skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A practical method to test the validity of the standard Gumbel distribution in logit-based multinomial choice models of travel behavior

Abstract

Most multinomial choice models (e.g., the multinomial logit model) adopted in practice assume an extreme-value Gumbel distribution for the random components (error terms) of utility functions. This distributional assumption offers a closed-form likelihood expression when the utility maximization principle is applied to model choice behaviors. As a result, model coefficients can be easily estimated using the standard maximum likelihood estimation method. However, maximum likelihood estimators are consistent and efficient only if distributional assumptions on the random error terms are valid. It is therefore critical to test the validity of underlying distributional assumptions on the error terms that form the basis of parameter estimation and policy evaluation. In this paper, a practical yet statistically rigorous method is proposed to test the validity of the distributional assumption on the random components 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. The proposed method allows traditional likelihood ratio tests to be used to test violations of the standard Gumbel distribution assumption. Simulation experiments are conducted to demonstrate that the proposed test yields acceptable Type-I andmore » 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 robust choice models that overcome adverse effects of violations of distributional assumptions on the error terms in random utility functions.« less

Authors:
 [1];  [2];  [3];  [4]
  1. Tongji Univ., Shanghai (China)
  2. National Renewable Energy Lab. (NREL), Golden, CO (United States)
  3. Maricopa Association of Governments, Phoenix, AZ (United States)
  4. Arizona State Univ., Tempe, AZ (United States)
Publication Date:
Research Org.:
National Renewable Energy Lab. (NREL), Golden, CO (United States)
Sponsoring Org.:
USDOE Office of Energy Efficiency and Renewable Energy (EERE)
OSTI Identifier:
1413182
Report Number(s):
NREL/JA-5400-70645
Journal ID: ISSN 0191-2615
Grant/Contract Number:
AC36-08GO28308
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Transportation Research, Part B: Methodological
Additional Journal Information:
Journal Volume: 106; Journal Issue: C; Journal ID: ISSN 0191-2615
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
30 DIRECT ENERGY CONVERSION; travel behavior models; discrete choice models; violations of distributional assumptions; test of validity of distributional assumption; multinomial logit model; multiple discrete-continuous extreme value model

Citation Formats

Ye, Xin, Garikapati, Venu M., You, Daehyun, and Pendyala, Ram M.. A practical method to test the validity of the standard Gumbel distribution in logit-based multinomial choice models of travel behavior. United States: N. p., 2017. Web. doi:10.1016/j.trb.2017.10.009.
Ye, Xin, Garikapati, Venu M., You, Daehyun, & Pendyala, Ram M.. A practical method to test the validity of the standard Gumbel distribution in logit-based multinomial choice models of travel behavior. United States. doi:10.1016/j.trb.2017.10.009.
Ye, Xin, Garikapati, Venu M., You, Daehyun, and Pendyala, Ram M.. 2017. "A practical method to test the validity of the standard Gumbel distribution in logit-based multinomial choice models of travel behavior". United States. doi:10.1016/j.trb.2017.10.009.
@article{osti_1413182,
title = {A practical method to test the validity of the standard Gumbel distribution in logit-based multinomial choice models of travel behavior},
author = {Ye, Xin and Garikapati, Venu M. and You, Daehyun and Pendyala, Ram M.},
abstractNote = {Most multinomial choice models (e.g., the multinomial logit model) adopted in practice assume an extreme-value Gumbel distribution for the random components (error terms) of utility functions. This distributional assumption offers a closed-form likelihood expression when the utility maximization principle is applied to model choice behaviors. As a result, model coefficients can be easily estimated using the standard maximum likelihood estimation method. However, maximum likelihood estimators are consistent and efficient only if distributional assumptions on the random error terms are valid. It is therefore critical to test the validity of underlying distributional assumptions on the error terms that form the basis of parameter estimation and policy evaluation. In this paper, a practical yet statistically rigorous method is proposed to test the validity of the distributional assumption on the random components 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. The proposed method allows traditional likelihood ratio tests to be used to test violations of the standard Gumbel distribution assumption. Simulation experiments are conducted to demonstrate that the proposed 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 robust choice models that overcome adverse effects of violations of distributional assumptions on the error terms in random utility functions.},
doi = {10.1016/j.trb.2017.10.009},
journal = {Transportation Research, Part B: Methodological},
number = C,
volume = 106,
place = {United States},
year = 2017,
month =
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on November 8, 2018
Publisher's Version of Record

