Journal
JOURNAL OF APPLIED STATISTICS
Volume 34, Issue 6, Pages 663-682Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/02664760701236905
Keywords
Bayesian inference; MCMC; Gibbs sampler; multivariate skew-normal distribution; skewness
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Linear mixed models (LMM) are frequently used to analyze repeated measures data, because they are more flexible to modelling the correlation within-subject, often present in this type of data. The most popular LMM for continuous responses assumes that both the random effects and the within-subjects errors are normally distributed, which can be an unrealistic assumption, obscuring important features of the variations present within and among the units ( or groups). This work presents skew-normal liner mixed models (SNLMM) that relax the normality assumption by using a multivariate skew-normal distribution, which includes the normal ones as a special case and provides robust estimation in mixed models. The MCMC scheme is derived and the results of a simulation study are provided demonstrating that standard information criteria may be used to detect departures from normality. The procedures are illustrated using a real data set from a cholesterol study.
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