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Variable selection in nonlinear function‐on‐scalar regression

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  • Rahul Ghosal
  • Arnab Maity

Abstract

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.

Suggested Citation

  • Rahul Ghosal & Arnab Maity, 2023. "Variable selection in nonlinear function‐on‐scalar regression," Biometrics, The International Biometric Society, vol. 79(1), pages 292-303, March.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:1:p:292-303
    DOI: 10.1111/biom.13564
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    References listed on IDEAS

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    4. Jeff Goldsmith & Tomoko Kitago, 2016. "Assessing systematic effects of stroke on motor control by using hierarchical function-on-scalar regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(2), pages 215-236, February.
    5. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
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