Variable Selection in General Multinomial Logit Models

The use of the multinomial logit model is typically restricted to
applications with few predictors, because in high-dimensional
settings maximum likelihood estimates tend to deteriorate. In this
paper we are proposing a sparsity-inducing penalty that accounts
for the special structure of multinomial models. In contrast to
existing methods, it penalizes the parameters that are linked to
one variable in a grouped way and thus yields variable selection
instead of parameter selection. We develop a proximal gradient
method that is able to efficiently compute stable estimates. In
addition, the penalization is extended to the important case of
predictors that vary across response categories. We apply our
estimator to the modeling of party choice of voters in Germany
including voter-specific variables like age and gender but also
party-specific features like stance on nuclear energy and
immigration.