Geographical Ratings with Spatial Random Effects in a Two-Part Model

Rating areas are commonly used to capture unexplained geographical variability of claims in insurance pricing. A new method for defining rating areas is proposed using a two-part generalized geoadditive model that models spatial effects smoothly using Gaussian Markov random fields. The first part handles zero/nonzero expenses in a logistic model; the second handles nonzero expenses (on log-scale) in a linear model. Both models are fit with R package INLA for Bayesian infer-ences. The resulting spatial effects are used to construct more representative ratings. The methodology is illustrated with simulated data based on zipcode areas, but modeled on zipcode- or county-level.