A general framework for functional regression modelling
A general framework for functional regression modelling
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DOI：
10.1177/1471082x16681317
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发表时间：
2017-02-01
影响因子：
1
通讯作者：
Scheipl, Fabian
中科院分区：
文献类型：
--
作者：
Greven, Sonja;Scheipl, Fabian
研究人员对函数数据的回归模型越来越感兴趣。本文以标量数据的相应模型为基础，基于重构函数回归的指导原则，讨论了功能反应和/或功能协变量的加性(混合)模型的综合框架，允许大量现有方法适用于这些新的任务。该框架包括许多现有的以及新的模型。它包括广义功能数据的回归、均值回归、分位数回归以及功能数据的广义加性位置、形状和尺度模型(GAMLSS)。它允许许多灵活的线性、光滑或相互作用的标量和泛函协变量项以及(泛函)随机效应，并允许灵活地选择基函数，特别是样条基和函数主成分，并对每个项进行相应的惩罚。它涵盖了在常见(密集)或特定于曲线(稀疏)网格上观察到的功能数据。基于惩罚似然的推理和基于梯度提升的推理分别在R包REFIGN和FDBoost中实现。我们还讨论了所涉及的函数回归模型的可辨识性和计算复杂性。一个纵向多发性硬化症成像研究的活生生的例子，用来说明所提议的模型类的灵活性和实用性。此案例研究的可重现代码可在网上获得。
Researchers are increasingly interested in regression models for functional data. This article discusses a comprehensive framework for additive (mixed) models for functional responses and/or functional covariates based on the guiding principle of reframing functional regression in terms of corresponding models for scalar data, allowing the adaptation of a large body of existing methods for these novel tasks. The framework encompasses many existing as well as new models. It includes regression for generalized' functional data, mean regression, quantile regression as well as generalized additive models for location, shape and scale (GAMLSS) for functional data. It admits many flexible linear, smooth or interaction terms of scalar and functional covariates as well as (functional) random effects and allows flexible choices of basesparticularly splines and functional principal componentsand corresponding penalties for each term. It covers functional data observed on common (dense) or curve-specific (sparse) grids. Penalized-likelihood-based and gradient-boosting-based inference for these models are implemented in R packages refund and FDboost, respectively. We also discuss identifiability and computational complexity for the functional regression models covered. A running example on a longitudinal multiple sclerosis imaging study serves to illustrate the flexibility and utility of the proposed model class. Reproducible code for this case study is made available online.