Goodness-of-fit measures for probabilistic travel demand models

This paper is concerned with the assessment of the goodness-of-fit of nonlinear models of the type currently being used in the development of the disaggregate, behavioral travel demand approach. These models are emerging as a potential new technique for many transportation planning problems, although much research is yet needed before they are sufficiently developed for operational use. In order to pursue the necessary research, and also for the later assessment of operational models, it is necessary to have adequate measures of the goodness-of-fit. The paper examines the adequacy of standard measures of goodness-of-fit as applied to any nonlinear estimating equation and they are found to be inappropriate and inadequate. A little-known statistic, called the correlation ratio, is then defined and derived, and is explored as a substitute for the standard measures. In both theoretical and empirical tests, the correlation ratio is found to be a significantly more useful and appropriate measure of goodness-of-fit. Some further properties of the correlation ratio are examined, and the ratio is found to possess some degree of arbitrariness when applied to typical travel demand models. This arbitrariness, however, only impairs the usefulness of the correlation ratio in the absolute assessment of a model, but not for the comparative assessment of two or more models. Finally, a number of research tasks, relating to the correlation ratio, are identified.