Bayesian Structured Antedependence Model Proposals for Longitudinal Data

Resumen

An important problem in Statistics is the study of longitudinal data taking into account the effect of explanatory variables such as treatments and time and, at the same time, incorporate into the model the time dependence between observations on the same individual. The latter is specially relevant in the case of having nonstationary correlation, as well as nonconstant variance for the different time point at which measurements are taken. Antedependence (AD) models constitute a well known commonly used set of models that can accommodate this behavior. In this paper, a new Bayesian approach for analyzing longitudinal data within the context of antedependence models is proposed. This innovative approach takes into account the possibility of having nonstationary correlations and variances, and proposes a robust and computationally effcient estimation method for this type of data. We consider the joint modelling of the mean and covariance structures for the general AD model, estimating their parameters in a longitudinal data context. Our Bayesian approach is based on a generalization of the Gibbs sampling and Metropolis-Hastings by blocks algorithm, properly adapted to the AD models longitudinal data settings. Finally, we illustrate the proposed methodology by analyzing the race dataset.