Robust Linear Mixed Models with Skew-Normal Independent Distributions from a Bayesian Perspective

Linear mixed models were developed to handle clustered data and have been a topic of increasing interest in statistics for the past fifty years. Generally, the normality (or symmetry) of the randomeffects is a common assumption in linear mixed models but it may, sometimes, be unrealistic, obscuring important features of among-subjects variation. In this article, we utilize skew-normal/independent distributions as a tool for robust modeling of linear mixed models under a Bayesian paradigm. The skew-normal/independent distributions is an attractive class of asymmetric heavy-tailed distributions that includes the skew-normal distribution, the skew-t distribution, the skew-slash distribution and the skew contaminated normal distribution as special cases, providing an appealing robust alternative to the routine use of symmetric distributions in this type of models. The methods developed are illustrated using a real data set from Framingham cholesterol study.