Representation of heteroskedasticity in discrete choice models
AbstractThe Multinomial Logit, discrete choice model of transport demand, has several restrictions when compared with the more general Multinomial Probit model. The most famous of these are that unobservable components of utilities should be mutually independent and homoskedastic. Correlation can be accommodated to a certain extent by the Hierarchical Logit model, but the problem of heteroskedasticity has received less attention in the literature. We investigate the consequences of disregarding heteroskedasticity, and make some comparisons between models that can and those that cannot represent it. These comparisons, which use synthetic data with known characteristics, are made in terms of parameter recovery and estimates of response to policy changes. The Multinomial Logit, Hierarchical Logit, Single Element Nested Logit, Heteroskedastic Extreme Value Logit and Multinomial Probit models are tested using data that are consistent with various error structures; only the last three can represent heteroskedasticity explicitly. Two different kinds of heteroskedasticity are analysed: between options and between observations. The results show that in the first case, neither the Multinomial Logit nor the Single Element Nested Logit models can be used to estimate the response to policy changes accurately, but the Hierarchical Logit model performs surprisingly well. By contrast, in a certain case of discrete heteroskedasticity between observations, the simulation results show that in terms of response to policy variations the Multinomial Logit model performs as well as the theoretically correct Single Element Nested Logit and Multinomial Probit models. Furthermore, the Multinomial Logit Model recovered all parameters of the utility function accurately in this case. We conclude that the simpler members of the Logit family appear to be fairly robust with respect to some homoskedasticity violations, but that use of the more resource-intensive Multinomial Probit model is justified for handling the case of heteroskedasticity between options.
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Bibliographic InfoArticle provided by Elsevier in its journal Transportation Research Part B: Methodological.
Volume (Year): 34 (2000)
Issue (Month): 3 (April)
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- Bolduc, Denis, 1999. "A practical technique to estimate multinomial probit models in transportation," Transportation Research Part B: Methodological, Elsevier, vol. 33(1), pages 63-79, February.
- Kenneth E. Train, 1998. "Recreation Demand Models with Taste Differences over People," Land Economics, University of Wisconsin Press, vol. 74(2), pages 230-239.
- Vassilis A. Hajivassiliou & Axel Borsch-Supan, 1990.
"Smooth Unbiased Multivariate Probability Simulators for Maximum Likelihood Estimation of Limited Dependent Variable Models,"
Cowles Foundation Discussion Papers
960, Cowles Foundation for Research in Economics, Yale University.
- Borsch-Supan, Axel & Hajivassiliou, Vassilis A., 1993. "Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models," Journal of Econometrics, Elsevier, vol. 58(3), pages 347-368, August.
- Vassilis A. Hajivassiliou & Daniel L. McFadden & Paul Ruud, 1993.
"Simulation of Multivariate Normal Rectangle Probabilities and their Derivatives: Theoretical and Computational Results,"
_024, Yale University.
- Hajivassiliou, Vassilis & McFadden, Daniel & Ruud, Paul, 1996. "Simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 85-134.
- Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
- McFadden, Daniel, 1989.
"A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration,"
Econometric Society, vol. 57(5), pages 995-1026, September.
- Daniel McFadden, 1987. "A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration," Working papers 464, Massachusetts Institute of Technology (MIT), Department of Economics.
- Bolduc, Denis, 1992. "Generalized autoregressive errors in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 26(2), pages 155-170, April.
- Daly, Andrew, 1987. "Estimating "tree" logit models," Transportation Research Part B: Methodological, Elsevier, vol. 21(4), pages 251-267, August.
- Stern, Steven, 1992. "A Method for Smoothing Simulated Moments of Discrete Probabilities in Multinomial Probit Models," Econometrica, Econometric Society, vol. 60(4), pages 943-52, July.
- Steckel, Joel H & Vanhonacker, Wilfried R, 1988. "A Heterogeneous Conditional Logit Model of Choice," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(3), pages 391-98, July.
- Bhat, Chandra R., 1995. "A heteroscedastic extreme value model of intercity travel mode choice," Transportation Research Part B: Methodological, Elsevier, vol. 29(6), pages 471-483, December.
- Bhat, Chandra R., 1998. "Accommodating flexible substitution patterns in multi-dimensional choice modeling: formulation and application to travel mode and departure time choice," Transportation Research Part B: Methodological, Elsevier, vol. 32(7), pages 455-466, September.
- Cantillo, Víctor & Heydecker, Benjamin & de Dios Ortúzar, Juan, 2006. "A discrete choice model incorporating thresholds for perception in attribute values," Transportation Research Part B: Methodological, Elsevier, vol. 40(9), pages 807-825, November.
- Kalouptsidis, N. & Koutroumbas, K. & Psaraki, V., 2007. "Classification methods for random utility models with i.i.d. disturbances under the most probable alternative rule," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1778-1794, February.
- Cantillo, Víctor & Ortúzar, Juan de Dios, 2005. "A semi-compensatory discrete choice model with explicit attribute thresholds of perception," Transportation Research Part B: Methodological, Elsevier, vol. 39(7), pages 641-657, August.
- Cantillo, Víctor & Amaya, Johanna & Ortúzar, J. de D., 2010. "Thresholds and indifference in stated choice surveys," Transportation Research Part B: Methodological, Elsevier, vol. 44(6), pages 753-763, July.
- Tsamboulas, Dimitrios A., 2001. "Parking fare thresholds: a policy tool," Transport Policy, Elsevier, vol. 8(2), pages 115-124, April.
- Espino, Raquel & de Dios Ortúzar, Juan & Román, Concepción, 2007. "Understanding suburban travel demand: Flexible modelling with revealed and stated choice data," Transportation Research Part A: Policy and Practice, Elsevier, vol. 41(10), pages 899-912, December.
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