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Linear mixed model with Laplace distribution (LLMM)

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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.

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Acknowledgments

The authors thank the Editor and two anonymous referees for valuable suggestions that greatly improved the paper.

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Authors and Affiliations

  1. Department of Statistics, Yildiz Technical University, Davutpaşa, 34220, Istanbul, Turkey

    Fulya Gokalp Yavuz

  2. Department of Statistics, Ankara University, Tandogan, 06100, Ankara, Turkey

    Olcay Arslan

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  1. Fulya Gokalp Yavuz
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  2. Olcay Arslan
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Correspondence to Fulya Gokalp Yavuz.

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Yavuz, F.G., Arslan, O. Linear mixed model with Laplace distribution (LLMM). Stat Papers 59, 271–289 (2018). https://doi.org/10.1007/s00362-016-0763-x

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  • DOI: https://doi.org/10.1007/s00362-016-0763-x

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