IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v39y2005i2p160-181.html
   My bibliography  Save this article

A Dynamic Kernel Logit Model for the Analysis of Longitudinal Discrete Choice Data: Properties and Computational Assessment

Author

Listed:
  • Karthik K. Srinivasan

    (BSB 235, Department of Civil Engineering, Indian Institute of Technology, Madras, Chennai 600036, India)

  • Hani S. Mahmassani

    (Department of Civil and Environmental Engineering, University of Maryland, College Park, Maryland 20742)

Abstract

This paper focuses on the application of the kernel logit formulation to model dynamic discrete choice data. A dynamic kernel logit (DKL) formulation with normal errors is presented to model unordered discrete choice panel data. Investigating the theoretical foundations of the kernel logit model, it is demonstrated that the mixed logit error structure converges in distribution asymptotically to a suitable multivariate normal error structure. This result provides support for both cross-sectional kernel logit (CKL) and DKL models with normal errors. The calibration, identification, and specification issues associated with the latter model are also discussed.The performance of the proposed DKL model is assessed from the perspective of computational efficiency and estimate accuracy relative to the multinomial probit (MNP) model using a series of numerical experiments. Complexity analysis reveals that the DKL has a lower computational complexity than the MNP frequency simulator, which has an exponential complexity. Thus, for choice situations with a large number of alternatives ( J ) in each time period, and/or large number of time periods ( T ), the DKL model is faster than the corresponding MNP by more than an order of magnitude. This is also confirmed by computational experiments conducted using 32 synthetic data sets. The computational performance of the DKL relative to MNP appears to be the result of a trade-off between the number of Monte-Carlo draws required, and the computational cost of each draw. With fewer than 25 alternatives ( JT ), the results suggest that it is more advantageous to use the probit model (MNP) compared to the DKL. There appears to be little advantage in applying the kernel logit formulation relative to the MNP to cross-sectional data with a few alternatives.Regarding computational accuracy, the numerical results suggest that the parameter estimates of both models (MNP and DKL) are comparable and close to the true values from which the data sets were generated. However, both DKL and MNP formulations may lead to the maximization of a nonconcave objective function, resulting in flat log-likelihood functions, and identification problems.

