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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Olcay Arslan, 2010. "An alternative multivariate skew Laplace distribution: properties and estimation," Statistical Papers, Springer, vol. 51(4), pages 865-887, December.
    4. 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.
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    Cited by:

    1. 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).
    2. Fulya Gokalp Yavuz & Barret Schloerke, 2020. "Parallel computing in linear mixed models," Computational Statistics, Springer, vol. 35(3), pages 1273-1289, September.
    3. 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.

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