Accurately selecting and estimating smooth functional effects in additive models with potentially many functions is a challenging task. We introduce a novel Demmler-Reinsch basis expansion to model the functional effects that allows us to orthogonally decompose an effect into its linear and nonlinear parts. We show that our representation allows to consistently estimate both parts as opposed to commonly employed mixed model representations. Equipping the reparameterized regression coefficients with normal beta prime spike and slab priors allows us to 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. We establish an efficient posterior estimation scheme and illustrate our approach along effect selection on the hazard rate of a time-to-event response in the geoadditive Cox regression model in simulations and data on survival with leukemia.

翻译：在包含多个函数的加性模型中，准确选择并估计光滑函数效应是一项具有挑战性的任务。我们引入了一种新颖的Demmler-Reinsch基展开来对函数效应进行建模，该展开允许我们将一个效应正交分解为线性部分和非线性部分。我们证明，与常用的混合模型表示相比，我们的表示法能够一致地估计这两部分。将重新参数化的回归系数配备正态贝塔先验的尖峰-平板先验，使我们能够判断一个连续协变量具有线性效应、非线性效应还是完全没有效应。我们为该先验提供了新的理论结果，并对其相较于尖峰-平板组套索方法在马尔可夫链蒙特卡洛混合性能上的优越性给出了令人信服的解释。我们建立了一种高效的后验估计方案，并通过模拟实验及白血病生存数据，在地理加性Cox回归模型中，针对时间-事件响应风险率的效应选择验证了我们的方法。