A flexible class of parametric distributions for Bayesian linear mixed models

• Activity Number: 358 - Contributed Poster Presentations: Biometrics Section
• Type: Contributed
• Date/Time: Tuesday, July 31, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Darren Wraith* and Mohsen Maleki and Reinaldo B. Arellano-Valle
• Companies: Queensland University of Technology and Shiraz University and Universidad Católica de Chile
• Keywords: Bayesian analysis; Linear mixed effect model; MCMC method; Unrestricted skew-normal generalized-hyperbolic distribution; Unrestricted skew-normal distribution

Abstract

We consider a linear mixed effect model (LMM) assuming that the random effect and error terms follow an unrestricted skew-normal generalized-hyperbolic (SUNGH) distribution. The SUNGH is a broad class of flexible distributions that includes various other well-known asymmetric and symmetric families such as the scale mixtures of skew-normal, the skew-normal generalized-hyperbolic and its corresponding symmetric versions. The class of distributions provides a much needed unified framework where the choice of the best fitting distribution can proceed quite naturally through either parameter estimation or by placing constraints on specific parameters and assessing through model choice criteria. The class has several desirable properties, including an analytically tractable density and ease of computation for simulation and estimation of parameters. The parameters of the new model are estimated via the Bayesian method, and the performance of the proposed methodology is examined on simulated and real data from a clinical trial on treatment options for schizophrenia.