IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2008.08048.html
   My bibliography  Save this paper

Learning Structure in Nested Logit Models

Author

Listed:
  • Youssef M. Aboutaleb
  • Moshe Ben-Akiva
  • Patrick Jaillet

Abstract

This paper introduces a new data-driven methodology for nested logit structure discovery. Nested logit models allow the modeling of positive correlations between the error terms of the utility specifications of the different alternatives in a discrete choice scenario through the specification of a nesting structure. Current nested logit model estimation practices require an a priori specification of a nesting structure by the modeler. In this we work we optimize over all possible specifications of the nested logit model that are consistent with rational utility maximization. We formulate the problem of learning an optimal nesting structure from the data as a mixed integer nonlinear programming (MINLP) optimization problem and solve it using a variant of the linear outer approximation algorithm. We exploit the tree structure of the problem and utilize the latest advances in integer optimization to bring practical tractability to the optimization problem we introduce. We demonstrate the ability of our algorithm to correctly recover the true nesting structure from synthetic data in a Monte Carlo experiment. In an empirical illustration using a stated preference survey on modes of transportation in the U.S. state of Massachusetts, we use our algorithm to obtain an optimal nesting tree representing the correlations between the unobserved effects of the different travel mode choices. We provide our implementation as a customizable and open-source code base written in the Julia programming language.

Suggested Citation

  • Youssef M. Aboutaleb & Moshe Ben-Akiva & Patrick Jaillet, 2020. "Learning Structure in Nested Logit Models," Papers 2008.08048, arXiv.org.
  • Handle: RePEc:arx:papers:2008.08048
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2008.08048
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dimitris Bertsimas & Angela King, 2016. "OR Forum—An Algorithmic Approach to Linear Regression," Operations Research, INFORMS, vol. 64(1), pages 2-16, February.
    2. Brownstone, David & Small, Kenneth A, 1989. "Efficient Estimation of Nested Logit Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(1), pages 67-74, January.
    3. Youssef M Aboutaleb & Mazen Danaf & Yifei Xie & Moshe Ben-Akiva, 2020. "Sparse Covariance Estimation in Logit Mixture Models," Papers 2001.05034, arXiv.org.
    4. Carlos F. Daganzo & Michael Kusnic, 1993. "Technical Note—Two Properties of the Nested Logit Model," Transportation Science, INFORMS, vol. 27(4), pages 395-400, November.
    5. Hensher, David A. & Greene, William H., 2002. "Specification and estimation of the nested logit model: alternative normalisations," Transportation Research Part B: Methodological, Elsevier, vol. 36(1), pages 1-17, January.
    6. Joseph Scott & Matthew Stuber & Paul Barton, 2011. "Generalized McCormick relaxations," Journal of Global Optimization, Springer, vol. 51(4), pages 569-606, December.
    7. Hausman, Jerry & McFadden, Daniel, 1984. "Specification Tests for the Multinomial Logit Model," Econometrica, Econometric Society, vol. 52(5), pages 1219-1240, September.
    8. Koppelman, Frank S. & Wen, Chieh-Hua, 1998. "Alternative nested logit models: structure, properties and estimation," Transportation Research Part B: Methodological, Elsevier, vol. 32(5), pages 289-298, June.
    9. Daly, Andrew, 1987. "Estimating "tree" logit models," Transportation Research Part B: Methodological, Elsevier, vol. 21(4), pages 251-267, August.
    Full references (including those not matched with items on IDEAS)

