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Variable selection in nonlinear function-on-scalar regression.

Rahul Ghosal1, Arnab Maity2

  • 1Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland.

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PubMed
Summary
This summary is machine-generated.

We introduce a novel variable selection method for nonlinear additive function-on-scalar regression (FOSR) models. This approach effectively identifies important predictors, accommodating nonlinear covariate effects and improving upon existing linear FOSR methods.

Keywords:
NHANESfunction-on-scalar regressionfunctional data analysisfunctional principal component analysisnonlinear regressionvariable selection

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Area of Science:

  • Statistics
  • Biostatistics
  • Machine Learning

Background:

  • Existing variable selection methods for function-on-scalar regression (FOSR) often assume linear effects of scalar predictors.
  • This linearity assumption can be overly restrictive when dealing with multiple continuous covariates.
  • There is a need for flexible methods that can capture nonlinear relationships in FOSR.

Purpose of the Study:

  • To develop a new, computationally efficient method for variable selection in nonlinear additive FOSR models.
  • To extend existing linear FOSR variable selection techniques to accommodate nonlinear covariate effects.
  • To provide a unified and flexible framework for variable selection in FOSR.

Main Methods:

  • Proposed a computationally efficient approach utilizing functional principal component scores of the functional response.
  • Extended the framework to handle nonlinear additive effects of scalar predictors within the FOSR model.
  • Evaluated the method through simulation studies and application to real-world accelerometer data.

Main Results:

  • The proposed method demonstrates advantages over existing variable selection techniques in FOSR, even when covariate effects are linear.
  • The method successfully identifies relevant variables and accommodates nonlinear relationships.
  • Application to NHANES accelerometer data reveals associations between physical activity patterns and participant characteristics.

Conclusions:

  • The developed method offers a flexible and unified approach for variable selection in nonlinear additive FOSR.
  • It effectively handles nonlinear covariate effects, outperforming existing methods in simulations.
  • The approach is valuable for analyzing complex functional data, such as physical activity patterns.