Using penalized likelihood to select parameters in a random coefficients multinomial logit model

Abstract

This paper is about estimating a random coefficients logit model in which the distribution of each coefficient is characterized by finitely many parameters, some of which may be zero. The paper gives conditions under which, with probability approaching 1 as the sample size increases, penalized maximum likelihood (PML) estimation with the adaptive LASSO (AL) penalty distinguishes correctly between zero and non-zero parameters. The paper also gives conditions under which PML reduces the asymptotic mean-square estimation error of any continuously differentiable function of the model’s parameters. The paper describes a method for computing PML estimates and presents the results of Monte Carlo experiments that illustrate their performance. It also presents the results of PML estimation of a random coefficients logit model of choice among brands of butter and margarine in the British groceries market.