IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v32y2023i1d10.1007_s11749-022-00835-w.html
   My bibliography  Save this article

A data-driven reversible jump for estimating a finite mixture of regression models

Author

Listed:
  • Gustavo Alexis Sabillón

    (Universidade Federal de São Carlos)

  • Luiz Gabriel Fernandes Cotrim

    (Boa Vista SCPC)

  • Daiane Aparecida Zuanetti

    (Universidade Federal de São Carlos)

Abstract

We propose a data-driven reversible jump (DDRJ) method for selecting and estimating a mixture of regression models in a single run, which can also be applied as a robust regression model to outliers. We compare the clustering and estimation performance of the proposed method with Expectation–Maximization and Gibbs sampler algorithms combined with model selection criteria in synthetic data sets. Under tested conditions, DDRJ outperforms these traditional methods in identifying the number of groups, classification and precision of estimates. When compared with traditional reversible jump algorithms, the data-driven procedure simplifies the calculations and implementation and shows a better mixing and faster convergence. Finally, we apply the proposed method to analyze two well-studied data sets: tone perception (a simple data set) and baseball salaries (a more complex data set with a larger number of covariates).

Suggested Citation

  • Gustavo Alexis Sabillón & Luiz Gabriel Fernandes Cotrim & Daiane Aparecida Zuanetti, 2023. "A data-driven reversible jump for estimating a finite mixture of regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 350-369, March.
    • Handle: RePEc:spr:testjl:v:32:y:2023:i:1:d:10.1007_s11749-022-00835-w
    DOI: 10.1007/s11749-022-00835-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-022-00835-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11749-022-00835-w?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. Mian Huang & Weixin Yao, 2012. "Mixture of Regression Models With Varying Mixing Proportions: A Semiparametric Approach," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 711-724, June.
    2. Bai, Xiuqin & Yao, Weixin & Boyer, John E., 2012. "Robust fitting of mixture regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2347-2359.
    3. Grazian, Clara & Robert, Christian P., 2018. "Jeffreys priors for mixture estimation: Properties and alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 149-163.
    4. repec:dau:papers:123456789/1906 is not listed on IDEAS
    5. Lee, Kuo-Jung & Chen, Ray-Bing & Wu, Ying Nian, 2016. "Bayesian variable selection for finite mixture model of linear regressions," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 1-16.
    6. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    7. Erlandson F. Saraiva & Luis A. Milan, 2012. "Clustering Gene Expression Data using a Posterior Split-Merge-Birth Procedure," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(3), pages 399-415, September.
    8. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
    9. repec:dau:papers:123456789/4648 is not listed on IDEAS
    10. Khalili, Abbas & Chen, Jiahua, 2007. "Variable Selection in Finite Mixture of Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1025-1038, September.
    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. Yao, Weixin & Wei, Yan & Yu, Chun, 2014. "Robust mixture regression using the t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 116-127.
    2. Marco Berrettini & Giuliano Galimberti & Saverio Ranciati, 2023. "Semiparametric finite mixture of regression models with Bayesian P-splines," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(3), pages 745-775, September.
    3. Saverio Ranciati & Giuliano Galimberti & Gabriele Soffritti, 2019. "Bayesian variable selection in linear regression models with non-normal errors," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 323-358, June.
    4. Xue, Jiacheng & Yao, Weixin, 2022. "Machine Learning Embedded Semiparametric Mixtures of Regressions with Covariate-Varying Mixing Proportions," Econometrics and Statistics, Elsevier, vol. 22(C), pages 159-171.
    5. Yan Li & Chun Yu & Yize Zhao & Weixin Yao & Robert H. Aseltine & Kun Chen, 2022. "Pursuing sources of heterogeneity in modeling clustered population," Biometrics, The International Biometric Society, vol. 78(2), pages 716-729, June.
    6. Sijia Xiang & Weixin Yao, 2018. "Semiparametric mixtures of nonparametric regressions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(1), pages 131-154, February.
    7. You, Na & Dai, Hongsheng & Wang, Xueqin & Yu, Qingyun, 2024. "Sequential estimation for mixture of regression models for heterogeneous population," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).
    8. Yuzhu Tian & Manlai Tang & Maozai Tian, 2016. "A class of finite mixture of quantile regressions with its applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(7), pages 1240-1252, July.
    9. Paul Viefers, 2011. "Bayesian Inference for the Mixed-Frequency VAR Model," Discussion Papers of DIW Berlin 1172, DIW Berlin, German Institute for Economic Research.
    10. Chun Yu & Weixin Yao & Guangren Yang, 2020. "A Selective Overview and Comparison of Robust Mixture Regression Estimators," International Statistical Review, International Statistical Institute, vol. 88(1), pages 176-202, April.
    11. Naderi, Mehrdad & Mirfarah, Elham & Wang, Wan-Lun & Lin, Tsung-I, 2023. "Robust mixture regression modeling based on the normal mean-variance mixture distributions," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    12. Sphiwe B. Skhosana & Salomon M. Millard & Frans H. J. Kanfer, 2023. "A Novel EM-Type Algorithm to Estimate Semi-Parametric Mixtures of Partially Linear Models," Mathematics, MDPI, vol. 11(5), pages 1-20, February.
    13. Meng Li & Sijia Xiang & Weixin Yao, 2016. "Robust estimation of the number of components for mixtures of linear regression models," Computational Statistics, Springer, vol. 31(4), pages 1539-1555, December.
    14. Cozzini, Alberto & Jasra, Ajay & Montana, Giovanni & Persing, Adam, 2014. "A Bayesian mixture of lasso regressions with t-errors," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 84-97.
    15. Pei, Youquan & Peng, Heng & Xu, Jinfeng, 2024. "A latent class Cox model for heterogeneous time-to-event data," Journal of Econometrics, Elsevier, vol. 239(2).
    16. Maruotti, Antonello & Punzo, Antonio, 2017. "Model-based time-varying clustering of multivariate longitudinal data with covariates and outliers," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 475-496.
    17. Paroli, Roberta & Spezia, Luigi, 2008. "Bayesian inference in non-homogeneous Markov mixtures of periodic autoregressions with state-dependent exogenous variables," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2311-2330, January.
    18. Lee, Kuo-Jung & Feldkircher, Martin & Chen, Yi-Chi, 2021. "Variable selection in finite mixture of regression models with an unknown number of components," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    19. Grazian, Clara & Villa, Cristiano & Liseo, Brunero, 2020. "On a loss-based prior for the number of components in mixture models," Statistics & Probability Letters, Elsevier, vol. 158(C).
    20. Hendry, David F. & Clements, Michael P., 2003. "Economic forecasting: some lessons from recent research," Economic Modelling, Elsevier, vol. 20(2), pages 301-329, March.

    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:spr:testjl:v:32:y:2023:i:1:d:10.1007_s11749-022-00835-w. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.