A robust approach to joint modeling of mean and scale covariance for longitudinal data

In this paper, we propose a multivariate t$t$ regression model with its mean and scale covariance modeled jointly for the analysis of longitudinal data. A modified Cholesky decomposition is adopted to factorize the dependence structure in terms of unconstrained autoregressive and scale innovation parameters. We present three distinct representations of the log-likelihood function of the model and study the associated properties. A computationally efficient Fisher scoring algorithm is developed for carrying out maximum likelihood estimation. The technique for the prediction of future responses in this context is also investigated. The implementation of the proposed methodology is illustrated through two real-life examples and extensive simulation studies.