cpr: An R Package For Finding Parsimonious B-Spline Regression Models via Control Polygon Reduction and Control Net Reduction

TL;DR

The paper introduces the R package cpr, which implements algorithms for efficiently reducing the complexity of B-spline regression models by selecting essential knots while preserving fit quality.

Contribution

It presents novel control polygon reduction and control net reduction algorithms for parsimonious B-spline model selection in R.

Findings

Algorithms are quick to implement and flexible for various data types.

The package offers tools for constructing B-spline bases, control polygons, and diagnostics.

Reduces large knot sequences to essential elements while maintaining high fit quality.

Abstract

The R package cpr provides tools for selection of parsimonious B-spline regression models via algorithms coined `control polygon reduction' (CPR) and `control net reduction' (CNR). B-Splines are commonly used in regression models to smooth data and approximate unknown functional forms. B-Splines are defined by a polynomial order and a knot sequence. Defining the knot sequence is non-trivial, but is critical with respect to the quality of the regression models. The focus of the CPR and CNR algorithms is to reduce a large knot sequence down to a parsimonious collection of elements while maintaining a high quality of fit. The algorithms are quick to implement and are flexible enough to support many types of data and regression approaches. The cpr package provides the end user collections of tools for the construction of B-spline basis matrices, construction of control polygons and control nets, and the use of diagnostics of the CPR and CNR algorithms.

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