Abstract–We provide a flexible framework for selecting among a class of additive partial linear models that allows both linear and nonlinear additive components. In practice, it is challenging to determine which additive components should be excluded from the model while simultaneously determining whether nonzero additive components should be represented as linear or nonlinear components in the final model. In this article, we propose a Bayesian model selection method that is facilitated by a carefully specified class of models, including the choice of a prior distribution and the nonparametric model used for the nonlinear additive components. We employ a series of latent variables that determine the effect of each variable among the three possibilities (no effect, linear effect, and nonlinear effect) and that simultaneously determine the knots of each spline for a suitable penalization of smooth functions. The use of a pseudo-prior distribution along with a collapsing scheme enables us to deploy well-behaved Markov chain Monte Carlo samplers, both for model selection and for fitting the preferred model. Our method and algorithm are deployed on a suite of numerical studies and are applied to a nutritional epidemiology study. The numerical results show that the proposed methodology outperforms previously available methods in terms of effective sample sizes of the Markov chain samplers and the overall misclassification rates.

摘要-我们提供了一个灵活的框架，用于在允许线性和非线性加性组件的一类加性部分线性模型中进行选择。在实践中，确定哪些加性成分应从模型中排除，同时确定非零加性成分是否应在最终模型中表示为线性或非线性成分是具有挑战性的。在本文中，我们提出了一种贝叶斯模型选择方法，该方法由精心指定的模型类促进，包括先验分布的选择和用于非线性加性分量的非参数模型。我们采用一系列潜在变量来确定每个变量在三种可能性中的影响（无影响、线性影响、和非线性效应），并同时确定每个样条的节点，以对平滑函数进行适当的惩罚。使用伪先验分布和折叠方案使我们能够部署表现良好的马尔可夫链蒙特卡罗采样器，用于模型选择和拟合首选模型。我们的方法和算法部署在一套数值研究中，并应用于营养流行病学研究。数值结果表明，就马尔可夫链采样器的有效样本量和总体错误分类率而言，所提出的方法优于以前可用的方法。用于模型选择和拟合首选模型。我们的方法和算法部署在一套数值研究中，并应用于营养流行病学研究。数值结果表明，就马尔可夫链采样器的有效样本量和总体错误分类率而言，所提出的方法优于以前可用的方法。用于模型选择和拟合首选模型。我们的方法和算法部署在一套数值研究中，并应用于营养流行病学研究。数值结果表明，就马尔可夫链采样器的有效样本量和总体错误分类率而言，所提出的方法优于以前可用的方法。