Smoothing Spline Models for the Analysis of Nested and Crossed Samples of Curves
提出一类针对嵌套和交叉因子分组的曲线加性分解模型，将平滑样条推广到此类样本，并用于缺失数据插补和方差分析，通过EM算法高效估计参数，应用于月经周期孕酮曲线分析。
Abstract 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.