Bayesian Inference for Skew-normal Linear Mixed Models

Arellano-Valle, R.B., H. Bolfarine and V.H. Lachos

Journal of Applied Statistics, 2007, vol. 34, issue 6, pages 663-682

Abstract: 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.

Keywords: Bayesian inference; MCMC; Gibbs sampler; multivariate skew-normal distribution; skewness (search for similar items in EconPapers)

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