Bayesian structured antedependence model proposals for longitudinal data
Castillo-Carreno, Edwin (Universidad Nacional de Colombia. Departamento de Estadística)
Cepeda-Cuervo, Edilberto (Universidad Nacional de Colombia. Departamento de Estadística)
Núñez-Antón, Vicente. (Universidad del País Vasco. Departamento de Economía Aplicada)

Date:	2020
Abstract:	An important problem in Statistics is the study of longitudinal data taking into account the effect of other explanatory variables, such as treatments and time and, simultaneously, the incorporation into the model of the time dependence between observations on the same individual. The latter is specially relevant in the case of nonstationary correlations, and nonconstant variances for the different time point at which measurements are taken. Antedependence models constitute a well known commonly used set of models that can accommodate this behaviour. These covariance models can include too many parameters and estimation can be a complicated optimization problem requiring the use of complex algorithms and programming. In this paper, a new Bayesian approach to analyse 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 efficient estimation method for this type of data. We consider the joint modelling of the mean and covariance structures for the general antedependence 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 antedependence models longitudinal data settings. Finally, we illustrate the proposed methodology by analysing several examples where antedependence models have been shown to be useful: the small mice, the speech recognition and the race data sets.
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Antedependence models ; Bayesian methods ; Gibbs sampling ; Mean-covariance modelling ; Nonstationary correlation
Published in:	SORT : statistics and operations research transactions, Vol. 44 Núm. 1 (January-June 2020) , p. 171-200 (Articles) , ISSN 2013-8830

Adreça alternativa: https://raco.cat/index.php/SORT/article/view/371188
DOI: 10.2436/20.8080.02.99

30 p, 262.9 KB

The record appears in these collections:
Articles > Published articles > SORT
Articles > Research articles