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The Generalized Multinomial Logit Model: Accounting for Scale and Coefficient Heterogeneity

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  • Denzil G. Fiebig

    (School of Economics, University of New South Wales, Sydney, New South Wales 2052, Australia)

  • Michael P. Keane

    (University of Technology Sydney, Sydney, New South Wales 2007; and Arizona State University, Tempe, Arizona 85287)

  • Jordan Louviere

    (School of Marketing, Centre for the Study of Choice, University of Technology Sydney, Sydney, New South Wales 2007, Australia)

  • Nada Wasi

    (School of Finance and Economics, Centre for the Study of Choice, University of Technology Sydney, Sydney, New South Wales 2007, Australia)

Abstract

The mixed or heterogeneous multinomial logit (MIXL) model has become popular in a number of fields, especially marketing, health economics, and industrial organization. In most applications of the model, the vector of consumer utility weights on product attributes is assumed to have a multivariate normal (MVN) distribution in the population. Thus, some consumers care more about some attributes than others, and the IIA property of multinomial logit (MNL) is avoided (i.e., segments of consumers will tend to switch among the subset of brands that possess their most valued attributes). The MIXL model is also appealing because it is relatively easy to estimate. Recently, however, some researchers have argued that the MVN is a poor choice for modelling taste heterogeneity. They argue that much of the heterogeneity in attribute weights is accounted for by a pure scale effect (i.e., across consumers, all attribute weights are scaled up or down in tandem). This implies that choice behaviour is simply more random for some consumers than others (i.e., holding attribute coefficients fixed, the scale of their error term is greater). This leads to a “scale heterogeneity” MNL model (S-MNL). Here, we develop a generalized multinomial logit model (G-MNL) that nests S-MNL and MIXL. By estimating the S-MNL, MIXL, and G-MNL models on 10 data sets, we provide evidence on their relative performance. We find that models that account for scale heterogeneity (i.e., G-MNL or S-MNL) are preferred to MIXL by the Bayes and consistent Akaike information criteria in all 10 data sets. Accounting for scale heterogeneity enables one to account for “extreme” consumers who exhibit nearly lexicographic preferences, as well as consumers who exhibit very “random” behaviour (in a sense we formalize below).

Suggested Citation

  • Denzil G. Fiebig & Michael P. Keane & Jordan Louviere & Nada Wasi, 2010. "The Generalized Multinomial Logit Model: Accounting for Scale and Coefficient Heterogeneity," Marketing Science, INFORMS, vol. 29(3), pages 393-421, 05-06.
  • Handle: RePEc:inm:ormksc:v:29:y:2010:i:3:p:393-421
    DOI: 10.1287/mksc.1090.0508
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    References listed on IDEAS

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