Semiparametric Multinomial Logit Models for Analysing Consumer Choice Behaviour

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.