AStA Advances in Statistical Analysis

, Volume 91, Issue 3, pp 225–244 | Cite as

Semiparametric multinomial logit models for analysing consumer choice behaviour

  • Thomas KneibEmail author
  • Bernhard Baumgartner
  • Winfried J. Steiner
Original Paper


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.


Brand choice Conditional logit model Mixed models Multinomial logit model Penalised splines Proper scoring rules Semiparametric regression  


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Thomas Kneib
    • 1
    Email author
  • Bernhard Baumgartner
    • 2
  • Winfried J. Steiner
    • 2
  1. 1.Department of StatisticsLudwig-Maximilians-UniversityMunichGermany
  2. 2.University of RegensburgRegensburgGermany

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