Save / Share:
  • Relationships among mine and injured miner characteristics and degrees of injury are examined for 91 404 injuries in underground bituminous coal mines in the United States from 1975 through 1982. Injury severity varies by the mining system, geographical region, circumstances surrounding the injury, the injured miner's age, whether the miner was using powered equipment, the year in which the injury occurred and the location in the mine where the injury happened. Injury severity is not related to the injured miner's total mining experience, job experience and experience in the mine in which the injury occurred.
  • The author develops a likelihood test to see if conditional logit in aggregate energy-choice models is appropriate for predicting the probability that alternative residential fuels will be purchased. Among the array of probability models available, the conditional logit model is the least valid because it is rejected by the data. Generalized logit models are more useful because they consider price, availability, and other factors. 27 references, 1 table.
  • As part of a larger evaluation we attempted to measure the detective quantum efficiency (DQE) of an amorphous silicon flat-panel detector using the method described in the International Electrotechnical Commission standard 62220-1 published in October 2003. To achieve the radiographic beam conditions specified in the standard, we purchased scientific-grade ultrahigh purity aluminum (99.999% purity, type-11999 alloy) filters in thicknesses ranging from 0.1 through 10.0 mm from a well-known, specialty metals supplier. Qualitative evaluation of flat field images acquired at 71 kV (RQA5 beam quality) with 21 mm of ultrahigh purity aluminum filtration demonstrated a low frequency mottle that was reproduciblemore » and was not observed when the measurement was repeated at 74 kV (RQA5 beam quality) with 21 mm of lower-purity aluminum (99.0% purity, type-1100 alloy) filtration. This finding was ultimately attributed to the larger grain size (approximately 1-2 mm) of high purity aluminum metal, which is a well-known characteristic, particularly in thicknesses greater than 1 mm. The impact of this low frequency mottle is to significantly overestimate the noise power spectrum (NPS) at spatial frequencies {<=}0.2 mm{sup -1}, which in turn would cause an underestimation of the DQE in this range. A subsequent evaluation of ultrahigh purity aluminum, purchased from a second source, suggests, that reduced grain size can be achieved by the process of annealing. Images acquired with this sample demonstrated vertical striated nonuniformities that are attributed to the manufacturing method and which do not appear to appreciably impact the NPS at spatial frequencies {>=}0.5 mm{sup -1}, but do result in an asymmetry in the x- and y-NPS at spatial frequencies {<=}0.2 mm{sup -1}. Our observations of markedly visible nonuniformities in images acquired with high purity aluminum filtration suggest that the uniformity of filter materials should be carefully evaluated and taken into consideration when measuring the DQE.« less
  • The (Cs,O)-activation procedure for p-GaAs(Cs,O)-photocathodes was studied with the aim of demarcating the domains of validity for the two practical models of the (Cs,O)-activation layer: The dipole layer (DL) model and the heterojunction (HJ) model. To do this, the photocathode was activated far beyond the normal maximum of quantum efficiency, and several photocathode parameters were measured periodically during this process. In doing so, the data obtained enabled us to determine the domains of validity for the DL- and HJ-models, to define more precisely the characteristic parameters of the photocathode within both of these domains and thus to reveal the peculiaritiesmore » of the influence of the (Cs,O)-layer on the photoelectron escape probability.« less
  • This method covers the calculation of the carbon distribution and ring content of olefin-free petroleum oils from measurements of refractive index, density and molecular weight (n-d-M). This method should not be applied to oils whose compositions are outside the following ranges: carbon distribution: up to 75% carbon atoms in ring structure; percentage in aromatic rings not larger than 1.5 times the percentage in naphthenic rings; ring content: up to four rings per molecule, with not more than half of them aromatic. A correction must be applied for oils containing significant quantities of sulfur. The refractive index and density of themore » oil are determined at 20/sup 0/C. The molecular weight is determined experimentally or estimated from measurements of viscosity at 100 and 210/sup 0/F (37.8 and 100/sup 0/C). These data are then used to calculate the carbon distribution (aromatic ring structure %C/sub A/ naphthene ring structure %C/sub N/, and paraffin chains %C/sub p/) or the ring analysis (R/sub A/, R/sub N/) using the appropriate set of equations.« less