Some limitations of the concordance correlation coefficient to characterise model accuracy

Perusal of the environmental modelling literature reveals that the Lin's concordance correlation coefficient is a popular validation statistic to characterise model or map quality. In this communication, we illustrate with synthetic examples three undesirable statistical properties of this coefficient. We argue that ignorance of these properties have led to a frequent misuse of this coefficient in modelling and mapping studies. The stand-alone use of the concordance correlation coefficient is insufficient because i) it does not inform on the relative contribution of bias and correlation, ii) the values cannot be compared across different datasets or studies and iii) it is prone to the same problems as other linear correlation statistics. The concordance coefficient was, in fact, thought initially for evaluating reproducibility studies over repeated trials of the same variable, not for characterising model accuracy. For the validation of models and maps, we recommend calculating statistics that, combined with the concordance correlation coefficient, represent various aspects of the model or map quality, which can be visualised together in a single figure with a Taylor or solar diagram.