The paired combinatorial logit model: properties, estimation and application

The Independence of Irrelevant Alternatives (IIA) property of the multinomial logit (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 share the same unobserved attributes. The nested logit (NL) model relaxes the zero covariance restriction of the MNL model but imposes the restriction of equal covariance among all alternatives in a common nest and zero covariance otherwise. The paired combinatorial logit (PCL) model relaxes these restrictions further by allowing different covariances for each pair of alternatives. This relaxation enables the estimation of differential competitive relationships between each pair of alternatives. The closed form of the PCL model retains the computational advantages of other logit models while the more flexible error correlation structure, compared to the MNL model and NL models, enables better representation of many choice situations. This paper describes the derivation, structure, properties and estimation of the PCL model. The empirical results demonstrate that the PCL model is statistically superior to the MNL and NL models and may lead to importantly different travel forecasts and policy decisions.