Incorporating variance and covariance heterogeneity in the Generalized Nested Logit model: an application to modeling long distance travel choice behavior

The assumption of independently and identically distributed (IID) error terms in the Multinomial Logit (MNL) model leads to its infamous IIA property. Relaxation of the IID assumption has been undertaken along a number of isolated dimensions leading to the development of a rich set of discrete choice models, that are more flexible than the MNL model. In some cases, these more general models lose the mathematically convenient closed-form structure of the MNL. In this paper, we combine the most flexible isolated closed-form extensions of the MNL and Nested Logit (NL) models in an integrated model structure to yield a behaviorally rich, yet computationally tractable choice model. Specifically, we combine the Generalized Nested Logit model that allows for non-independent errors, the Heteroscedastic MNL which allows non-constant errors across observations, and the Covariance Heterogeneous NL model which allows for non-constant correlation structure across observations. The resulting model, called the Heterogeous GNL model extends our ability to represent the complex behavioral processes involved in choice decision-making. The value and need for the additional modeling complexity of the HGNL model is tested in the empirical context of mode and rail service class choice behavior for long distance intercity travel. An incremental modeling approach is adopted, i.e., we start from the simple MNL model and sequentially relax some of its restrictive assumptions to estimate progressively more flexible model structures. The statistical fit and behavioral appeal of the estimated models improve substantially with each additional relaxation, strongly supporting the concept of integrating isolated generalizations.