IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v59y2018i1d10.1007_s00362-016-0763-x.html
   My bibliography  Save this article

Linear mixed model with Laplace distribution (LLMM)

Author

Listed:
  • Fulya Gokalp Yavuz

    (Yildiz Technical University)

  • Olcay Arslan

    (Ankara University)

Abstract

Linear mixed modeling (LMM) is a comprehensive technique used for clustered, panel and longitudinal data. The main assumption of classical LMM is having normally distributed random effects and error terms. However, there are several situations for that we need to use heavier tails distributions than the (multivariate) normal to handle outliers and/or heavy tailness in data. In this study, we focus on LMM using the multivariate Laplace distribution which is known as the heavy tailed alternative to the normal distribution. The parameter estimators of interest are generated with EM algorithm for the proposed model. A simulation study is provided to illustrate the performance of the Laplace distribution over the normal distribution for LMM. Also, a real data example is used to explore the behavior of the proposed estimators over the counterparts.

Suggested Citation

  • Fulya Gokalp Yavuz & Olcay Arslan, 2018. "Linear mixed model with Laplace distribution (LLMM)," Statistical Papers, Springer, vol. 59(1), pages 271-289, March.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:1:d:10.1007_s00362-016-0763-x
    DOI: 10.1007/s00362-016-0763-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-016-0763-x
    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/s00362-016-0763-x?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. Olcay Arslan, 2010. "An alternative multivariate skew Laplace distribution: properties and estimation," Statistical Papers, Springer, vol. 51(4), pages 865-887, December.
    2. Kleinbaum, David G., 1973. "A generalization of the growth curve model which allows missing data," Journal of Multivariate Analysis, Elsevier, vol. 3(1), pages 117-124, March.
    3. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2007. "Assessment of local influence in elliptical linear models with longitudinal structure," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4354-4368, May.
    4. Michael Healy & Michael Westmacott, 1956. "Missing Values in Experiments Analysed on Automatic Computers," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 5(3), pages 203-206, November.
    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. Lang Zhao & Yuan Zeng & Zhidong Wang & Yizheng Li & Dong Peng & Yao Wang & Xueying Wang, 2023. "Robust Optimal Scheduling of Integrated Energy Systems Considering the Uncertainty of Power Supply and Load in the Power Market," Energies, MDPI, vol. 16(14), pages 1-14, July.
    2. 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).
    3. Fulya Gokalp Yavuz & Barret Schloerke, 2020. "Parallel computing in linear mixed models," Computational Statistics, Springer, vol. 35(3), pages 1273-1289, September.

    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. Russo, Cibele M. & Paula, Gilberto A. & Aoki, Reiko, 2009. "Influence diagnostics in nonlinear mixed-effects elliptical models," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4143-4156, October.
    2. Cibele M. Russo & Gilberto A. Paula & Francisco Jos� A. Cysneiros & Reiko Aoki, 2012. "Influence diagnostics in heteroscedastic and/or autoregressive nonlinear elliptical models for correlated data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1049-1067, October.
    3. Aldo M. Garay & Victor H. Lachos & Heleno Bolfarine & Celso R. B. Cabral, 2017. "Linear censored regression models with scale mixtures of normal distributions," Statistical Papers, Springer, vol. 58(1), pages 247-278, March.
    4. Robert G. Aykroyd & Víctor Leiva & Carolina Marchant, 2018. "Multivariate Birnbaum-Saunders Distributions: Modelling and Applications," Risks, MDPI, vol. 6(1), pages 1-25, March.
    5. Barros, Michelli & Paula, Gilberto A. & Leiva, Víctor, 2009. "An R implementation for generalized Birnbaum-Saunders distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1511-1528, February.
    6. Fernanda De Bastiani & Audrey Mariz de Aquino Cysneiros & Miguel Uribe-Opazo & Manuel Galea, 2015. "Influence diagnostics in elliptical spatial linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 322-340, June.
    7. Michelli Barros & Manuel Galea & Víctor Leiva & Manoel Santos-Neto, 2018. "Generalized Tobit models: diagnostics and application in econometrics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 145-167, January.
    8. Lucia Santana & Filidor Vilca & V�ctor Leiva, 2011. "Influence analysis in skew-Birnbaum--Saunders regression models and applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1633-1649, July.
    9. Matos, Larissa A. & Bandyopadhyay, Dipankar & Castro, Luis M. & Lachos, Victor H., 2015. "Influence assessment in censored mixed-effects models using the multivariate Student’s-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 104-117.
    10. Julio M. Singer & Francisco M.M. Rocha & Juvêncio S. Nobre, 2017. "Graphical Tools for Detecting Departures from Linear Mixed Model Assumptions and Some Remedial Measures," International Statistical Review, International Statistical Institute, vol. 85(2), pages 290-324, August.
    11. Wang, Qihua & Su, Miaomiao & Wang, Ruoyu, 2021. "A beyond multiple robust approach for missing response problem," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    12. Zhuo, Shuaihe, 2018. "Local influence analysis of stochastic frontier estimation: A case-weights perturbation approach," Economics Letters, Elsevier, vol. 164(C), pages 79-81.
    13. Avner Bar-Hen, 2002. "Influence of missing data on compact designs for spacing experiments," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(8), pages 1229-1240.
    14. Ash Abebe & Huybrechts F. Bindele & Masego Otlaadisa & Boikanyo Makubate, 2021. "Robust estimation of single index models with responses missing at random," Statistical Papers, Springer, vol. 62(5), pages 2195-2225, October.
    15. Patriota, Alexandre G., 2011. "A note on influence diagnostics in nonlinear mixed-effects elliptical models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 218-225, January.
    16. Paula, Gilberto A. & Medeiros, Marcio & Vilca-Labra, Filidor E., 2009. "Influence diagnostics for linear models with first-order autoregressive elliptical errors," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 339-346, February.
    17. Joelmir A. Borssoi & Gilberto A. Paula & Manuel Galea, 2020. "Elliptical linear mixed models with a covariate subject to measurement error," Statistical Papers, Springer, vol. 61(1), pages 31-69, February.
    18. Chamberlain Mbah & Kris Peremans & Stefan Van Aelst & Dries F. Benoit, 2019. "Robust Bayesian seemingly unrelated regression model," Computational Statistics, Springer, vol. 34(3), pages 1135-1157, September.
    19. Adeniyi, Isaac Adeola, 2020. "Bayesian Generalized Linear Mixed Effects Models Using Normal-Independent Distributions: Formulation and Applications," MPRA Paper 99165, University Library of Munich, Germany.
    20. 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).

    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:stpapr:v:59:y:2018:i:1:d:10.1007_s00362-016-0763-x. 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.