The paired combinatorial logit model: properties, estimation and application

The Independence of Irrelevant Alternatives (IIA) property of the multinomi al legit (MNL) model imposes the restriction of zero covariance between the utilities of pairs of alternatives. This restriction is inappropriate for many choice situations; those in which some pairs or sets of alternatives s hare the same unobserved attributes. The nested legit (NL) model relaxes th e zero covariance restriction of the MNL model but imposes the restriction of equal covariance among all alternatives in a common nest and zero covari ance otherwise. The paired combinatorial legit (PCL) model relaxes these re strictions further by allowing different covariances for each pair of alter natives. This relaxation enables the estimation of differential competitive relationships between each pair of alternatives. The closed form of the PC L model retains the computational advantages of other legit models while th e more flexible error correlation structure, compared to the MNL model and NL models, enables better representation of many choice situations. This pa per describes the derivation, structure, properties and estimation of the P CL model. The empirical results demonstrate that the PCL model is statistic ally superior to the MNL and NL models and may lead to importantly differen t travel forecasts and policy decisions. (C) 2000 Elsevier Science Ltd. All rights reserved.