The Factor of Revisited Path Size Alternative Derivation

The concept of path size attempts to capture correlations among routes in route choice modeling by including a correction term in the multinormial logit formulation. Several correction terms were proposed in the literature, yet no satisfactory derivation based on theoretical arguments is presented, raising doubts about the correct specification of the correction terms. This paper proposes the detailed and systematic derivation of a new formulation of the measure of path size and explicitly defines the assumptions involved in its derivation. The path size correction (PSC) factor results from the notion of aggregate alternative as well from the simplification of nested logit models. The new measure of path size offers a more natural interpretation of the correlation due to spatial overlap of alternative routes. Estimation of PSC-logit models in two real-world networks and calculation of predicted choice probabilities in synthetic networks allow comparison of the new path size measure with respect to the classic one. Estimates show similar performances between the models, and predictions illustrate better performances of the new version of the path size factor.