Rice J A, Wu C O
Department of Statistics, University of California at Berkeley, 94720, USA.
Biometrics. 2001 Mar;57(1):253-9. doi: 10.1111/j.0006-341x.2001.00253.x.
We propose a method of analyzing collections of related curves in which the individual curves are modeled as spline functions with random coefficients. The method is applicable when the individual curves are sampled at variable and irregularly spaced points. This produces a low-rank, low-frequency approximation to the covariance structure, which can be estimated naturally by the EM algorithm. Smooth curves for individual trajectories are constructed as best linear unbiased predictor (BLUP) estimates, combining data from that individual and the entire collection. This framework leads naturally to methods for examining the effects of covariates on the shapes of the curves. We use model selection techniques--Akaike information criterion (AIC), Bayesian information criterion (BIC), and cross-validation--to select the number of breakpoints for the spline approximation. We believe that the methodology we propose provides a simple, flexible, and computationally efficient means of functional data analysis.
我们提出了一种分析相关曲线集合的方法，其中将个体曲线建模为具有随机系数的样条函数。当个体曲线在可变且不规则间隔的点上采样时，该方法适用。这会产生协方差结构的低秩、低频近似，可通过期望最大化（EM）算法自然地进行估计。个体轨迹的平滑曲线通过结合该个体和整个集合的数据，构建为最佳线性无偏预测器（BLUP）估计。这个框架自然地引出了用于检验协变量对曲线形状影响的方法。我们使用模型选择技术——赤池信息准则（AIC）、贝叶斯信息准则（BIC）和交叉验证——来选择样条近似的断点数量。我们相信我们提出的方法提供了一种简单、灵活且计算高效的函数数据分析手段。
