Fast smoothing parameter separation in multidimensional generalized P-splines: the SAP algorithm
Fast smoothing parameter separation in multidimensional generalized P-splines: the SAP algorithm
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DOI：
10.1007/s11222-014-9464-2
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发表时间：
2015-09-01
影响因子：
2.2
通讯作者：
Eilers, Paul
中科院分区：
文献类型：
--
作者：
Xose Rodriguez-Alvarez, Maria;Lee, Dae-Jin;Eilers, Paul
提出了一种估计具有各向异性惩罚的多维惩罚样条广义线性模型光滑参数的新算法。这个新的建议是基于多维P样条的混合模型表示，其中每个协变量的平滑参数表示的方差分量。在惩罚拟似然方法的基础上，得到了方差分量估计的封闭表达式。这种提法导致一个有效的实施，大大减少了计算负担。所提出的算法可以看作是Schall（1991）方差分量估计算法的推广，用于处理随机效应协方差矩阵的非标准结构。通过仿真对该算法的实际性能进行了评估，并在均方误差准则和计算时间的基础上与其他方法进行了比较。最后，我们用两个真实的数据集的分析来说明我们的建议：一个二维的例子，美国的月降水量数据的历史记录和一个三维的呼吸系统疾病的死亡率数据，根据死亡年龄，死亡年份和死亡月份。
A new computational algorithm for estimating the smoothing parameters of a multidimensional penalized spline generalized linear model with anisotropic penalty is presented. This new proposal is based on the mixed model representation of a multidimensional P-spline, in which the smoothing parameter for each covariate is expressed in terms of variance components. On the basis of penalized quasi-likelihood methods, closed-form expressions for the estimates of the variance components are obtained. This formulation leads to an efficient implementation that considerably reduces the computational burden. The proposed algorithm can be seen as a generalization of the algorithm by Schall (1991)-for variance components estimation-to deal with non-standard structures of the covariance matrix of the random effects. The practical performance of the proposed algorithm is evaluated by means of simulations, and comparisons with alternative methods are made on the basis of the mean square error criterion and the computing time. Finally, we illustrate our proposal with the analysis of two real datasets: a two dimensional example of historical records of monthly precipitation data in USA and a three dimensional one of mortality data from respiratory disease according to the age at death, the year of death and the month of death.