Modeling multiplicative interaction effects in Gaussian structured additive regression models

Gaussian Structured Additive Regression provides a flexible framework for additive decomposition of the expected value with nonlinear covariate effects and time trends, unit- or cluster-specific heterogeneity, spatial heterogeneity, and complex interactions between covariates of different types. Within this framework, we present a simultaneous estimation approach for highly complex multiplicative interaction effects. In particular, a possibly nonlinear function f(z) of a covariate z may be scaled by a multiplicative effect of the form exp(˜η), where ˜η is another possibly structured additive predictor. Inference is fully Bayesian and based on highly efficient Markov Chain Monte Carlo (MCMC) algorithms. We investigate the statistical properties of our approach in extensive simulation experiments. Furthermore, we apply and illustrate the methodology to an analysis of asking prices for 200000 dwellings in Germany.