Discrete choice models with multiplicative error terms

• Published in: Transportation research. Part B: methodological Vol. 43; no. 5; pp. 494 - 505
• Main Authors: Fosgerau, M., Bierlaire, M.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.06.2009; Elsevier
• Series: Transportation Research Part B: Methodological
• Subjects: Applied sciences; Discrete choice; Discrete choice Multiplicative specification Multivariate extreme value Random scale Heteroscedasticity; Exact sciences and technology; Ground, air and sea transportation, marine construction; Heteroscedasticity; Multiplicative specification; Multivariate extreme value; Random scale; Multiplicative specification; Multivariate extreme value; Discrete choice; Random scale; Heteroscedasticity; Empirical method; Theoretical study; Specification; Multivariate analysis; Random distribution; Modeling; Multiplicative logic; Extreme value; Formulation; Application
• ISSN: 0191-2615; 1879-2367
• DOI: 10.1016/j.trb.2008.10.004

The conditional indirect utility of many random utility maximization (RUM) discrete choice models is specified as a sum of an index V depending on observables and an independent random term ε . In general, the universe of RUM consistent models is much larger, even fixing some specification of V due to theoretical and practical considerations. In this paper, we explore an alternative RUM model where the summation of V and ε is replaced by multiplication. This is consistent with the notion that choice makers may sometimes evaluate relative differences in V between alternatives rather than absolute differences. We develop some properties of this type of model and show that in several cases the change from an additive to a multiplicative formulation, maintaining a specification of V, may lead to a large improvement in fit, sometimes larger than that gained from introducing random coefficients in V.