Smoothing spline models for the analysis of nested and crossed samples of curves
Smoothing spline models for the analysis of nested and crossed samples of curves
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DOI：
10.2307/2669837
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发表时间：
1998-09-01
影响因子：
3.7
通讯作者：
Rice, JA
中科院分区：
文献类型：
--
作者：
Brumback, BA;Rice, JA
我们介绍了一类模型的添加剂分解的交叉和嵌套的因素分层的曲线组，推广平滑样条到这样的样本，将它们与相应的混合效应模型。该模型也适用于缺失数据的插补和探索性方差分析。我们证明了最好的线性无偏预测（BLUPs）从扩展的混合效应模型对应于解决方案的广义惩罚回归平滑参数直接相关的方差分量，我们表明，这些解决方案是自然的三次样条。模型参数估计使用一个高效的EM算法的限制最大似然（REML）估计的基础上初步的特征向量分解。计算的估计值的变异性可以用渐近技术或嵌套混合效应模型的新的分层Bootstrap回归方案进行评估。我们的方法适用于月经周期的数据，从生殖功能的研究，测量每日尿孕酮;孕酮曲线的样本是分层的周期内嵌套的概念和非概念组内嵌套的受试者。
We introduce a class of models for an additive decomposition of groups of curves stratified by crossed and nested factors, generalizing smoothing splines to such samples by associating them with a corresponding mixed-effects model. The models are also useful for imputation of missing data and exploratory analysis of variance. We prove that the best linear unbiased predictors (BLUPs) from the extended mixed-effects model correspond to solutions of a generalized penalized regression where smoothing parameters are directly related to variance components, and we show that these solutions are natural cubic splines. The model parameters are estimated using a highly efficient implementation of the EM algorithm for restricted maximum likelihood (REML) estimation based on a preliminary eigenvector decomposition. Variability of computed estimates can be assessed with asymptotic techniques or with a novel hierarchical bootstrap resampling scheme for nested mixed-effects models. Our methods are applied to menstrual cycle data from studies of reproductive function that measure daily urinary progesterone; the sample of progesterone curves is stratified by cycles nested within subjects nested within conceptive and nonconceptive groups.