A practical test for the choice of mixing distribution in discrete choice models

Fosgerau, Mogens and Bierlaire, Michel (2007): A practical test for the choice of mixing distribution in discrete choice models. Published in: Transportation Research Part B , Vol. 41, (2007): pp. 784-794.

Abstract

The choice of a specific distribution for random parameters of discrete choice models is a critical issue in transportation analysis. Indeed, various pieces of research have demonstrated that an inappropriate choice of the distribution may lead to serious bias in model forecast and in the estimated means of random parameters. In this paper, we propose a practical test, based on seminonparametric techniques. The test is analyzed both on synthetic and real data, and is shown to be simple and powerful.

• Item Type: MPRA Paper
• Language: English
• Keywords: Mixed logit; Random parameters; Nonparametric; Seminonparametric; Hypothesis testing
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C25 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions ; Probabilities

References

Abramowitz, M., Stegun, I.A. (Eds.), 1972. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, nineth ed. Dover, New York.

Algers, S., Bergstrom, P., Dahlberg, M., Dillen, J., 1998. Mixed logit estimation of the value of travel time. Tech. Rep. 1998:15, Uppsala – working paper series, available at <http://ideas.repec.org/p/fth/uppaal/199815.html>.

Bekhor, S., Ben-Akiva, M., Ramming, M.S., 2002. Adaptation of logit kernel to route choice situations. Transportation Research Record 1805, 78–85.

Ben-Akiva, M., Bolduc, D., Walker, J., 2001. Specification, identification, and estimation of the logit kernel (or continuous mixed logit) model. Tech. rep., Department of Civil Engineering, MIT, Cambridge, MA.

Bhat, C.R., Castelar, S., 2002. A unified mixed logit framework for modeling revealed and stated preferences: Formulation and application to congestion pricing analysis in the San Francisco Bay area. Transportation Research Part B 36 (7), 593–616.

Bierens, H.J., in preparation. Semi-nonparametric modeling of densities on the unit interval, with applications to censored mixed proportional hazard models and ordered probability models: Identification and consistency results. Econometric Theory.

Bierlaire, M., 2003. BIOGEME: A free package for the estimation of discrete choice models. In: Proceedings of the third Swiss Transportation Research Conference. Ascona, Switzerland,<www.strc.ch>.

Bierlaire, M., 2005. An introduction to BIOGEME version 1.4, biogeme.epfl.ch.

Brownstone, D., Bunch, D., Train, K., 2000. Joint mixed logit models of stated and revealed preferences for alternative-fuel vehicles. Transportation Research Part B 34, 315–338.

Brownstone, D., Small, K., 2005. Valuing time and reliability: Assessing the evidence from road pricing demonstrations. Transportation Research Part A 39 (4), 279–293.

M. Fosgerau, M. Bierlaire / Transportation Research Part B 41 (2007) 784–794 793

Burge, P., Rohr, C., Vuk, G., Bates, J., 2004. Review of international experience in VOT study design. In: Proceedings of the European Transport Conference.

Carrier, E., 2003. Modeling airline passenger choice: Passenger preference for schedule in the passenger origin–destination simulator (PODS). Ph.D. thesis. Massachusetts Institute of Technology.

Doornik, J.A., 2001. Ox: An Object-Oriented Matrix Language. Timberlake Consultants Press, London. Electric Power Research Institute, 1977. Methodology for predicting the demand for new electricity-using goods. Final report. Project 488- 1 EA-593. Electric Power Research Institute, Palo Alto, CA.

Fosgerau, M., 2005. Unit income elasticity of the value of travel time savings. In: European Transport Conference.

Fosgerau, M., 2006. Investigating the distribution of the value of travel time savings. Transportation Research Part B 40 (8), 688–707.

Fosgerau, M. (2007). Using nonparametrics to specify a model to measure the value of travel time. Transportation Research Part A: Policy and Practice, Volume 41/9, pp. 842-856.

Frejinger, E., Bierlaire, M., 2007. Capturing correlation with subnetworks in route choice models. Transportation Research Part B 41 (3), 363–378.

Gallant, A.R., Nychka, D.W., 1987. Semi-nonparametric maximum likelihood estimation. Econometrica 55 (2), 363–390.

Greene, W.H., Hensher, D.A., Rose, J., 2006. Accounting for heterogeneity in the variance of unobserved effects in mixed logit models. Transportation Research Part B 40 (1), 75–92.

Han, B., Algers, S., Engelson, L., 2001. Accommodating drivers’ taste variation and repeated choice correlation in route choice modeling by using the mixed logit model. In: Eightieth Annual Meeting of the Transportation Research Board.

Hensher, D., Greene, W., 2003. The mixed logit model: The state of practice. Transportation 30 (2), 133–176.

Hess, S., Axhausen, K.W., 2005. Distributional assumptions in the representation of random taste heterogeneity. In: Proceedings of the Fifth Swiss Transportation Research Conference.<www.strc.ch>.

Hess, S., Bierlaire, M., Polak, J., 2005. Estimation of value of travel-time savings using mixed logit models. Transportation Research Part A 39 (3), 221–236.

Hess, S., Polak, J., 2005. Mixed logit modelling of airport choice in multi-airport regions. Journal of Air Transport Management 11 (2), 59–68.

Hess, S., Train, K., Polak, J., 2006. On the use of modified latin hypercube sampling (MLHS) method in the estimation of mixed logit model for vehicle choice. Transportation Research Part B 40 (2), 147–163.

Horowitz, J., 1993. Semiparametric estimation of a work trip mode choice model. Journal of Econometrics 58, 49–70.

Klein, R., Spady, R., 1993. An efficient semiparametric estimator for binary response models. Econometrica 61 (2), 387–422.

McFadden, D., 1978. Modelling the choice of residential location. In: Karlquist, A. et al. (Eds.), Spatial Interaction Theory and Residential Location. North-Holland, Amsterdam, pp. 75–96.

McFadden, D., Train, K., 2000. Mixed MNL models for discrete response. Journal of Applied Econometrics 15 (5), 447–470.

Pagan, A., Ullah, A., 1999. Nonparametric Econometrics. Cambridge University Press.

Revelt, D., Train, K., 1998. Mixed logit with repeated choices: Households’ choices of applicance efficiency level. Review of Economics and Statistics LXXX (4), 647–657.

Small, K.A., Winston, C., Yan, J., 2005. Uncovering the distribution of motorists’ preferences for travel time and reliability. Econometrica 73 (4), 1367–1382.

Train, K., 1998. Recreation demand models with taste differences over people. Land Economics 74 (2), 230–239.

Train, K., 2003. Discrete Choice Methods with Simulation. Cambridge University Press <http://emlab.berkeley.edu/books/choice.html> .

Viton, P.A., 2004. Will mixed logit change urban transport policies? Journal of Transport Economics and Policy 38 (3), 403–423.