A Practical Method to Test the Validity of the Standard Gumbel Distribution in Logit-Based Multinomial Choice Models of Human Travel Behavior

Most multinomial choice models, particularly in practice (e.g., multinomial logit model), assume an extreme-value Gumbel distribution for the random components of utility functions. The use of this distribution offers a closed-form likelihood expression when the utility maximization principle is applied to model choice behaviors. The maximum likelihood estimation method can be easily applied to estimate model coefficients. However, maximum likelihood estimators are consistent and efficient only if distributional assumptions on the random error terms are valid. It is therefore important to test the validity of underlying distributional assumptions that form the basis of parameter estimation and policy evaluation. In this paper, a practical but strict method is proposed to test the distributional assumption of the random component of utility functions in both the multinomial logit (MNL) model and multiple discrete-continuous extreme value (MDCEV) model. Based on a semi-nonparametric approach, a closed-form likelihood function that nests the MNL or MDCEV model being tested is derived. Then, the traditional likelihood ratio test can be applied to test violations of the standard Gumbel distribution assumption. Simulation experiments are conducted to show that the test yields acceptable Type-I and Type-II error probabilities at commonly available sample sizes. The test is then applied to three real-world discrete and discrete-continuous choice models. For all three models, the proposed test rejects the validity of the standard Gumbel distribution in most utility functions, calling for the development of approaches that overcome adverse effects of violations of distributional assumptions.

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• Supplemental Notes:
  • This paper was sponsored by TRB committee ADB40 Standing Committee on Transportation Demand Forecasting.
• Corporate Authors:

  Transportation Research Board

  500 Fifth Street, NW
  Washington, DC  United States  20001
• Authors:
  • Ye, Xin
  • Garikapati, Venu M
  • You, Daehyun
  • Pendyala, Ram M
• Conference:
  • Transportation Research Board 96th Annual Meeting
  • Location: Washington DC, United States
  • Date: 2017-1-8 to 2017-1-12
• Date: 2017

Language

• English

Media Info

• Media Type: Digital/other
• Features: Appendices; Figures; References; Tables;
• Pagination: 21p
• Monograph Title: TRB 96th Annual Meeting Compendium of Papers

Subject/Index Terms

• TRT Terms: Choice models; Distributions (Statistics); Methodology; Simulation; Travel behavior; Validity
• Subject Areas: Planning and Forecasting; Transportation (General);

Filing Info

• Accession Number: 01629510
• Record Type: Publication
• Report/Paper Numbers: 17-05407
• Files: PRP, TRIS, TRB, ATRI
• Created Date: Mar 20 2017 9:23AM