IDEAS home Printed from https://ideas.repec.org/a/eee/eejocm/v28y2018icp41-55.html
   My bibliography  Save this article

Estimation of factor structured covariance mixed logit models

Author

Listed:
  • James, Jonathan

Abstract

Mixed logit models with normally distributed random coefficients are typically estimated under the extreme assumptions that either the random coefficients are completely independent or fully correlated. A factor structured covariance offers a range of alternatives between these two assumptions. However, because these models are more difficult to estimate they are not frequently used to model preference heterogeneity. This paper develops a simple expectation-maximization algorithm for estimating mixed logit models when preferences are generated from a factor structured covariance. The algorithm is easy to implement for both exploratory and confirmatory factor models. The estimator is applied to stated-preference survey data from residential energy customers (Train, 2007). Comparing the fit across five different models, which differed in their assumptions on the covariance of preferences, the results show that all three factor specifications produced a better fit of the data than the fully correlated model measured by BIC and two out of three performed better in terms of AIC.

Suggested Citation

  • James, Jonathan, 2018. "Estimation of factor structured covariance mixed logit models," Journal of choice modelling, Elsevier, vol. 28(C), pages 41-55.
    • Handle: RePEc:eee:eejocm:v:28:y:2018:i:c:p:41-55
    DOI: 10.1016/j.jocm.2018.05.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S175553451730204X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jocm.2018.05.006?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ruud, Paul A., 1991. "Extensions of estimation methods using the EM algorithm," Journal of Econometrics, Elsevier, vol. 49(3), pages 305-341, September.
    2. Joel Huber and Kenneth Train., 2000. "On the Similarity of Classical and Bayesian Estimates of Individual Mean Partworths," Economics Working Papers E00-289, University of California at Berkeley.
    3. Goettler, Ronald L & Shachar, Ron, 2001. "Spatial Competition in the Network Television Industry," RAND Journal of Economics, The RAND Corporation, vol. 32(4), pages 624-656, Winter.
    4. Terry Elrod, 1988. "Choice Map: Inferring a Product-Market Map from Panel Data," Marketing Science, INFORMS, vol. 7(1), pages 21-40.
    5. Jonathan James, 2017. "MM Algorithm for General Mixed Multinomial Logit Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(4), pages 841-857, June.
    6. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, October.
    7. Denzil G. Fiebig & Michael P. Keane & Jordan Louviere & Nada Wasi, 2010. "The Generalized Multinomial Logit Model: Accounting for Scale and Coefficient Heterogeneity," Marketing Science, INFORMS, vol. 29(3), pages 393-421, 05-06.
    8. Donald Rubin & Dorothy Thayer, 1982. "EM algorithms for ML factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 47(1), pages 69-76, March.
    9. Cherchi, Elisabetta & Guevara, Cristian Angelo, 2012. "A Monte Carlo experiment to analyze the curse of dimensionality in estimating random coefficients models with a full variance–covariance matrix," Transportation Research Part B: Methodological, Elsevier, vol. 46(2), pages 321-332.
    10. Elrod, Terry & Keane, Michael, 1995. "A Factor-Analytic Probit Model for Representing the Market Structure in Panel Data," MPRA Paper 52434, University Library of Munich, Germany.
    11. Chandra R. Bhat, 1997. "An Endogenous Segmentation Mode Choice Model with an Application to Intercity Travel," Transportation Science, INFORMS, vol. 31(1), pages 34-48, February.
    12. Michael Keane & Nada Wasi, 2013. "Comparing Alternative Models Of Heterogeneity In Consumer Choice Behavior," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(6), pages 1018-1045, September.
    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. Youssef M Aboutaleb & Mazen Danaf & Yifei Xie & Moshe Ben-Akiva, 2020. "Sparse Covariance Estimation in Logit Mixture Models," Papers 2001.05034, arXiv.org.
    2. Youssef M. Aboutaleb & Mazen Danaf & Yifei Xie & Moshe Ben-Akiva, 2021. "Discrete Choice Analysis with Machine Learning Capabilities," Papers 2101.10261, arXiv.org.
    3. Coote, Leonard V. & Swait, Joffre & Adamowicz, Wiktor, 2021. "Separating generalizable from source-specific preference heterogeneity in the fusion of revealed and stated preferences," Journal of choice modelling, Elsevier, vol. 40(C).

