Linear mixed models with skew-elliptical distributions: A Bayesian approach

• DOI: 10.1016/j.csda.2008.04.027
• Publication Date: 2008-05-04T06:59:20Z
• Authors: Alejandro Jara; Fernando Quintana; Ernesto San Martín
• Keywords: PITFALLS; T-DISTRIBUTION; MULTIVARIATE; REGRESSION-MODELS; 330; LONGITUDINAL DATA; 03 Salud y bienestar; 0502 economics and business; 05 social sciences; 03 Good Health and Well-being; COMPUTATION; POPULATION

Normality of random effects and error terms is a routine assumption for linear mixed models. However, such an assumption may be unrealistic, obscuring important features of within- and among-unit variation. A simple and robust Bayesian parametric approach that relaxes this assumption by using a multivariate skew-elliptical distribution, which includes the Skew-t, Skew-normal, t-Student, and Normal distributions as special cases and provides flexibility in capturing a broad range of non-normal and asymmetric behavior is presented. An appropriate posterior simulation scheme is developed and the methods are illustrated with an application to a longitudinal data example.