Nonlinear Regression Modelling: A Primer with Applications and Caveats

by  Timothy O'Brien & Jack Silcox

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In their applied studies, researchers often find that nonlinear regression models are more applicable for modelling various biological, physical, and chemical processes than are linear ones since they tend to fit the data well and since these models – and especially the associated model parameters – are usually more scientifically meaningful.  For example in relative potency, drug synergy, and similar compound interaction modelling, key model parameters aid researchers in making important decisions regarding comparisons of drugs or compounds and/or whether combinations of these substances would enhance effects.

These researchers may be at a loss for how best to perform this nonlinear modelling, including choosing between various growth models or binary logistic models, how these work and which analysis methods are best and why.  Working through several key examples, this paper provides a gentle yet informative hands-on introduction to nonlinear modelling, provides key R code which can be easily adapted to fit ones own nonlinear models, and underscores key caveats regarding often-problematic Wald confidence intervals and p-values as well as the lack of penalizing for overfitting in a certain large-sample likelihood-based approach.

About the Authors: Tim O’Brien is a professor of Mathematics and Statistics (with a joint appointment in Environmental Sustainability) at Loyola University Chicago.  Jack Silcox is a postdoctoral researcher in the Department of Psychology at the University of Utah.