    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. Jonathan James, 2018. "Estimation of Factor Structured Covariance Mixed Logit Models," Working Papers 1802, California Polytechnic State University, Department of Economics.
    2. Bansal, Prateek & Daziano, Ricardo A & Guerra, Erick, 2018. "Minorization-Maximization (MM) algorithms for semiparametric logit models: Bottlenecks, extensions, and comparisons," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 17-40.
    3. Robert Donnelly & Francisco J.R. Ruiz & David Blei & Susan Athey, 2021. "Counterfactual inference for consumer choice across many product categories," Quantitative Marketing and Economics (QME), Springer, vol. 19(3), pages 369-407, December.
    4. Keane, Michael & Ketcham, Jonathan & Kuminoff, Nicolai & Neal, Timothy, 2021. "Evaluating consumers’ choices of Medicare Part D plans: A study in behavioral welfare economics," Journal of Econometrics, Elsevier, vol. 222(1), pages 107-140.
    5. Arne Risa Hole & Hong Il Yoo, 2017. "The use of heuristic optimization algorithms to facilitate maximum simulated likelihood estimation of random parameter logit models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(5), pages 997-1013, November.
    6. Akshay Vij & Rico Krueger, 2018. "Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions," Papers 1802.02299, arXiv.org.
    7. Vij, Akshay & Krueger, Rico, 2017. "Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 76-101.
    8. Hong il Yoo, 2012. "The perceived unreliability of rank-ordered data: an econometric origin and implications," Discussion Papers 2012-46, School of Economics, The University of New South Wales.
    9. Bansal, Prateek & Daziano, Ricardo A. & Achtnicht, Martin, 2018. "Comparison of parametric and semiparametric representations of unobserved preference heterogeneity in logit models," Journal of choice modelling, Elsevier, vol. 27(C), pages 97-113.
    10. Sarrias, Mauricio & Daziano, Ricardo A., 2018. "Individual-specific point and interval conditional estimates of latent class logit parameters," Journal of choice modelling, Elsevier, vol. 27(C), pages 50-61.
    11. Marco Costanigro & Yuko Onozaka, 2020. "A Belief‐Preference Model of Choice for Experience and Credence Goods," Journal of Agricultural Economics, Wiley Blackwell, vol. 71(1), pages 70-95, February.
    12. Johanna Lena Dahlhausen & Cam Rungie & Jutta Roosen, 2018. "Value of labeling credence attributes—common structures and individual preferences," Agricultural Economics, International Association of Agricultural Economists, vol. 49(6), pages 741-751, November.
    13. Friederike Paetz & Winfried J. Steiner, 2017. "The benefits of incorporating utility dependencies in finite mixture probit models," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(3), pages 793-819, July.
    14. Susan Athey & Guido W. Imbens, 2007. "Discrete Choice Models With Multiple Unobserved Choice Characteristics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1159-1192, November.
    15. Michael P. Keane & Nada Wasi, 2013. "The Structure of Consumer Taste Heterogeneity in Revealed vs. Stated Preference Data," Economics Papers 2013-W10, Economics Group, Nuffield College, University of Oxford.
    16. Kettlewell, Nathan & Walker, Matthew J. & Yoo, Hong Il, 2024. "Alternative Models of Preference Heterogeneity for Elicited Choice Probabilities," IZA Discussion Papers 16821, Institute of Labor Economics (IZA).
    17. Kim, Sung Hoo & Mokhtarian, Patricia L., 2023. "Finite mixture (or latent class) modeling in transportation: Trends, usage, potential, and future directions," Transportation Research Part B: Methodological, Elsevier, vol. 172(C), pages 134-173.
    18. Haile, Kaleab K. & Tirivayi, Nyasha & Tesfaye, Wondimagegn, 2019. "Farmers’ willingness to accept payments for ecosystem services on agricultural land: The case of climate-smart agroforestry in Ethiopia," Ecosystem Services, Elsevier, vol. 39(C).
    19. Mariel, Petr & Ayala, Amaya de & Hoyos, David & Abdullah, Sabah, 2013. "Selecting random parameters in discrete choice experiment for environmental valuation: A simulation experiment," Journal of choice modelling, Elsevier, vol. 7(C), pages 44-57.
    20. Wendong Zhang & Brent Sohngen, 2018. "Do U.S. Anglers Care about Harmful Algal Blooms? A Discrete Choice Experiment of Lake Erie Recreational Anglers," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 100(3), pages 868-888.

    More about this item

    Keywords

    Discrete choice; Mixed logit; EM algorithm; Factor models;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis

    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:eee:eejocm:v:28:y:2018:i:c:p:41-55. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/journal-of-choice-modelling .

    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.