IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v212y2025ics0167947325001094.html

Bayesian selection approach for categorical responses via multinomial probit models

Author

Listed:
  • Chu, Chi-Hsiang
  • Lee, Kuo-Jung
  • Hsu, Chien-Chin
  • Chen, Ray-Bing

Abstract

A multinomial probit model is proposed to examine a categorical response variable, with the main objective being the identification of the influential variables in the model. To this end, a Bayesian selection technique using two hierarchical indicators is employed. The first indicator denotes a variable's relevance to the categorical response, and the subsequent indicator relates to the variable's importance at a specific categorical level, which aids in assessing its impact at that level. The selection process relies on the posterior indicator samples generated through an MCMC algorithm. The efficacy of our Bayesian selection strategy is demonstrated through both simulation and an application to a real-world example.

Suggested Citation

  • Chu, Chi-Hsiang & Lee, Kuo-Jung & Hsu, Chien-Chin & Chen, Ray-Bing, 2025. "Bayesian selection approach for categorical responses via multinomial probit models," Computational Statistics & Data Analysis, Elsevier, vol. 212(C).
    • Handle: RePEc:eee:csdana:v:212:y:2025:i:c:s0167947325001094
    DOI: 10.1016/j.csda.2025.108233
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947325001094
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2025.108233?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Jones, Galin L. & Haran, Murali & Caffo, Brian S. & Neath, Ronald, 2006. "Fixed-Width Output Analysis for Markov Chain Monte Carlo," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1537-1547, December.
    2. McCulloch, Robert E. & Polson, Nicholas G. & Rossi, Peter E., 2000. "A Bayesian analysis of the multinomial probit model with fully identified parameters," Journal of Econometrics, Elsevier, vol. 99(1), pages 173-193, November.
    3. Imai, Kosuke & Van Dyk, David A., 2005. "MNP: R Package for Fitting the Multinomial Probit Model," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i03).
    4. Imai, Kosuke & van Dyk, David A., 2005. "A Bayesian analysis of the multinomial probit model using marginal data augmentation," Journal of Econometrics, Elsevier, vol. 124(2), pages 311-334, February.
    5. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    6. Aijun Yang & Yunxian Li & Niansheng Tang & Jinguan Lin, 2015. "Bayesian variable selection in multinomial probit model for classifying high-dimensional data," Computational Statistics, Springer, vol. 30(2), pages 399-418, June.
    7. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    8. Chi‐Hsiang Chu & Mong‐Na Lo Huang & Shih‐Feng Huang & Ray‐Bing Chen, 2019. "Bayesian structure selection for vector autoregression model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 38(5), pages 422-439, August.
    9. Yang, Aijun & Jiang, Xuejun & Liu, Pengfei & Lin, Jinguan, 2016. "Sparse Bayesian multinomial probit regression model with correlation prior for high-dimensional data classification," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 241-247.
    10. Naijun Sha & Marina Vannucci & Mahlet G. Tadesse & Philip J. Brown & Ilaria Dragoni & Nick Davies & Tracy C. Roberts & Andrea Contestabile & Mike Salmon & Chris Buckley & Francesco Falciani, 2004. "Bayesian Variable Selection in Multinomial Probit Models to Identify Molecular Signatures of Disease Stage," Biometrics, The International Biometric Society, vol. 60(3), pages 812-819, September.
    11. Aijun Yang & Xuejun Jiang & Lianjie Shu & Jinguan Lin, 2017. "Bayesian variable selection with sparse and correlation priors for high-dimensional data analysis," Computational Statistics, Springer, vol. 32(1), pages 127-143, March.
    12. Zhang, Xiao & Boscardin, W. John & Belin, Thomas R., 2008. "Bayesian analysis of multivariate nominal measures using multivariate multinomial probit models," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3697-3708, March.
    13. Uddin, Md Nazir & Gaskins, Jeremy T., 2023. "Shared Bayesian variable shrinkage in multinomial logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    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. Rubén Loaiza-Maya & Didier Nibbering, 2023. "Fast Variational Bayes Methods for Multinomial Probit Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1352-1363, October.
