Bayesian inference in joint modelling of location and scale parameters of the \(t\) distribution for longitudinal data. (English) Zbl 1204.62040
Summary: This paper presents a fully Bayesian approach to multivariate \(t\) regression models whose mean vector and scale covariance matrix are modelled jointly for analyzing longitudinal data. The scale covariance structure is factorized in terms of unconstrained autoregressive and scale innovation parameters through a modified Cholesky decomposition. A computationally flexible data augmentation sampler coupled with the Metropolis-within-Gibbs scheme is developed for computing the posterior distributions of parameters. The Bayesian predictive inference for the future response vector is also investigated. The proposed methodologies are illustrated through a real example from a sleep dose-response study.
MSC:
| 62F15 | Bayesian inference |
| 62H12 | Estimation in multivariate analysis |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 65C60 | Computational problems in statistics (MSC2010) |
Keywords:
Cholesky decomposition; data augmentation; deviance information criterion; maximum likelihood estimation; outliers; predictive distributionSoftware:
lme4References:
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