Bayesian analysis of skew-normal independent linear mixed models with heterogeneity in the random-effects population

• Published in: Journal of statistical planning and inference Vol. 142; no. 1; pp. 181 - 200
• Main Authors: Rômulo Barbosa Cabral, Celso, Hugo Lachos, Víctor, Regina Madruga, Maria
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 2012; Elsevier
• Subjects: Bayesian estimation; Distribution theory; Exact sciences and technology; Finite mixtures; General topics; Linear mixed models; Mathematics; MCMC; Multivariate analysis; Parametric inference; Probability and statistics; Sciences and techniques of general use; Skew-normal distribution; Statistics; Linear mixed models; MCMC; Bayesian estimation; Finite mixtures; Skew-normal distribution; Statistical distribution; Gaussian distribution; Multivariate analysis; Economic sciences; Linear model; Symmetric law; Coefficient of skewness; Markov chain; Heterogeneity; Skewness; Random effect; Approximation theory; Posterior distribution; Bayes estimation; Mixed distribution; Monte Carlo method; Heavy tail; Normal form; Random error; Multivariate distribution; Statistical decision; Symmetric function; Random distribution; Joint distribution; Algorithm; Statistical method; Mixed model; Skewness measure; Distribution tail; Econometrics
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2011.07.007

We present a new class of models to fit longitudinal data, obtained with a suitable modification of the classical linear mixed-effects model. For each sample unit, the joint distribution of the random effect and the random error is a finite mixture of scale mixtures of multivariate skew-normal distributions. This extension allows us to model the data in a more flexible way, taking into account skewness, multimodality and discrepant observations at the same time. The scale mixtures of skew-normal form an attractive class of asymmetric heavy-tailed distributions that includes the skew-normal, skew-Student-
t, skew-slash and the skew-contaminated normal distributions as special cases, being a flexible alternative to the use of the corresponding symmetric distributions in this type of models. A simple efficient MCMC Gibbs-type algorithm for posterior Bayesian inference is employed. In order to illustrate the usefulness of the proposed methodology, two artificial and two real data sets are analyzed.
► A simple efficient MCMC Gibbs algorithm for Bayesian inference is employed. ► The scale mixtures of skew-normal distributions are used. ► This extension allows us to model the data in a more flexible way. ► The model selection issue is considered.