Publication

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

Michel Bierlaire
2017
Conference Papers

Abstract

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.

Official source

https://infoscience.epfl.ch/entities/publication/88b89079-3f5f-404e-bce4-0ee06c2a2dc9

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Michel Bierlaire
2017
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/88b89079-3f5f-404e-bce4-0ee06c2a2dc9

About this result

Related concepts (32)

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.

Estimation theory

Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.

Likelihood function

In statistical inference, the likelihood function quantifies the plausibility of parameter values characterizing a statistical model in light of observed data. Its most typical usage is to compare possible parameter values (under a fixed set of observations and a particular model), where higher values of likelihood are preferred because they correspond to more probable parameter values.

Related publications (32)

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

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