Statistics and Its Interface

Volume 7 (2014)

Number 1

We dedicate this special issue to Dr. Gang Zheng, a great colleague and dear friend to many of us.

Linear mixed models for multiple outcomes using extended multivariate skew-$t$ distributions

Pages: 101 – 111



Binbing Yu (Laboratory of Epidemiology and Population Sciences, National Institute on Aging, Bethesda, Maryland, U.S.A.)

A. James O’Malley (Harvard Medical School, Department of Health Care Policy, Boston, Massachusetts, U.S.A.)

Pulak Ghosh (Department of Quantitative Methods and Information Sciences, Indian Institute of Management, Bangalore, India)


Multivariate outcomes with heavy skewness and thick tails often arise from clustered experiments or longitudinal studies. Linear mixed models with multivariate skew-$t$ (MST) distributions for the random effects and the error terms is a popular tool of robust modeling for such outcomes. However the usual MST distribution only allows a common degree of freedom for all marginal distributions, which is only appropriate when each marginal has the same amount of tail heaviness. In this paper, we introduce a new class of extended MST distributions, which allow different degrees of freedom and thereby can accommodate heterogeneity in tail-heaviness across outcomes. The extended MST distributions yield a flexible family of models for multivariate outcomes. The hierarchical representation of the MST distribution allows MCMC methods to be easily applied to compute the parameter estimates. The proposed model is applied to data from two biomedical studies: one on bivariate markers of AIDS progression and the other on sexual behavior from a longitudinal study.


multivariate skew-$t$, robust method, scale-mixture representation

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