How well does your model fit the data?

Abstract

Despite almost five decades of activity on the computer modelling of input-output relationships, little general agreement has emerged on appropriate indices for the goodness-of-fit of a model to a set of observations of the pertinent variables. The coefficient of efficiency, which is closely allied in form to the coefficient of determination, has been widely adopted in many data mining and modelling exercises. Values of this coefficient close to unity are taken as evidence of good matching between observed and computed flows. However, studies using synthetic data have demonstrated that negative values of the coefficient of efficiency can occur both in the presence of bias in computed outputs, and when the computed volume of flow greatly exceeds the observed volume of flow. In contrast, the coefficient of efficiency lacks discrimination for cases close to perfect reproduction. In the latter case, a coefficient based upon the first differences of the data proves to be more helpful.