| Generalized extreme value (GEV) models provide a convenient way to model choice behavior that is consistent with utility maximization theory, but the development of specific new models within the GEV family has been slow, due to the difficulty of ensuring new formulations comply with all the GEV rules. The network GEV structure (NetGEV) introduced by Daly and Bierlaire (2006) provides a tool to verify that proposed new models satisfy the GEV conditions, without the burden of complex analysis of the new model to ensure its properties. This dissertation further develops and expands the NetGEV tool. It describes several methodologies for applying constraints to correctly normalize the allocation parameters in such models, allowing parameter identification while ensuring that utilities are not biased due to the network structure. These methods vary depending on the structure of the underlying network.; Additionally, a modification of the allocation parameters is presented, which transforms them to create an alternative set of parameters that are unconstrained. This change also allows the inclusion of data within the allocation formulations, which creates a new heterogeneous network GEV (HeNGEV) model, with the opportunity for heterogeneous covariance structures, while maintaining the closed form probabilities common to GEV models. Including the heterogeneity in the allocation structure, as opposed to the logsum parameters (as in Bhat, 1997), allows variations in both the magnitude and structure of the covariance. This heterogeneity is useful in sub-market analysis, where small differences in the competitive dynamic between alternatives in a segment of the population may drive large changes for revenue management systems or environmental justice evaluations. Various derivatives and elasticities of the HeNGEV model are derived, utilizing the network structure underlying the model to simplify the formulations.; The performance of the HeNGEV model is compared against a homogeneous NetGEV model, using two different synthetic data sets. The first data set is designed to maximize the effect of the heterogeneous error covariance, while the second reduces the effect to a more subtle level. In each case, the HeNGEV model performs better than the NetGEV model, recovering parameters that are closer to their (known) true values, and with improvements in log likelihoods well above a statistically significant threshold. |
