From R-squared to coefficient of model accuracy for assessing "goodness-of-fits"
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Date
2020
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Geoscientific Model Development Discussions
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, R2 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. MATLAB
and R codes as well as an illustrative MS Excel file to compute the CMA were provided.
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Citation
Onyutha, C. (2020). From R-squared to coefficient of model accuracy for assessing "goodness-of-fits". Geoscientific Model Development Discussions , 1-25. Muñozhttps:// doi.org/10.5194/gmd-2020-51