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

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  • Marzano, Vittorio

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.

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  • Marzano, Vittorio, 2014. "A simple procedure for the calculation of the covariances of any Generalized Extreme Value model," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 151-162.
    • Handle: RePEc:eee:transb:v:70:y:2014:i:c:p:151-162
    DOI: 10.1016/j.trb.2014.08.011
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    Cited by:

    1. Tinessa, Fiore & Marzano, Vittorio & Papola, Andrea, 2020. "Mixing distributions of tastes with a Combination of Nested Logit (CoNL) kernel: Formulation and performance analysis," Transportation Research Part B: Methodological, Elsevier, vol. 141(C), pages 1-23.
    2. Papola, Andrea, 2016. "A new random utility model with flexible correlation pattern and closed-form covariance expression: The CoRUM," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 80-96.
    3. Papola, Andrea & Tinessa, Fiore & Marzano, Vittorio, 2018. "Application of the Combination of Random Utility Models (CoRUM) to route choice," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 304-326.
    4. Fiore Tinessa & Vittorio Marzano & Andrea Papola, 2021. "Choice probabilities and correlations in closed-form route choice models: specifications and drawbacks," Papers 2110.07224, arXiv.org.
    5. Tinessa, Fiore, 2021. "Closed-form random utility models with mixture distributions of random utilities: Exploring finite mixtures of qGEV models," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 262-288.

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