Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland.
Department of Statistics, North Carolina State University, Raleigh, North Carolina.
Biometrics. 2023 Mar;79(1):292-303. doi: 10.1111/biom.13564. Epub 2021 Sep 27.
We develop a new method for variable selection in a nonlinear additive function-on-scalar regression (FOSR) model. Existing methods for variable selection in FOSR have focused on the linear effects of scalar predictors, which can be a restrictive assumption in the presence of multiple continuously measured covariates. We propose a computationally efficient approach for variable selection in existing linear FOSR using functional principal component scores of the functional response and extend this framework to a nonlinear additive function-on-scalar model. The proposed method provides a unified and flexible framework for variable selection in FOSR, allowing nonlinear effects of the covariates. Numerical analysis using simulation study illustrates the advantages of the proposed method over existing variable selection methods in FOSR even when the underlying covariate effects are all linear. The proposed procedure is demonstrated on accelerometer data from the 2003-2004 cohorts of the National Health and Nutrition Examination Survey (NHANES) in understanding the association between diurnal patterns of physical activity and demographic, lifestyle, and health characteristics of the participants.
我们提出了一种新的方法，用于非线性加性函数-标量回归（FOSR）模型中的变量选择。现有的 FOSR 变量选择方法主要集中在标量预测因子的线性效应上，而在存在多个连续测量的协变量的情况下，这可能是一个限制性的假设。我们提出了一种在现有的线性 FOSR 中使用功能响应的功能主成分得分进行变量选择的计算效率高的方法，并将该框架扩展到非线性加性函数-标量模型。所提出的方法为 FOSR 中的变量选择提供了一个统一而灵活的框架，允许协变量的非线性效应。使用模拟研究的数值分析表明，即使潜在的协变量效应都是线性的，所提出的方法也优于 FOSR 中的现有变量选择方法。该程序在 2003-2004 年全国健康和营养检查调查（NHANES）的加速度计数据上进行了演示，以了解日间体力活动模式与参与者的人口统计学、生活方式和健康特征之间的关联。
