Direct generalized additive modeling with penalized likelihood
Direct generalized additive modeling with penalized likelihood
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DOI：
10.1016/s0167-9473(98)00033-4
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发表时间：
1998-08-07
影响因子：
1.8
通讯作者：
Eilers, PHC
中科院分区：
文献类型：
--
作者：
Marx, BD;Eilers, PHC
广义加性模型（GAM）已经成为模型构建中一个优雅而实用的选择。平滑GAM分量的估计传统上需要一种算法，该算法循环并更新每个平滑，同时将其他分量保持在其当前估计的拟合，直到指定的收敛。我们的目标是同时拟合所有光滑部件。这可以通过对每个平滑分量使用惩罚B样条或P样条平滑器来实现，从而将GAM转换为广义线性模型框架。使用大量等距节点，P样条故意过拟合每个B样条分量。为了减少灵活性，相邻的B-样条系数的差异罚款被纳入惩罚版本的Fisher评分算法。每个分量都有一个单独的平滑参数，并通过交叉验证或信息准则的扩展来优化调整惩罚。一个使用逻辑加法模型的例子提供了发展的说明。(C)1998 Elsevier Science B. V.保留所有权利。
Generalized additive models (GAMs) have become an elegant and practical option in model building. Estimation of a smooth GAM component traditionally requires an algorithm that cycles through and updates each smooth, while holding other components at their current estimated fit, until specified convergence. We aim to fit all the smooth components simultaneously. This can be achieved using penalized B-spline or P-spline smoothers for every smooth component, thus transforming GAMs into the generalized linear model framework. Using a large number of equally spaced knots, P-splines purposely overfit each B-spline component. To reduce flexibility, a difference penalty on adjacent B-spline coefficients is incorporated into a penalized version of the Fisher scoring algorithm. Each component has a separate smoothing parameter, and the penalty is optimally regulated through extensions of cross validation or information criterion. An example using logistic additive models provides illustrations of the developments. (C) 1998 Elsevier Science B.V. All rights reserved.