Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/31083 
Year of Publication: 
2006
Series/Report no.: 
Discussion Paper No. 501
Publisher: 
Ludwig-Maximilians-Universität München, Sonderforschungsbereich 386 - Statistische Analyse diskreter Strukturen, München
Abstract: 
The multinomial logit model (MNL) is one of the most frequently used statistical models in marketing applications. It allows 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 proper scoring rules and compare parametric and semiparametric approaches for a number of brand choice data sets.
Subjects: 
mixed models
multinomial logit model
brand choice
penalised splines
proper scoring rules
semiparametric regression
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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