Goodness-of-Fit Measures and the Predictive Power of Discrete Models

Although a number of goodness-of-fit measures for discrete choice models have been proposed and are widely in use, there have been few attempts at interpreting their physical meaning at a practical level. This paper presents a family of goodness-of-fit measures, which contains currently used measures such as the pseudo-correlation coefficient and the percent right, and shows how its members are related. More important, it is shown that one of these measures has an interpretation identical to the correlation coefficient of multiple regression in that it can be used to calculate the expected reduction in the root-mean-square prediction error afforded by a model. This goodness-of-fit measure, d, is uniquely defined for binary models, and can be approximated by an easy to calculate consistent statistic, D. For models with more than two alternatives, the same can be done, but the measure depends on the alternative under consideration. The d-measure usually takes values in between the commonly used normalized percent right measure and the pseudo-correlation coefficient.