Stable and efficient multiple smoothing parameter estimation for generalized additive models
Stable and efficient multiple smoothing parameter estimation for generalized additive models
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DOI：
10.1198/016214504000000980
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发表时间：
2004-09-01
影响因子：
3.7
通讯作者：
Wood, SN
中科院分区：
文献类型：
--
作者：
Wood, SN
使用惩罚回归样条表示广义加性模型（GAM）允许GAM以直接的方式使用惩罚回归方法。这种方法不仅便于推理，而且还可以使用诸如广义交叉验证之类的有根据的标准以计算高效的方式将平滑参数选择形式的模型选择集成到模型拟合中。目前这种模型的拟合和平滑参数选择方法通常是有效的，但不能提供线性回归软件包用户所习惯的数值稳定性水平。特别是现有的方法不能充分处理GAM拟合问题的数值秩不足，并且考虑到秩不足的程度可能是平滑参数相关的，因此产生可以这样做的方法并不简单。此外，具有GAM潜在灵活性的模型也可能由于模型似然性的不确定性而出现实际拟合困难：具有多个零点的数据由具有对数链接的模型拟合就是一个很好的例子。在这篇文章中，它提出了GAM的脊罚款提供了一个实际的解决方案，在这种情况下，和一个多平滑参数的选择方法，适合使用在存在这样的惩罚。该方法是基于枢轴QR分解和奇异值分解，使有或没有脊惩罚，它具有良好的误差传播特性，是能够检测和处理优雅的数值秩不足。该方法还允许混合用户指定的和估计的平滑参数和平滑参数的下限的设置。在计算效率方面，该方法与现有的方法相比。模拟研究比较现有的方法，包括治疗GAM的混合模型的方法。
Representation of generalized additive models (GAM's) using penalized regression splines allows GAM's to be employed in a straightforward manner using penalized regression methods. Not only is inference facilitated by this approach, but it is also possible to integrate model selection in the form of smoothing parameter selection into model fitting in a computationally efficient manner using well founded criteria such as generalized cross-validation. The current fitting and smoothing parameter selection methods for such models are usually effective, but do not provide the level of numerical stability to which users of linear regression packages, for example, are accustomed. In particular the existing methods cannot deal adequately with numerical rank deficiency of the GAM fitting problem, and it is not straightforward to produce methods that can do so, given that the degree of rank deficiency can be smoothing parameter dependent. In addition, models with the potential flexibility of GAM's can also present practical fitting difficulties as a result of indeterminacy in the model likelihood: Data with many zeros fitted by a model with a log link are a good example. In this article it is proposed that GAM's with a ridge penalty provide a practical solution in such circumstances, and a multiple smoothing parameter selection method suitable for use in the presence of such a penalty is developed. The method is based on the pivoted QR decomposition and the singular value decomposition, so that with or without a ridge penalty it has good error propagation properties and is capable of detecting and coping elegantly with numerical rank deficiency. The method also allows mixtures of user specified and estimated smoothing parameters and the setting of lower bounds on smoothing parameters. In terms of computational efficiency, the method compares well with existing methods. A simulation study compares the method to existing methods, including treating GAM's as mixed models.