Beware of R2: simple, unambiguous assessment of the prediction accuracy of QSAR and QSPR models

By D. Alexander, Alexander Tropsha, David A. Winkler. Journal of Chemical Information and Modeling, 2015

696 citations recorded by the source corpus.

The statistical metrics used to characterize the external predictivity of a model, i.e., how well it predicts the properties of an independent test set, have proliferated over the past decade. This paper clarifies some apparent confusion over the use of the coefficient of determination, R2, as a measure of model fit and predictive power in QSAR and QSPR modelling. R2 (or R2) has been used in various contexts in the literature in conjunction with training and test data, for both ordinary linear regression and regression through the origin as well as with linear and nonlinear regression models. We analyze the widely adopted model fit criteria suggested by Golbraikh and Tropsha1 in a strict statistical manner. Shortcomings in these criteria are identified and a clearer and simpler alternative method to characterize model predictivity is provided. The intent is not to repeat the well-documented arguments for model validation using test data, but to guide the application of R2 as a model fit statistic. Examples are used to illustrate both correct and incorrect use of R2. Reporting the root mean squared error or equivalent measures of dispersion, typically of more practical importance than R2, is also encouraged and important challenges in addressing the needs of different categories of users such as computational chemists, experimental scientists, and regulatory decision support specialists are outlined.

Subfields: Analytical Chemistry, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9f1e85856abe57d174ee3b917014e19c866947ad

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In Analytical Chemistry

C. Onyutha

In Computational Theory and Mathematics

In Statistics and Probability

Citations in the corpus

Artificial intelligence in drug discovery: recent advances and future perspectives (2021, background): “Additionally, many efforts have been dedicated to the use of proper performance metrics for classification and regression models, and the limitations thereof [105–108].”
Ten simple rules for predictive modeling of individual differences in neuroimaging (2019, background): “…definition of R 2 is the equivalent to the squared correlation between the predicted and observed values and reflects the error between the predicted values and its fit to the regression line, not the error between the predicted and observed values (Alexander et al., 2015; Dubois et al., 2018a).”
From R-squared to coefficient of model accuracy for assessing "goodness-of-fits" (2020, methodology): “Despite the advances in methods of statistical and mathematical modeling, Alexander et al. (2015) asserts that there continues to exist considerable lack of focus on improving ways to judge the quality of the models.”