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Multiple discrete-continuous choice models with bounds on consumptions

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  • Saxena, Shobhit
  • Pinjari, Abdul Rawoof
  • Roy, Ananya
  • Paleti, Rajesh

Abstract

This paper derives a multiple discrete–continuous (MDC) choice model formulation with constraints that specify upper bounds on consumption. To do so, considering the conventional utility maximization problem of a consumer, the Karush-Kuhn-Tucker (KKT) conditions are laid out for the MDC model with a general set of linear constraints that include inequalities. Subsequently, we derive a model with constraints that accommodate upper bounds on consumptions and an additive utility structure that accommodates lower bounds on consumptions. The likelihood expression for the proposed model takes a closed form. Furthermore, we extend the formulation to impose bounds on an MDC choice model with activity episode-level choice alternatives that accommodates a logical ordering among different episodes of an activity. The proposed models are derived for two different specifications of the outside good utility – (1) nonlinear utility with respect to consumption and (2) linear utility with respect to consumption. The proposed models are applied to an empirical context to analyze activity-level as well as episode-level activity participation and time allocation while considering bounds on time allocations. Empirical results suggest that the models that consider upper bounds on consumption offer a better fit to data, avoid predictions of unrealistically large time allocations, and result in overall better predictions than those from models without bounds. The proposed models are useful in situations, such as microsimulation models of travel demand, where it is crucial to avoid unrealistically large predictions.

Suggested Citation

  • Saxena, Shobhit & Pinjari, Abdul Rawoof & Roy, Ananya & Paleti, Rajesh, 2021. "Multiple discrete-continuous choice models with bounds on consumptions," Transportation Research Part A: Policy and Practice, Elsevier, vol. 149(C), pages 237-265.
  • Handle: RePEc:eee:transa:v:149:y:2021:i:c:p:237-265
    DOI: 10.1016/j.tra.2021.03.016
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    References listed on IDEAS

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    1. Bhat, Chandra R. & Mondal, Aupal & Asmussen, Katherine E. & Bhat, Aarti C., 2020. "A multiple discrete extreme value choice model with grouped consumption data and unobserved budgets," Transportation Research Part B: Methodological, Elsevier, vol. 141(C), pages 196-222.
    2. Bhat, Chandra R., 2018. "A new flexible multiple discrete–continuous extreme value (MDCEV) choice model," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 261-279.
    3. Pinjari, Abdul Rawoof & Bhat, Chandra, 2021. "Computationally efficient forecasting procedures for Kuhn-Tucker consumer demand model systems: Application to residential energy consumption analysis," Journal of choice modelling, Elsevier, vol. 39(C).
    4. Caleb Van Nostrand & Vijayaraghavan Sivaraman & Abdul Pinjari, 2013. "Analysis of long-distance vacation travel demand in the United States: a multiple discrete–continuous choice framework," Transportation, Springer, vol. 40(1), pages 151-171, January.
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    8. Astroza, Sebastian & Bhat, Aarti C., 2016. "On allowing a general form for unobserved heterogeneity in the multiple discrete–continuous probit model: Formulation and application to tourism travelAuthor-Name: Bhat, Chandra R," Transportation Research Part B: Methodological, Elsevier, vol. 86(C), pages 223-249.
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    1. Saxena, Shobhit & Pinjari, Abdul Rawoof & Bhat, Chandra R., 2022. "Multiple discrete-continuous choice models with additively separable utility functions and linear utility on outside good: Model properties and characterization of demand functions," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 526-557.
    2. Saxena, Shobhit & Pinjari, Abdul Rawoof & Paleti, Rajesh, 2022. "A multiple discrete-continuous extreme value model with ordered preferences (MDCEV-OP): Modelling framework for episode-level activity participation and time-use analysis," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 259-283.

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