A Toolbox for Nonlinear Regression in<i>R</i>: The Package<b>nlstools</b>

TLDR

Nonlinear regression models, widely used across scientific fields, are typically fitted in R using functions such as nls(), but their reliance on non‑trivial assumptions and iterative least‑squares estimation requires users to understand model parameterization, plausible parameter ranges, diagnostic procedures, and the limitations of underlying hypotheses, a need unmet by current modules that lack dedicated diagnostic functionality. The authors aim to provide an extended toolbox of functions for careful evaluation of nonlinear regression fits by introducing a unified diagnostic framework in the R package nlstools. The package implements a unified diagnostic framework, whose features are presented and illustrated through a pulmonary‑medicine example.

Abstract

Nonlinear regression models are applied in a broad variety of scientific fields. Various R functions are already dedicated to fitting such models, among which the function nls() has a prominent position. Unlike linear regression fitting of nonlinear models relies on non-trivial assumptions and therefore users are required to carefully ensure and validate the entire modeling. Parameter estimation is carried out using some variant of the leastsquares criterion involving an iterative process that ideally leads to the determination of the optimal parameter estimates. Therefore, users need to have a clear understanding of the model and its parameterization in the context of the application and data considered, an a priori idea about plausible values for parameter estimates, knowledge of model diagnostics procedures available for checking crucial assumptions, and, finally, an understanding of the limitations in the validity of the underlying hypotheses of the fitted model and its implication for the precision of parameter estimates. Current nonlinear regression modules lack dedicated diagnostic functionality. So there is a need to provide users with an extended toolbox of functions enabling a careful evaluation of nonlinear regression fits. To this end, we introduce a unified diagnostic framework with the R package nlstools. In this paper, the various features of the package are presented and exemplified using a worked example from pulmonary medicine.