Suggested Citation

  • Karthik K. Srinivasan & Hani S. Mahmassani, 2005. "A Dynamic Kernel Logit Model for the Analysis of Longitudinal Discrete Choice Data: Properties and Computational Assessment," Transportation Science, INFORMS, vol. 39(2), pages 160-181, May.
    • Handle: RePEc:inm:ortrsc:v:39:y:2005:i:2:p:160-181
    DOI: 10.1287/trsc.1040.0093
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/trsc.1040.0093
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.1040.0093?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. C F Daganzo & Y Sheffi, 1982. "Multinomial Probit with Time-Series Data: Unifying State Dependence and Serial Correlation Models," Environment and Planning A, , vol. 14(10), pages 1377-1388, October.
    2. 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.
    3. Lee, Lung-Fei, 1992. "On Efficiency of Methods of Simulated Moments and Maximum Simulated Likelihood Estimation of Discrete Response Models," Econometric Theory, Cambridge University Press, vol. 8(4), pages 518-552, December.
    4. Bhat, Chandra R., 2001. "Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 677-693, August.
    5. Brownstone, David & Train, Kenneth, 1998. "Forecasting new product penetration with flexible substitution patterns," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 109-129, November.
    6. Dansie, B. R., 1985. "Parameter estimability in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 19(6), pages 526-528, December.
    7. David Revelt & Kenneth Train, 1998. "Mixed Logit With Repeated Choices: Households' Choices Of Appliance Efficiency Level," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 647-657, November.
    8. Koppelman, Frank S. & Wen, Chieh-Hua, 2000. "The paired combinatorial logit model: properties, estimation and application," Transportation Research Part B: Methodological, Elsevier, vol. 34(2), pages 75-89, February.
    9. Rishin Roy & Pradeep K. Chintagunta & Sudeep Haldar, 1996. "A Framework for Investigating Habits, “The Hand of the Past,” and Heterogeneity in Dynamic Brand Choice," Marketing Science, INFORMS, vol. 15(3), pages 280-299.
    10. Liu, Yu-Hsin & Mahmassani, Hani S., 2000. "Global maximum likelihood estimation procedure for multinomial probit (MNP) model parameters," Transportation Research Part B: Methodological, Elsevier, vol. 34(5), pages 419-449, June.
    11. Keane, Michael P, 1992. "A Note on Identification in the Multinomial Probit Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 193-200, April.
    12. Kitamura, Ryuichi, 1990. "Panel Analysis in Transportation Planning: An Overview," University of California Transportation Center, Working Papers qt86v0f7zh, University of California Transportation Center.
    13. Horowitz, Joel L., 1991. "Reconsidering the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 25(6), pages 433-438, December.
    14. Geweke, John F. & Keane, Michael P. & Runkle, David E., 1997. "Statistical inference in the multinomial multiperiod probit model," Journal of Econometrics, Elsevier, vol. 80(1), pages 125-165, September.
    15. 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.
    16. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    17. Kenneth E. Train, 1998. "Recreation Demand Models with Taste Differences over People," Land Economics, University of Wisconsin Press, vol. 74(2), pages 230-239.
    18. David Hensher & William Greene, 2003. "The Mixed Logit model: The state of practice," Transportation, Springer, vol. 30(2), pages 133-176, May.
    19. Andrew A. Goett & Kathleen Hudson & Kenneth E. Train, 2000. "Customers' Choice Among Retail Energy Suppliers: The Willingness-to-Pay for Service Attributes," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4), pages 1-28.
    20. Garrido, Rodrigo A. & Mahmassani, Hani S., 2000. "Forecasting freight transportation demand with the space-time multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 34(5), pages 403-418, June.
    21. Bunch, David S., 1991. "Estimability in the Multinomial Probit Model," University of California Transportation Center, Working Papers qt1gf1t128, University of California Transportation Center.
    22. Bunch, David S., 1991. "Estimability in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 25(1), pages 1-12, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Park, Arim & Chen, Roger & Cho, Soohyun & Zhao, Yao, 2023. "The determinants of online matching platforms for freight services," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 179(C).
    2. Pierpaolo De Blasi & Lancelot F. James & John W. Lau, 2007. "Bayesian Nonparametric Estimation and Consistency of Mixed Multinomial Logit Choice Models," ICER Working Papers - Applied Mathematics Series 15-2007, ICER - International Centre for Economic Research.
    3. Karthik Srinivasan & P. Bhargavi, 2007. "Longer-term changes in mode choice decisions in Chennai: a comparison between cross-sectional and dynamic models," Transportation, Springer, vol. 34(3), pages 355-374, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ziegler Andreas, 2010. "Z-Tests in Multinomial Probit Models under Simulated Maximum Likelihood Estimation: Some Small Sample Properties," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 230(5), pages 630-652, October.
    2. Victoria Prowse, 2012. "Modeling Employment Dynamics With State Dependence and Unobserved Heterogeneity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 411-431, April.
    3. Rennings, Klaus & Ziegler, Andreas & Zwick, Thomas, 2001. "Employment changes in environmentally innovative firms," ZEW Discussion Papers 01-46, ZEW - Leibniz Centre for European Economic Research.
    4. Klaus Rennings & Andreas Ziegler & Thomas Zwick, 2004. "The effect of environmental innovations on employment changes: an econometric analysis," Business Strategy and the Environment, Wiley Blackwell, vol. 13(6), pages 374-387, November.
    5. GRAMMIG, Joachim & HUJER, Reinhard & SCHEIDLER, Michael, 2001. "The econometrics of airline network management," LIDAM Discussion Papers CORE 2001055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Paleti, Rajesh, 2018. "Generalized multinomial probit Model: Accommodating constrained random parameters," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 248-262.
    7. Rinus Haaijer & Michel Wedel & Marco Vriens & Tom Wansbeek, 1998. "Utility Covariances and Context Effects in Conjoint MNP Models," Marketing Science, INFORMS, vol. 17(3), pages 236-252.
    8. Geweke, John & Keane, Michael P & Runkle, David, 1994. "Alternative Computational Approaches to Inference in the Multinomial Probit Model," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 609-632, November.
    9. Daziano, Ricardo A. & Achtnicht, Martin, 2012. "Forecasting adoption of ultra-low-emission vehicles using the GHK simulator and Bayes estimates of a multinomial probit model," ZEW Discussion Papers 12-017, ZEW - Leibniz Centre for European Economic Research.
    10. Heiss, Florian & Winschel, Viktor, 2008. "Likelihood approximation by numerical integration on sparse grids," Journal of Econometrics, Elsevier, vol. 144(1), pages 62-80, May.
    11. Campbell, Danny & Hutchinson, W. George & Scarpa, Riccardo, 2006. "Using Discrete Choice Experiments to Derive Individual-Specific WTP Estimates for Landscape Improvements under Agri-Environmental Schemes: Evidence from the Rural Environment Protection Scheme in Irel," Sustainability Indicators and Environmental Valuation Working Papers 12220, Fondazione Eni Enrico Mattei (FEEM).
    12. Ziegler, Andreas, 2001. "Simulated z-tests in multinomial probit models," ZEW Discussion Papers 01-53, ZEW - Leibniz Centre for European Economic Research.
    13. Danny Campbell & George Hutchinson & Riccardo Scarpa, 2006. "Using mixed logit models to derive individual-specific WTP estimates for landscape improvements under agri-environmental schemes: evidence from the Rural Environment Protection Scheme in Ireland," Working Papers 0607, Rural Economy and Development Programme,Teagasc.
    14. Tinessa, Fiore & Marzano, Vittorio & Papola, Andrea, 2020. "Mixing distributions of tastes with a Combination of Nested Logit (CoNL) kernel: Formulation and performance analysis," Transportation Research Part B: Methodological, Elsevier, vol. 141(C), pages 1-23.
    15. Andreas Ziegler, 2010. "Individual Characteristics and Stated Preferences for Alternative Energy Sources and Propulsion Technologies in Vehicles: A Discrete Choice Analysis," CER-ETH Economics working paper series 10/125, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    16. Haghani, Milad & Bliemer, Michiel C.J. & Hensher, David A., 2021. "The landscape of econometric discrete choice modelling research," Journal of choice modelling, Elsevier, vol. 40(C).
    17. Tinessa, Fiore, 2021. "Closed-form random utility models with mixture distributions of random utilities: Exploring finite mixtures of qGEV models," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 262-288.
    18. Danny Campbell & George Hutchinson & Riccardo Scarpa, 2006. "Integrating landscape improvement indices and discrete choice experiments: evidence from the Rural Environment Protection Scheme in Ireland," Working Papers 0609, Rural Economy and Development Programme,Teagasc.
    19. Campbell, Danny, 2007. "Combining mixed logit models and random effects models to identify the determinants of willingness to pay for rural landscape improvements," 81st Annual Conference, April 2-4, 2007, Reading University, UK 7975, Agricultural Economics Society.
    20. Kalouptsidis, N. & Psaraki, V., 2010. "Approximations of choice probabilities in mixed logit models," European Journal of Operational Research, Elsevier, vol. 200(2), pages 529-535, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ortrsc:v:39:y:2005:i:2:p:160-181. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.