utmx utmy), we utilized the 2-dimensional version of the basis function, specifically, the thin plate spline function.