Preprints
https://doi.org/10.5194/gmd-2020-51
https://doi.org/10.5194/gmd-2020-51

Submitted as: methods for assessment of models 04 May 2020

Submitted as: methods for assessment of models | 04 May 2020

Review status: a revised version of this preprint is currently under review for the journal GMD.

From R-squared to coefficient of model accuracy for assessing "goodness-of-fits"

Charles Onyutha Charles Onyutha
  • Department of Civil and Building Engineering, Kyambogo University, P.O Box 1, Kyambogo, Kampala, Uganda

Abstract. Modelers tend to focus more on advancing methods of statistical and mathematical modeling than developing novel techniques for comparing modeled results with observations or establishing metrics for model performance assessment. Perhaps solely the most extensively applied "goodness-of-fit" measure especially for assessing performance of regression models is the coefficient of determination R2. Normally, high R2 tends to be associated with an efficient model. Nevertheless, R2 has been cited to have no importance in the classical model of regression. Even in its use in descriptive statistics, R2 is known to have questionable justification. R2 is inadequate in assessing model performance because it does not give any information on the model residuals. Furthermore, R-squared can be low for an effective model. Contrastingly, a very poor model fit can yield high R2. Regressing X on Y yields R2 which is the same as that if Y is regressed on X thereby invalidating its use as a coefficient of determination. Taking into account the drawbacks of using R2, this paper introduces coefficient of model accuracy (CMA) the derivation of which comprises an analogy to the R2. However, instead of simply squaring an ordinary Pearson's product-moment correlation coefficient to obtain R2, CMA comprises the product of nonparametric sample correlation and model bias. Acceptability of the introduced method can be found demonstrated through comparison of results from simulations by hydrological models calibrated using CMA and other existing objective functions.

Charles Onyutha

 
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Charles Onyutha

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Short summary
R2 despite its wide use in assessing model performance has several drawbacks. While taking into account the drawbacks, this paper introduces another metric (coefficient of model accuracy MCA) which is capable of assessing "goodness-of-fits". Stepwise derivation of CMA comprises an analogy to the R2. Suitability of CMA for assessing model performance was demonstrated through comparison of simulations by hydrological models calibrated using CMA and other existing objective functions.