  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.