    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. Judith Yates & Gavin Wood, 2005. "Affordable Rental Housing: Lost, Stolen and Strayed," The Economic Record, The Economic Society of Australia, vol. 81(s1), pages 82-95, August.
    2. Hess, Stephane & Palma, David, 2019. "Apollo: A flexible, powerful and customisable freeware package for choice model estimation and application," Journal of choice modelling, Elsevier, vol. 32(C), pages 1-1.
    3. Honora Smith & Christine Currie & Pornpimol Chaiwuttisak & Andreas Kyprianou, 2018. "Patient choice modelling: how do patients choose their hospitals?," Health Care Management Science, Springer, vol. 21(2), pages 259-268, June.
    4. Danis, Michelle A. & Pennington-Cross, Anthony, 2008. "The delinquency of subprime mortgages," Journal of Economics and Business, Elsevier, vol. 60(1-2), pages 67-90.
    5. Brian Whitacre & Bradford Mills, 2010. "A need for speed? Rural Internet connectivity and the no access/dial-up/high-speed decision," Applied Economics, Taylor & Francis Journals, vol. 42(15), pages 1889-1905.
    6. Birolini, Sebastian & Cattaneo, Mattia & Malighetti, Paolo & Morlotti, Chiara, 2020. "Integrated origin-based demand modeling for air transportation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).
    7. Nalin Kumar Ramaul & Pinki Ramaul, 2018. "Regional Incentives and Location Choice of New Firms in India: A Nested Logit Model," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 16(2), pages 501-525, June.
    8. Bodas Freitas, Isabel Maria & Geuna, Aldo & Rossi, Federica, 2013. "Finding the right partners: Institutional and personal modes of governance of university–industry interactions," Research Policy, Elsevier, vol. 42(1), pages 50-62.
    9. Ahmadi Azari, Kian & Arintono, Sulistyo & Hamid, Hussain & Rahmat, Riza Atiq O.K., 2013. "Modelling demand under parking and cordon pricing policy," Transport Policy, Elsevier, vol. 25(C), pages 1-9.
    10. Bhat, Chandra R., 1997. "Covariance heterogeneity in nested logit models: Econometric structure and application to intercity travel," Transportation Research Part B: Methodological, Elsevier, vol. 31(1), pages 11-21, February.
    11. Siedschlag, Iulia & Smith, Donal & Turcu, Camelia & Zhang, Xiaoheng, 2009. "What Determines the Attractiveness of the European Union to the Location R&D Multinational Firms?," Papers DYNREG46, Economic and Social Research Institute (ESRI).
    12. Sánchez Navarro, Dennis, 2013. "Análisis de elasticidades en el mercado automotor colombiano (2009 - 2011) mediante un modelo logit anidado [Analysis Of Elasticity In Colombian Automotive Market (2009 - 2011) Through A Nested Log," MPRA Paper 46043, University Library of Munich, Germany.
    13. Bliemer, Michiel C.J. & Rose, John M. & Hensher, David A., 2009. "Efficient stated choice experiments for estimating nested logit models," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 19-35, January.
    14. Kaoru, Yoshiaki, 1995. "Measuring marine recreation benefits of water quality improvements by the nested random utility model," Resource and Energy Economics, Elsevier, vol. 17(2), pages 119-136, August.
    15. Poirier, Dale J., 1996. "A Bayesian analysis of nested logit models," Journal of Econometrics, Elsevier, vol. 75(1), pages 163-181, November.
    16. Koppelman, Frank S. & Wen, Chieh-Hua, 1998. "Alternative nested logit models: structure, properties and estimation," Transportation Research Part B: Methodological, Elsevier, vol. 32(5), pages 289-298, June.
    17. Levine, Jonathan C., 1990. "Employment Suburbanization and the Journey to Work," University of California Transportation Center, Working Papers qt05c8750h, University of California Transportation Center.
    18. Mavra Stithou & Stephen Hynes & Nick Hanley & Danny Campbell, 2012. "Estimating the Value of Achieving “Good Ecological Status”in the Boyne River Catchmentin Ireland Using Choice Experiments," The Economic and Social Review, Economic and Social Studies, vol. 43(3), pages 397-422.
    19. R.K. Blamey & J.W. Bennett & J.J. Louviere & M.D. Morrison & J.C. Rolfe, 2002. "Attribute Causality in Environmental Choice Modelling," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 23(2), pages 167-186, October.
    20. Daly, Andrew, 2001. "Alternative tree logit models: comments on a paper of Koppelman and Wen," Transportation Research Part B: Methodological, Elsevier, vol. 35(8), pages 717-724, September.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:2008.08048. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://arxiv.org/ .

    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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.