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Discrete choice models with multiplicative error terms

Fosgerau, Mogens and Bierlaire, Michel (2009): Discrete choice models with multiplicative error terms. Published in: Transportation Research Part B , Vol. 43, No. 5 (2009): pp. 494-505.

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Abstract

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 e. 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 e 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.

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