    2. Zhang, Xiao & Boscardin, W. John & Belin, Thomas R., 2008. "Bayesian analysis of multivariate nominal measures using multivariate multinomial probit models," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3697-3708, March.
    3. Raja Chakir & Olivier Parent, 2009. "Determinants of land use changes: A spatial multinomial probit approach," Papers in Regional Science, Wiley Blackwell, vol. 88(2), pages 327-344, June.
    4. Rubén Loaiza-Maya & Didier Nibbering, 2022. "Scalable Bayesian Estimation in the Multinomial Probit Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1678-1690, October.
    5. Patil, Priyadarshan N. & Dubey, Subodh K. & Pinjari, Abdul R. & Cherchi, Elisabetta & Daziano, Ricardo & Bhat, Chandra R., 2017. "Simulation evaluation of emerging estimation techniques for multinomial probit models," Journal of choice modelling, Elsevier, vol. 23(C), pages 9-20.
    6. Robert Zeithammer & Peter Lenk, 2006. "Bayesian estimation of multivariate-normal models when dimensions are absent," Quantitative Marketing and Economics (QME), Springer, vol. 4(3), pages 241-265, September.
    7. Daziano, Ricardo A., 2015. "Inference on mode preferences, vehicle purchases, and the energy paradox using a Bayesian structural choice model," Transportation Research Part B: Methodological, Elsevier, vol. 76(C), pages 1-26.
    8. Bhat, Chandra R., 2018. "New matrix-based methods for the analytic evaluation of the multivariate cumulative normal distribution function," Transportation Research Part B: Methodological, Elsevier, vol. 109(C), pages 238-256.
    9. Zhang, Xiao & Boscardin, W. John & Belin, Thomas R. & Wan, Xiaohai & He, Yulei & Zhang, Kui, 2015. "A Bayesian method for analyzing combinations of continuous, ordinal, and nominal categorical data with missing values," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 43-58.
    10. Benjamin Heuclin & Frédéric Mortier & Catherine Trottier & Marie Denis, 2021. "Bayesian varying coefficient model with selection: An application to functional mapping," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(1), pages 24-50, January.
    11. Moffa, Giusi & Kuipers, Jack, 2014. "Sequential Monte Carlo EM for multivariate probit models," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 252-272.
    12. Ricardo A. Daziano & Martin Achtnicht, 2014. "Forecasting Adoption of Ultra-Low-Emission Vehicles Using Bayes Estimates of a Multinomial Probit Model and the GHK Simulator," Transportation Science, INFORMS, vol. 48(4), pages 671-683, November.
    13. Seongkyoon Jeong & Jae Young Choi & Jaeyun Kim, 2011. "The determinants of research collaboration modes: exploring the effects of research and researcher characteristics on co-authorship," Scientometrics, Springer;Akadémiai Kiadó, vol. 89(3), pages 967-983, December.
    14. Sylvia Kaufmann, 2016. "Hidden Markov models in time series, with applications in economics," Working Papers 16.06, Swiss National Bank, Study Center Gerzensee.
    15. Chiew, Esther & Daziano, Ricardo A., 2016. "A Bayes multinomial probit model for random consumer-surplus maximization," Journal of choice modelling, Elsevier, vol. 21(C), pages 56-59.
    16. Ruggieri, Eric & Lawrence, Charles E., 2012. "On efficient calculations for Bayesian variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1319-1332.
    17. Michelle Sovinsky & Liana Jacobi & Alessandra Allocca & Tao Sun, 2023. "More than Joints: Multi-Substance Use, Choice Limitations, and Policy Implications," Rationality and Competition Discussion Paper Series 487, CRC TRR 190 Rationality and Competition.
    18. Yiyi Wang & Kara Kockelman & Paul Damien, 2014. "A spatial autoregressive multinomial probit model for anticipating land-use change in Austin, Texas," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 52(1), pages 251-278, January.
    19. Xia Cui & Heng Peng & Songqiao Wen & Lixing Zhu, 2013. "Component Selection in the Additive Regression Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 491-510, September.
    20. Uddin, Md Nazir & Gaskins, Jeremy T., 2023. "Shared Bayesian variable shrinkage in multinomial logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    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:csdana:v:212:y:2025:i:c:s0167947325001094. 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.elsevier.com/locate/csda .

    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.