Discrete-continuous maximum likelihood for the estimation of nested logit models

In this paper we aim at integrating the selection of a nesting structure to the maximum likelihood framework of the parameter estimation. Given a finite set of nesting structures, the traditional approach is to estimate the models corresponding to each of them and select a posteriori the most appropriate one based on some fit statistics and informal testing procedures. However, the number of possible nesting structures grows as a function of the number of alternatives. Our approach simultaneously solves the problem of selecting the optimal nesting structure and estimating its corresponding parameters with maximum likelihood. We call this discrete-continuous maximum likelihood (DCML). We are able to linearize the logarithm in the objective function so that it results in a mixed integer linear problem.