Random utility theory represents one of the most common and well-established paradigms for the simulation of discrete choice contexts. Several models have been proposed within this theoretical framework, depending on different assumptions about the joint distribution function of decision makers' perceived utilities. A wide class of random utility models, namely the General Extreme Value (GEV) models defined by McFadden's (1978) theorem, hypothesizes random residuals to follow a multivariate extreme value distribution, assumption leading to interesting and useful model properties. In spite of their diffusion, some fundamental issues concerning the propertiesof GEV models remain unsolved. Mainly, except for GEV models whose correlation structure can be drawn as a tree (i.e. Multinomial and Nested Logit models), the actual covariance figures underlying whatever network correlation structure (i.e. Cross-Nested Logit and RNEV/Network GEV) cannot be expressed through a closed-form statement. This circumstance prevents addressing some theoretical and operative issues, i.e. whether and how a choice context characterized by a known covariance matrix can be reproduced through a GEV model. This paper proposes therefore a systematic analysis of this aspect. The operative importance of the multi-level generalization of the CNL model provided by the Network GEV model has also been investigated. Therefore, through these analyses the paper provides for a general overview of the covariances underlying network-based (i.e. CNL and Network GEV) GEV models, consistently defining some operative rules-of-thumb for the specification of a GEV model able to face a choice context with a given/expected covariance structure.For the covering abstract see ITRD E135582.
Abstract