A general skew-t mixed model that allows different degrees of freedom for random effects and error distributions

Abstract

This paper develops a robust mixed model that assumes a multivariate skew-t distribution for random effects and an independent multivariate t-distribution for errors. It simultaneously captures skewness and heavy tailedness in data, while allowing the random effects and error distributions to have different degrees of freedom. It is fit using an EM-type algorithm. Simulations show that its efficiency for estimating mean response is comparable to that of the recent skew-t mixed model. But it may be considerably more efficient than the latter for estimating variance–covariance parameters when at least one of the random effects distribution or the error distribution has heavy tails, possibly due to outliers. The proposed model is used to analyze a data set consisting of lengths of claws of fiddler crabs (Uca mjoebergi).