the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
From R-squared to coefficient of model accuracy for assessing "goodness-of-fits"
Charles Onyutha
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.
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Charles Onyutha


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SC1: 'Experiences using the newly introduced "Coefficient of Model Agreement"', Ulrich Schumann, 25 Jun 2020
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AC1: 'Reply to the comments of Ulrich Schumann regarding the discussion paper with ID gmd-2020-51', Charles Onyutha, 05 Jul 2020
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RC1: 'gmd-2020-51', Anonymous Referee #1, 07 Sep 2020
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AC2: 'Reply to the comments of anonymous reviewer 1', Charles Onyutha, 27 Sep 2020
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AC2: 'Reply to the comments of anonymous reviewer 1', Charles Onyutha, 27 Sep 2020
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SC2: 'Review', Barry Croke, 03 Oct 2020
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AC3: 'Reply to Barry Croke', Charles Onyutha, 24 Oct 2020
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AC3: 'Reply to Barry Croke', Charles Onyutha, 24 Oct 2020
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AC4: 'Reply to Barry Croke', Charles Onyutha, 24 Oct 2020
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RC2: 'review of gmd-2020-51', Barry Croke, 01 Nov 2020
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AC5: 'Reply to Barry Croke', Charles Onyutha, 01 Nov 2020


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SC1: 'Experiences using the newly introduced "Coefficient of Model Agreement"', Ulrich Schumann, 25 Jun 2020
-
AC1: 'Reply to the comments of Ulrich Schumann regarding the discussion paper with ID gmd-2020-51', Charles Onyutha, 05 Jul 2020
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RC1: 'gmd-2020-51', Anonymous Referee #1, 07 Sep 2020
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AC2: 'Reply to the comments of anonymous reviewer 1', Charles Onyutha, 27 Sep 2020
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AC2: 'Reply to the comments of anonymous reviewer 1', Charles Onyutha, 27 Sep 2020
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SC2: 'Review', Barry Croke, 03 Oct 2020
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AC3: 'Reply to Barry Croke', Charles Onyutha, 24 Oct 2020
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AC3: 'Reply to Barry Croke', Charles Onyutha, 24 Oct 2020
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AC4: 'Reply to Barry Croke', Charles Onyutha, 24 Oct 2020
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RC2: 'review of gmd-2020-51', Barry Croke, 01 Nov 2020
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AC5: 'Reply to Barry Croke', Charles Onyutha, 01 Nov 2020
Charles Onyutha
Charles Onyutha
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