Smoothing Parameter and Model Selection for General Smooth Models
Smoothing Parameter and Model Selection for General Smooth Models
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DOI：
10.1080/01621459.2016.1180986
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发表时间：
2016-12-01
影响因子：
3.7
通讯作者：
Saefken, Benjamin
中科院分区：
文献类型：
--
作者：
Wood, Simon N.;Pya, Natalya;Saefken, Benjamin
本文讨论了一个一般框架的平滑参数估计的模型与规则似然构造的未知光滑函数的协变量。高斯随机效应和参数项也可能存在。通过构造，该方法是数值稳定和收敛的，并使平滑参数的不确定性被量化。后者使我们能够解决AIC在这类模型中的一个众所周知的问题，从而改善了可用的模型选择工具的范围。光滑函数用降秩样条光滑函数表示，并用相关的二次罚函数度量函数的光滑性。模型估计是通过惩罚似然最大化，其中控制惩罚程度的平滑参数由拉普拉斯近似边缘似然估计。例如，这些方法涵盖了非指数家族反应的广义加性模型（例如，β、有序分类、标度t分布、负二项分布和Tweedie分布）、位置标度和形状的广义加性模型（例如，两阶段零膨胀模型和高斯位置标度模型）、考克斯比例风险模型和多变量加性模型。该框架将新模型类的实现减少到对数似然的一些标准导数的编码。本文的补充材料可在网上查阅。
This article discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be present. By construction the method is numerically stable and convergent, and enables smoothing parameter uncertainty to be quantified. The latter enables us to fix a well known problem with AIC for such models, thereby improving the range of model selection tools available. The smooth functions are represented by reduced rank spline like smoothers, with associated quadratic penalties measuring function smoothness. Model estimation is by penalized likelihood maximization, where the smoothing parameters controlling the extent of penalization are estimated by Laplace approximate marginal likelihood. The methods cover, for example, generalized additive models for nonexponential family responses (e.g., beta, ordered categorical, scaled t distribution, negative binomial and Tweedie distributions), generalized additive models for location scale and shape (e.g., two stage zero inflation models, and Gaussian location scale models), Cox proportional hazards models and multivariate additive models. The framework reduces the implementation of new model classes to the coding of some standard derivatives of the log-likelihood. Supplementary materials for this article are available online.