Nonlinear Mixed-effects Scalar-on-function Models and Variable Selection for Kinematic Upper Limb Movement Data

TL;DR

This paper introduces a novel nonlinear mixed-effects scalar-on-function regression model with a new variable selection algorithm, fLARS, tailored for high-dimensional kinematic data to improve clinical assessment predictions after stroke.

Contribution

It develops a new variable selection method, fLARS, for nonlinear mixed-effects models handling large scalar and functional variable sets, with proven efficiency and accuracy.

Findings

fLARS outperforms existing variable selection methods in simulations.

The nonlinear mixed-effects model improves prediction accuracy for clinical assessments.

The approach effectively handles high-dimensional data with more variables than samples.

Abstract

This paper arises from collaborative research the aim of which was to model clinical assessments of upper limb function after stroke using 3D kinematic data. We present a new nonlinear mixed-effects scalar-on-function regression model with a Gaussian process prior focusing on variable selection from large number of candidates including both scalar and function variables. A novel variable selection algorithm has been developed, namely functional least angle regression (fLARS). As they are essential for this algorithm, we studied the representation of functional variables with different methods and the correlation between a scalar and a group of mixed scalar and functional variables. We also propose two new stopping rules for practical usage. This algorithm is able to do variable selection when the number of variables is larger than the sample size. It is efficient and accurate for both variable selection and parameter estimation. Our comprehensive simulation study showed that the method is superior to other existing variable selection methods. When the algorithm was applied to the analysis of the 3D kinetic movement data the use of the non linear random-effects model and the function variables significantly improved the prediction accuracy for the clinical assessment.