Linear mixed model with Laplace distribution (LLMM)

Yavuz F., Arslan O.

STATISTICAL PAPERS, cilt.59, sa.1, ss.271-289, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Sayı: 1
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s00362-016-0763-x
  • Dergi Adı: STATISTICAL PAPERS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.271-289
  • Anahtar Kelimeler: Laplace, Mixed models, Robust distributions, EM, Orthodont, MAXIMUM-LIKELIHOOD, LONGITUDINAL DATA, T-DISTRIBUTION, EM ALGORITHM, REGRESSION
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

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.