IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v40y2025i8d10.1007_s00180-025-01618-1.html

Robust mixture of linear mixed modeling via multivariate Laplace distribution

Author

Listed:
  • Xiongya Li

    (Kansas State University)

  • Xiuqin Bai

    (Kansas State University)

  • Weixing Song

    (Kansas State University)

Abstract

The assumption of normality in random effects and regression errors is the primary cause of the lack of robustness in the maximum likelihood estimation procedure for linear mixed models. In this paper, we introduce a robust method for estimating regression parameters in these models, by positing that the random effects and regression errors follow a multivariate Laplace distribution. This new methodology, implemented via an EM algorithm, is computationally more efficient compared to the existing robust t procedure in the literature. Simulation studies suggest that the performance of the proposed estimation method in finite samples either surpasses or is at least on par with the robust t procedure.

Suggested Citation

  • Xiongya Li & Xiuqin Bai & Weixing Song, 2025. "Robust mixture of linear mixed modeling via multivariate Laplace distribution," Computational Statistics, Springer, vol. 40(8), pages 4209-4230, November.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:8:d:10.1007_s00180-025-01618-1
    DOI: 10.1007/s00180-025-01618-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-025-01618-1
    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/s00180-025-01618-1?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. Gilles Celeux & Gilda Soromenho, 1996. "An entropy criterion for assessing the number of clusters in a mixture model," Journal of Classification, Springer;The Classification Society, vol. 13(2), pages 195-212, September.
    2. Anderson, Dale N., 1992. "A multivariate Linnik distribution," Statistics & Probability Letters, Elsevier, vol. 14(4), pages 333-336, July.
    3. Yau, Kelvin K. W. & Lee, Andy H. & Ng, Angus S. K., 2003. "Finite mixture regression model with random effects: application to neonatal hospital length of stay," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 359-366, January.
    4. L. A. García‐Escudero & A. Gordaliza & R. San Martín & S. Van Aelst & R. Zamar, 2009. "Robust linear clustering," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 301-318, January.
    5. Fulya Gokalp Yavuz & Olcay Arslan, 2018. "Linear mixed model with Laplace distribution (LLMM)," Statistical Papers, Springer, vol. 59(1), pages 271-289, March.
    6. Neykov, N. & Filzmoser, P. & Dimova, R. & Neytchev, P., 2007. "Robust fitting of mixtures using the trimmed likelihood estimator," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 299-308, 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. 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.
    3. García-Escudero, L.A. & Gordaliza, A. & Mayo-Iscar, A. & San Martín, R., 2010. "Robust clusterwise linear regression through trimming," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3057-3069, December.
    4. 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.
    5. Andrea Cerioli & Domenico Perrotta, 2014. "Robust clustering around regression lines with high density regions," 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. 8(1), pages 5-26, March.
    6. Hu, Hao & Yao, Weixin & Wu, Yichao, 2017. "The robust EM-type algorithms for log-concave mixtures of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 14-26.
    7. Luísa Novais & Susana Faria, 2025. "Robust order selection of mixtures of regression models with random effects," Computational Statistics, Springer, vol. 40(6), pages 3205-3228, July.
    8. Guney, Yesim & Arslan, Olcay & Yavuz, Fulya Gokalp, 2022. "Robust estimation in multivariate heteroscedastic regression models with autoregressive covariance structures using EM algorithm," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    9. Antonio Punzo & Paul. D. McNicholas, 2017. "Robust Clustering in Regression Analysis via the Contaminated Gaussian Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 249-293, July.
    10. Luca Greco, 2022. "Robust fitting of mixtures of GLMs by weighted likelihood," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(1), pages 25-48, March.
    11. Luis García-Escudero & Alfonso Gordaliza & Carlos Matrán & Agustín Mayo-Iscar, 2010. "A review of robust clustering methods," 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. 4(2), pages 89-109, September.
    12. Luca Greco & Antonio Lucadamo & Claudio Agostinelli, 2021. "Weighted likelihood latent class linear regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 711-746, June.
    13. Li, Xiongya & Bai, Xiuqin & Song, Weixing, 2017. "Robust mixture multivariate linear regression by multivariate Laplace distribution," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 32-39.
    14. Shouchuang Zhang & Ting Wang & Lanyue Zhang & Yuehui Wei & Weiyan Jian & Jing Guo, 2024. "Relationship between social inequality perception patterns and depressive symptoms among Chinese adults: A national representative longitudinal study," International Journal of Social Psychiatry, , vol. 70(5), pages 933-944, August.
    15. Julian Aichholzer & Sylvia Kritzinger & Carolina Plescia, 2021. "National identity profiles and support for the European Union," European Union Politics, , vol. 22(2), pages 293-315, June.
    16. Nicoleta Serban & Huijing Jiang, 2012. "Multilevel Functional Clustering Analysis," Biometrics, The International Biometric Society, vol. 68(3), pages 805-814, September.
    17. Jacky C. K. Ng & Joanne Y. H. Chong & Hilary K. Y. Ng, 2023. "The way I see the world, the way I envy others: a person-centered investigation of worldviews and the malicious and benign forms of envy among adolescents and adults," Humanities and Social Sciences Communications, Palgrave Macmillan, vol. 10(1), pages 1-11, December.
    18. Gillian C. Williams & Karen A. Patte & Mark A. Ferro & Scott T. Leatherdale, 2021. "Associations between Longitudinal Patterns of Substance Use and Anxiety and Depression Symptoms among a Sample of Canadian Secondary School Students," IJERPH, MDPI, vol. 18(19), pages 1-14, October.
    19. Frauke Kreuter & Bengt Muthén, 2008. "Analyzing Criminal Trajectory Profiles: Bridging Multilevel and Group-based Approaches Using Growth Mixture Modeling," Journal of Quantitative Criminology, Springer, vol. 24(1), pages 1-31, March.
    20. Mélissa Lemoine & Gerhard Gmel & Simon Foster & Simon Marmet & Joseph Studer, 2020. "Multiple trajectories of alcohol use and the development of alcohol use disorder: Do Swiss men mature-out of problematic alcohol use during emerging adulthood?," PLOS ONE, Public Library of Science, vol. 15(1), pages 1-17, January.

    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:spr:compst:v:40:y:2025:i:8:d:10.1007_s00180-025-01618-1. 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.