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Semiparametric multinomial logit models for analysing consumer choice behaviour

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Abstract

The multinomial logit model (MNL) is one of the most frequently used statistical models in marketing applications. It allows one to relate an unordered categorical response variable, for example representing the choice of a brand, to a vector of covariates such as the price of the brand or variables characterising the consumer. In its classical form, all covariates enter in strictly parametric, linear form into the utility function of the MNL model. In this paper, we introduce semiparametric extensions, where smooth effects of continuous covariates are modelled by penalised splines. A mixed model representation of these penalised splines is employed to obtain estimates of the corresponding smoothing parameters, leading to a fully automated estimation procedure. To validate semiparametric models against parametric models, we utilise different scoring rules as well as predicted market share and compare parametric and semiparametric approaches for a number of brand choice data sets.

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Authors and Affiliations

  1. Department of Statistics, Ludwig-Maximilians-University, 80539, Munich, Germany

    Thomas Kneib

  2. University of Regensburg, Universitätsstrasse 31, 93053, Regensburg, Germany

    Bernhard Baumgartner & Winfried J. Steiner

Authors
  1. Thomas Kneib
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  2. Bernhard Baumgartner
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  3. Winfried J. Steiner
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Correspondence to Thomas Kneib.

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Kneib, T., Baumgartner, B. & Steiner, W.J. Semiparametric multinomial logit models for analysing consumer choice behaviour . AStA 91, 225–244 (2007). https://doi.org/10.1007/s10182-007-0033-2

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  • DOI: https://doi.org/10.1007/s10182-007-0033-2

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