Geometrically Designed Splines (GeDS) regression is a non-parametric geometrically motivated method for fitting variable knots spline predictor models which are generalized (non)-linear, (i.e. GNM (GLM)) models. The GeDS regression is fitted based on a sample of \(N\) observations of a response variable \(y\), dependent on a set of (currently up to two) covariates, assuming \(y\) has a distribution from the exponential family.
The GeDS estimation method is based on: first constructing a piecewise linear fit (spline fit of order 2) at stage A which captures the shape of the data and; second approximating this fit with shape preserving (variation diminishing) spline fits of higher orders 3, 4,\(\dots\) (i.e. degrees 2, 3,\(\dots\)) at stage B. As a result of this, GeDS estimates the number and location of the knots and the order of the spline fit in a fast and efficient way.
The GeDS method was originally developed by Kaishev et al. (2016) assuming the response \(y\) is normally distributed and a corresponding Mathematica code was provided.
The GeDS method was recently extended by Dimitrova et al. (2017) to cover any distribution from the exponential
family. The GeDS R package presented here includes an enhanced R implementation of the original
Normal GeDS Mathematica code due to Kaishev et al. (2016), implemented as the NGeDS function and a generalization of it in the function
GGeDS which covers the case of any distribution from the exponential family.
The GeDS package allows also to fit two dimensional response surfaces
currently implemented only in the Normal case via the function NGeDS. It also allows
to construct multivariate (predictor) models with a GeD spline
component and a parametric component (see the functions f, formula,
NGeDS and GGeDS for details).
The outputs of both NGeDS and GGeDS functions are GeDS-class objects.
As described in Kaishev et al. (2016) and Dimitrova et al. (2017)
the final GeDS fit is the one whose order is chosen according to a strategy described
in stage B of the algorithm. However, GeDS-class objects contain second, third and fourth
order spline fits and the user has the possibility to choose among them.
This package also includes some datasets where GeDS regression proves to be very efficient
and some user friendly functions that are designed to easily extract required
information. Several methods are also provided to handle GeDS output results (see GeDS-class).
Throughout this document, we use the terms GeDS predictor model, GeDS regression and GeDS fit interchangeably.
Please report any issue arising or bug in the code to andrea.lattuada@unicatt.it.
| Package: | GeDS |
| Version: | 0.1.2 |
| Date: | 2017-11-08 |
| License: | GPL-3 |
Kaishev, V.K., Dimitrova, D.S., Haberman, S., & Verrall, R.J. (2016). Geometrically designed, variable knot regression splines. Computational Statistics, 31, 1079--1105. DOI: doi.org/10.1007/s00180-015-0621-7
Dimitrova, D.S., Kaishev, V.K., Lattuada A. and Verrall, R.J. (2017). Geometrically designed, variable knot splines in Generalized (Non-)Linear Models. Available at openaccess.city.ac.uk