Abstract

Semiparametric regression models offer considerable flexibility for disease mapping due to their ability to combine effects as diverse as nonlinear effects of continuous covariates, spatial effects, random effects, or varying coefficients in an additive regression predictor. In the context of disease mapping, spatio-temporal extensions that allow for investigating spatial and temporal trends are particularly attractive. In this talk, we discuss a generic concept for defining interaction effects in semiparametric regression models based on tensor products of main effects. These interactions can be anisotropic, i.e. different amounts of smoothness will be associated with the interacting covariates (space and time in the spatio-temporal setup). We study identifiability and the decomposition of interactions into main effects and pure interaction effects (similar as in a smoothing spline analysis of variance) to facilitate a modular model building process. The decomposition is based on orthogonality in function spaces which allows for considerable flexibility in setting up the effect decomposition. Inference is based on Markov chain Monte Carlo simulations with iteratively weighted least squares proposals under constraints to ensure identifiability and effect decomposition. The performance of the proposed methodology is demonstrated along complex spatio-temporal datasets where, beyond the mean, other distributional aspects of the response are of particular relevance.