Consistent Effect Estimation in Generalised Sparse Partially Linear Additive Models

Oregon Convention Center 

Accurately selecting and estimating smooth functional effects in additive models with potentially many functions is a challenging task, especially if the components are decomposed into linear and nonlinear effects. We provide a rigorous definition of the true linear and nonlinear effects of an additive component using projections and introduce a new construction of the Demmler-Reinsch basis for penalised splines. We prove that our representation allows to consistently estimate the true effects as opposed to the commonly employed mixed model representations. Equipping the reparameterised regression coefficients with normal beta prime spike and slab priors allows us to automatically determine whether a continuous covariate has a linear, a nonlinear or no effect at all. We provide new theoretical results for the prior and a compelling explanation for its superior Markov chain Monte Carlo mixing performance compared to the spike-and-slab group lasso prior. Finally, we illustrate the developed methodology along effect selection on the hazard rate of a time-to-event response in the additive Cox regression model in simulations and on leukemia survival data.