A new flexible multiple discrete–continuous extreme value (MDCEV) choice model

• Published in: Transportation research. Part B: methodological Vol. 110; pp. 261 - 279
• Main Author: Bhat, Chandra R.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01-04-2018; Elsevier Science Ltd
• Subjects: Closed form solutions; Consumer theory; Consumption; Data processing; Discrete element method; Exact solutions; Extreme values; Forecasting; Mathematical models; Multiple discrete–continuous choice models; Multiple discrete–continuous extreme value model; Parameter identification; Probability; Studies; Time use; Utilities; Utility theory; Consumer theory; Utility theory; Time use; Multiple discrete–continuous extreme value model; Multiple discrete–continuous choice models
• ISSN: 0191-2615; 1879-2367
• DOI: 10.1016/j.trb.2018.02.011

•Proposes a new flexible MDC model breaking the tight linkage between discrete and continuous choices.•Develops a closed-form model for our new utility-based formulation.•Formulates new forecasting approaches for the model.•Undertakes empirical comparison of performance of proposed model with traditional MDCEV model.
Traditional multiple discrete–continuous (MDC) models generally predict the continuous consumption quantity component reasonably component well, but not necessarily the discrete choice component. In this paper, we propose, for the first time, a new flexible closed-form MDCEV model that breaks the tight linkage between the discrete and continuous choice dimensions of the traditional MDC models. We do so by (1) employing a linear utility function of consumption for the first outside good (which removes the continuous consumption quantity of the outside good from the discrete consumption decision, and also helps in forecasting), and (2) using separate baseline utilities for the discrete and continuous consumption decisions. In the process of proposing our new formulation, we also revisit two issues related to the traditional MDC model. The first relates to clarification regarding the identification of the scale parameter of the error terms, and the second relates to the probability of the discrete choice component of the traditional MDC model (that is, the multivariate probability of consumption or not of the alternatives). We show why the scale parameter of the error terms is indeed estimable when a γ-profile is used, as well as show how one may develop a closed-form expression for the discrete choice consumption probability. The latter contribution also presents a methodology to estimate pure multiple discrete choice models without the need for information on the continuous consumptions. Finally, we also develop forecasting procedures for our new MDC model structure.
We demonstrate an application of the proposed model to the case of time-use of individuals. In a comparative empirical assessment of the fit from the proposed model and from the traditional MDCEV models, our proposed model performs better in terms of better predicting both the discrete outcome data as well as the continuous consumptions.