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Open Access Highly Accessed Open Badges Research article

An evaluation of R2 as an inadequate measure for nonlinear models in pharmacological and biochemical research: a Monte Carlo approach

Andrej-Nikolai Spiess1* and Natalie Neumeyer2

Author Affiliations

1 Department of Andrology, University Hospital Hamburg-Eppendorf, Hamburg, Germany

2 Department of Mathematics, University of Hamburg, Hamburg, Germany

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BMC Pharmacology 2010, 10:6  doi:10.1186/1471-2210-10-6

Published: 7 June 2010



It is long known within the mathematical literature that the coefficient of determination R2 is an inadequate measure for the goodness of fit in nonlinear models. Nevertheless, it is still frequently used within pharmacological and biochemical literature for the analysis and interpretation of nonlinear fitting to data.


The intensive simulation approach undermines previous observations and emphasizes the extremely low performance of R2 as a basis for model validity and performance when applied to pharmacological/biochemical nonlinear data. In fact, with the 'true' model having up to 500 times more strength of evidence based on Akaike weights, this was only reflected in the third to fifth decimal place of R2. In addition, even the bias-corrected R2adj exhibited an extreme bias to higher parametrized models. The bias-corrected AICc and also BIC performed significantly better in this respect.


Researchers and reviewers should be aware that R2 is inappropriate when used for demonstrating the performance or validity of a certain nonlinear model. It should ideally be removed from scientific literature dealing with nonlinear model fitting or at least be supplemented with other methods such as AIC or BIC or used in context to other models in question.