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Variable selection with P-splines in functional linear regression: Application in graft-versus-host disease.

M Carmen Aguilera-Morillo1,2, Ismael Buño3,4, Rosa E Lillo2,5

  • 1Department of Applied Statistics and Operations Research and Quality, Universitat Poltècnica de València, Valencia, Spain.

Biometrical Journal. Biometrische Zeitschrift
|June 11, 2020
PubMed
Summary

This study introduces P-splines for functional linear regression, enhancing variable selection and parameter estimation for functional response and scalar covariates. Six penalized and non-penalized methods were compared, with the best applied to graft-versus-host disease data.

Keywords:
LASSOP-splinesfunction-on-scalar regressionvariable selection

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Area of Science:

  • Statistics
  • Functional Data Analysis

Background:

  • Functional linear regression models (FLM) are crucial for analyzing data with functional responses and scalar covariates.
  • Challenges exist in simultaneous variable selection and parameter estimation within FLM.

Purpose of the Study:

  • To propose P-splines as a robust tool for variable selection and parameter estimation in FLM.
  • To evaluate and compare penalized (L1, L2) and non-penalized regression approaches combined with response variable smoothing.

Main Methods:

  • A functional LASSO approach using basis representation for the response variable.
  • A penalized FLM incorporating a P-spline penalty into the least squares fitting criterion.
  • Comparison of six distinct methods, including penalized/non-penalized regression and presmoothing techniques (regression splines, P-splines).

Main Results:

  • P-splines demonstrate effectiveness for simultaneous variable selection and functional parameter estimation.
  • The study identified the most competitive approach through simulation schemes.
  • The chosen method was successfully applied to real-world graft-versus-host disease data.

Conclusions:

  • P-splines offer a powerful and integrated solution for estimation and variable selection in functional linear regression.
  • The findings provide practical insights for analyzing complex functional data, particularly in medical applications like allogeneic stem-cell transplantation.