An evaluation of R2 as an inadequate measure for nonlinear models in pharmacological and biochemical research: a Monte Carlo approach
By Andrej-Nikolai Spiess, Natalie Neumeyer. BMC Pharmacology, 2010
825 citations recorded by the source corpus.
BackgroundIt 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.ResultsThe 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.ConclusionResearchers 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.
Subfields: Computational Theory and Mathematics, Epidemiology, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/7dad371c864295bc490312a75bfebb41c4025287
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Citations in the corpus
- SimpleTree —An Efficient Open Source Tool to Build Tree Models from TLS Clouds (2015, background): “It needs to be mentioned, that the usage of the R(2) for non linear model fits is criticized [87].”
- Model discrimination for drying and rehydration kinetics of freeze‐dried tomatoes (2020, methodology): “Three different measures were employed to estimate the goodnessof-fit of each fitted model (Spiess & Neumeyer, 2010): adjusted R2 (R2adj), corrected AIC (AICC), and the BIC.”
- Contribution of neutral processes to the assembly of gut microbial communities in the zebrafish over host development (2015, background): “While generalized r-squared is a useful measure for comparing the fit of multiple data sets with a single model, it is a poor choice for comparing the fit of multiple models with a single data set (Spiess and Neumeyer, 2010).”
- An ensemble model for predicting the remaining useful performance of lithium-ion batteries (2013, background): “The lower the AIC is, the better the model will be [25].”
- Evaluating calibration methods for predicting soil available nutrients using hyperspectral VNIR data (2018, background): “…for a long period (Shmueli, 2010), generally defined as (e.g., Kvalseth, 1985; Weisberg, 2005): ∑ ∑= − − − = = f x y y yR 1 ( ( ) ) / ( ) i m i i i m i 2 1 2 1 2 (1) which was proved to be an inadequate measure for linear no-intercept models and non-linear models (Spiess and Neumeyer, 2010).”