A simple procedure for the calculation of the covariances of any Generalized Extreme Value model

Abstract

This paper illustrates a simple procedure for calculating the covariances underlying any Generalized Extreme Value (GEV) model, based on an appropriate generalization of a result already established in the literature for the Cross-Nested Logit model (i.e. a particular GEV model). Specifically, the paper proves that the covariances in any GEV model are always expressed by a one-dimensional integral, whose integrand function is available in closed form as a function of the generating function of the GEV model. This integral may be simulated very easily with a parsimonious computational burden. Two practical examples are also presented. The first is an application to the CNL model, so as to check the consistency of the proposed method with the results already established in the literature. The second deals with the calculation of the covariances of the Network GEV (NGEV) model: notably, the NGEV is the most general type of GEV model available so far, and its covariances have not yet been calculated. On this basis, insights on the domain of the covariances reproduced by the NGEV model are also presented.