Calibration Performance for the Multinomial Probit Model



Calibration Performance for the Multinomial Probit Model

Authors

GARRIDO RA, Pontificia Universidad Catblica de Chile, Chile

Description

The Multinomial Probit model (MNP) is considered as one of the most robust, flexible, and general modelling frameworks in discrete choice analysis. This is especially true in the transport field due to the presence of correlation between alternatives, het

Abstract

The Multinomial Probit model (MNP) is considered as one of the most robust, flexible, and general modelling frameworks in discrete choice analysis. This is especially true in the transport field due to the presence of correlation between alternatives, heteroskedasticity, dynamic dependence, or spatial interactions. The MNP use has been avoided by many practitioners and researchers due, mainly, to the computational difficulty associated to the evaluation of choice probabilities (multidimensional normal integrals) and the numerical optimisation process involved in the maximisation of the simulated likelihood function (Daganzo, 1979; Sparman, et al, 1981). However, recent developments in Monte Carlo simulation methods and parallel computing (see Geweke et a1 1994; Lam and Mabmassani, 1991) have reduced the computation times significantly. The latter has motivated a renewed interest in the MNP as a modelling tool for real-world applications (see Bolduc, 1999; Garrido, 1998).

The aim of this paper is to provide a set of estimates of the computation time and complexity for different modelÕs characteristics such as number of alternatives, number of attributes, number of observations, variance-covariance structure and utilities functional form.

Two choice probability-simulators were used in the estimation of the calibration performance: GHK, and crude frequency simulator (Hajivassiliou et al, 1996), as they are nowadays the most widely used methods.

A set of calibration performance models are estimated, in order to be used as a mean of approximation of the performance of families of models not considered explicitly in this research.

Publisher

Association for European Transport