Bayesian structured antedependence model proposals for longitudinal data

  1. Edwin Castillo-Carreno 1
  2. Edilberto Cepeda-Cuervo 1
  3. Vicente Núñez-Antón 2
  1. 1 Universidad Nacional de Colombia
    info

    Universidad Nacional de Colombia

    Bogotá, Colombia

    ROR https://ror.org/059yx9a68

  2. 2 University of the Basque Country UPV/EHU.
Revista:
Sort: Statistics and Operations Research Transactions

ISSN: 1696-2281

Año de publicación: 2020

Volumen: 44

Número: 1

Páginas: 171-200

Tipo: Artículo

DOI: 10.2436/20.8080.02.99 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Sort: Statistics and Operations Research Transactions

Resumen

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.

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Información de financiación

This work was supported by the Department of Statistics, Faculty of Sciences of the Uni-versidad Nacional de Colombia, Ministerio de Economía y Competitividad, Agencia Es-tatal de Investigación (AEI), Fondo Europeo de Desarrollo Regional (FEDER), the Department of Education of the Basque Government (UPV/EHU Econometrics Research Group), and Universidad del País Vasco UPV/EHU under research grants MTM2013-40941-P (AEI/FEDER, UE), MTM2016-74931-P (AEI/FEDER, UE), IT-642-13, IT1359-19 and UFI11/03.

Financiadores

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