Mixed Logit (or Logit Kernel) Model: Dispelling Misconceptions of Identification

Abstract

Mixed logit is a discrete choice model that has both probit-like disturbances and an additive independent and identically distributed extreme value (or Gumbel) disturbance à la multinomial logit. The result is an intuitive, practical, and powerful model that combines the flexibility of probit (and more) with the tractability of logit. For that reason mixed logit has been deemed the “model of the future” and is becoming extremely popular in the literature. It has been experimented with in almost all stages of transportation modeling and has been included in widely used statistical software packages as well as a recent edition of a popular econometrics textbook. Although the basic structure of mixed logit models is well understood, there are important identification issues that are often overlooked. Misunderstanding these issues can lead to biased estimates as well as a significant loss of fit. Some misconceptions concerning identification of mixed logit models that have led to misspecified models in the literature are highlighted. The purpose is simply to whet the appetite for the identification issue. The important idea presented here is that seemingly obvious specifications and estimation practices (starting with a multinomial logit specification and adding random parameters) can have unintended consequences. Technical details are not provided; rather the emphasis is on highlighting some of the interesting identification issues and providing empirical and conceptual supporting arguments. Readers interested in rigorous arguments behind these results are encouraged to read the parallel papers, which are referenced throughout.

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References

Ben-Akiva

, Bolduc

, and Walker

. Specification, Identification, and Estimation of the Logit Kernel (or Continuous Mixed Logit) Model. Working paper. Massachusetts Institute of Technology, 2001. http://web.mit.edu/jwalker/www/home.htm. Accessed April 1, 2002.

Walker

J. L.

Extended Discrete Choice Models: Integrated Framework, Flexible Error Structures, and Latent Variables. Ph.D. dissertation. Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, 2001.

McFadden

, and Train

. Mixed MNL Models for Discrete Response. Journal of Applied Econometrics, Vol. 15, No. 5, 2000, pp. 447–470.

Bhat

C. R.

Accommodating Flexible Substitution Patterns in Multidimensional Choice Modeling: Formulation and Application to Travel Mode and Departure Time Choice. Transportation Research B, Vol. 32, No. 7, 1997, pp. 455–466.

Bhat

C. R.

Accommodating Variations in Responsiveness to Level-of-Service Measures in Travel Mode Choice Modeling. Transportation Research A, Vol. 32, No. 7, 1998, pp. 495–507.

Bolduc

, Fortin

, and Fournier

M. A.

. The Impact of Incentive Policies to Influence Practice Location of General Practitioners: A Multinomial Probit Analysis. Journal of Labor Economics, Vol. 14, 1996, pp. 703–732.

Brownstone

, Bunch

D. S.

, and Train

. Joint Mixed Logit Models of Stated and Revealed Preferences for Alternative-Fuel Vehicles. Transportation Research B, Vol. 34, 2000, pp. 315–338.

Brownstone

, and Train

. Forecasting New Product Penetration with Flexible Substitution Patterns. Journal of Econometrics, Vol. 89, 1999, pp. 109–129.

Goett

, Hudson

, and Train

. Customers’ Choice Among Retail Energy Suppliers: The Willingness-to-Pay for Service Attributes. Energy Journal, Vol. 21, No. 4, 2000, pp. 1–28.

10.

Gönül

, and Srinivasan

. Modeling Multiple Sources of Heterogeneity in Multinomial Logit Models: Methodological and Managerial Issues. Marketing Science, Vol. 12, No. 3, 1993, pp. 213–229.

11.

Greene

W. H.

Econometric Analysis, 4th ed. Prentice Hall, Upper Saddle River, N.J., 2000.

12.

Mehndiratta

R. M.

, and Hansen

. Analysis of Discrete Choice Data with Repeated Observations: Comparison of Three Techniques in Intercity Travel Case. In Transportation Research Record 1607, TRB, National Research Council, Washington, D.C., 1997, pp. 69–73.

13.

Revelt

, and Train

. Mixed Logit with Repeated Choices: Households’ Choice of Appliance Efficiency Level. Review of Economics and Statistics, Vol. 80, No. 4, 1998, pp. 647–657.

14.

Train

K. E.

Recreational Demand Models with Taste Differences over People. Land Economics, Vol. 74, No. 2, 1998, pp. 230–239.

15.

Bunch

D. S.

Estimability in the Multinomial Probit Model. Transportation Research B, Vol. 25, 1991, pp. 1–12.

16.

Ben-Akiva

, and Lerman

. Discrete Choice Analysis: Theory and Application to Travel Demand. MIT Press, Cambridge, Mass., 1985.

17.

Train

, McFadden

, and Ben-Akiva

. The Demand for Local Telephone Service: A Fully Discrete Model of Residential Calling Patterns and Service Choices. Rand Journal of Economics, Vol. 18, No. 1, 1987, pp. 109–123.

18.

Ben-Akiva

, and Bolduc

. Multinomial Probit with a Logit Kernel and a General Parametric Specification of the Covariance Structure. Working paper. Massachusetts Institute of Technology, Cambridge, 1996.

19.

Train

Discrete Choice Methods with Simulation. Cambridge University Press, 2002 (in press).

20.

Bunch

D. S.

Information and Sample Size Requirements for Estimating Non-IID Discrete Choice Models Using Stated-Choice Experiments. Working paper. Graduate School of Management, University of California, Davis, 2001.

21.

Louviere

J. J.

, Hensher

D. A.

, and Swait

J. D.

. Stated Choice Methods: Analysis and Application. Cambridge University Press, 2000.