Use of composite likelihood methods for the estimation of probit models

• Applicant: Professor Dr. Dietmar Bauer
• Subject Area: Statistics and Econometrics ; Urbanism, Spatial Planning, Transportation and Infrastructure Planning, Landscape Planning
• Term: from 2017 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 356500581

Mobility demand models are usually based on discrete choice models with often a large number of choice alternatives. The predominant model classes are constituted by the multinomial logit (MNL) and -probit (MNP) models. For different flavors of (mixed) MNL model numerically and statistically efficient estimation algorithms exist based on the (simulated) maximum likelihood paradigm which, however, show disadvantages with respect to the representation of correlation between the random utility terms for different alternatives as well as the choice of the mixing distributions. For large data sets a large number of simulations are needed in order to ensure consistency and asymptotic efficiency of the estimators. MNP models on the other hand in particular in a panel context provide good modeling capabilities, however, lead to numerically demanding estimation problems as these necessitate the evaluation of high dimensional Gaussian cumulative distribution functions (CDF). As an alternative the group around Chandra Bhat proposed the "maximum composite marginal likelihood" (MaCML) approach linking two ideas: the likelihood is replaced by a so called "composite marginal likelihood" (CML) and second the Gaussian CDF is analytically approximated. Bhat's proposal has up to now only been motivated by a number of simulation exercises. A thorough theoretical investigation is currently not available. Investigating simple examples it can be verified easily that the MaCML approach does not guarantee consistent estimation. Also the particular choice of the approximation method used by Bhat as well as the chosen CML has been criticised. Thus this project will deal with a detailed investigation of the properties of estimator on the basis of the MaCML idea, examining the effects of the choice of the CML function and the CDF approximation with respect to (i) the asymptotic bias, (ii) the relative efficiency and (iii) the properties of model selection procedures based on the MaCML estimation. It is the main goal of this project to develop numerically efficient and statistically sound estimation procedures (including adequate initialisation routines) for MNP-models in panel data settings showing a large number of alternatives. The methods developed within the project will be used to investigate the determinants of the choice of so called motifs (representations of the trips of a day of an individual as directed graphs). In a number of different data sets in different cities it has been shown that out of a potentially large number of motifs people only choose one out of 17 motifs. Currently there is little knowledge as to the determinants underlying this choices as well as the dependence on sociodemographic characteristics. Additionally the temporal evolution of the relative frequency of choice are unknown. This knowledge is of importance for the development of activity based mobility demand models.

• DFG Programme: Research Grants