The generalized nested logit model

Abstract

The generalized nested logit (GNL) model is a new member of the generalized extreme value family of models. The GNL provides a higher degree of flexibility in the estimation of substitution or cross-elasticity between pairs of alternatives than previously developed generalized extreme value (GEV) models. The GNL model includes the paired combinatorial logit (PCL) and cross-nested logit (CNL) models as special cases. It also includes the product differentiation (PD) model, which represents the elasticity structure associated with multi-dimensional choices, and the ordered generalized extreme value model, which represents the elasticity structure associated with ordered alternatives, as special cases. The GNL model includes the two-level nested logit (NL) model as a special case and can approximate closely multi-level nested logit models. It accommodates differential cross-elasticity among pairs of alternatives through the fractional allocation of each alternative to a set of nests, each of which has a distinct logsum or dissimilarity parameter. An empirical example of intercity mode choice confirms the statistical superiority of the GNL model to the paired combinatorial logit, cross-nested logit and nested logit models and indicates important differences in cross-elasticity relationships across pairs of alternatives.