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  • Ökonometrie

    Prof. Dr. Dietmar Bauer

    © Universität Bielefeld

Using the Composite Likelihood Methods for Estimation of the probit-models

Principal Investigator: Prof. Dr. Dietmar Bauer

Project Duration: 01.01.2018 - 31.12.2021

Transportation demand models are frequently based on discrete choice models with a relatively large choice set. The predominant class of models used for such applications are different variants of random utility models (RUMs), in particular multinomial logit- (MNL) and Probit-(MNP) models.

Some variants of MNL models use mixture models in order to account for unobserved hetergeneity in preferences. Such models are estimated using simulated likelihood maximization, which account for the mixing by averaging a large number of random draws of the parameters representing the preferences of a decider. While the theoretical properties are well known, such methods can be numerically expensive in particular for large panel data sets.

MNP models on the contrary show good modelling capabilities in particular for the correlations of the repeated choices of one decider typical for panel data sets. In this setting the evaluation of multivariate Gaussian CDFs poses a challenge.

The group by Chandra Bhat proposed a solution to this problem in their "maximum composite marginal likelihood" (MaCML) approach. This combines the concept of the composite marginal likelihood of replacing the numerically hard likelihood by a more tractable criterion function with approaches to approximate the Gaussian CDF.

The approach has been demonstrated to be favourable in a number of simulation settings. Analytic results in this respect are not fully available as of the start of the project.

The focus of the project hence is to investigate the properties of the MaCML approach with respect to (i) asymptotic bias, (ii) relative efficiency depending on the specification of the CML as well as (iii) the power of model selection procedures based on the MaCML approach.

Beside the methodological goals of the project we also want to apply the approach to modelling the choice of the mobility motif of people. The motif summarizes the mobility of a person within a day. Empirically it has been demonstrated that out of a large number of motifs only a few (approximately 12-17) are actually often used by people. There appears to be a remarkable stabilty of the distribution of the motifs making them a prime canidate for modeling the dependence of the motif choice on the socio-demongraphic characteristics of the decider.

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