Bayesian modelling of the mean and covariance matrix in normal nonlinear models

  1. Cepeda-Cuervo, Edilberto 2
  2. Núñez-Antón, Vicente 1
  1. 1 Universidad del País Vasco/Euskal Herriko Unibertsitatea
    info

    Universidad del País Vasco/Euskal Herriko Unibertsitatea

    Lejona, España

    ROR https://ror.org/000xsnr85

  2. 2 Universidad Nacional de Colombia
    info

    Universidad Nacional de Colombia

    Bogotá, Colombia

    ROR https://ror.org/059yx9a68

Revista:
Journal of Statistical Computation and Simulation

ISSN: 0094-9655,  1563-5163

Año de publicación: 2009

Volumen: 79

Número: 6

Páginas: 837-853

Tipo: Artículo

DOI: 10.1080/00949650801967403 WoS: WOS:000266244900006 GOOGLE SCHOLAR

Otras publicaciones en: Journal of Statistical Computation and Simulation

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. In this paper, a new Bayesian approach for analysing longitudinal data is proposed. This innovative approach takes into account the possibility of having nonlinear regression structures on the mean and linear regression structures on the variance–covariance matrix of normal observations, and it is based on the modelling strategy suggested by Pourahmadi [M. Pourahmadi, Joint mean-covariance models with applications to longitudinal data: Unconstrained parameterizations, Biometrika, 87 (1999), pp. 667–690.]. We initially extend the classical methodology to accommodate the fitting of nonlinear mean models then we propose our Bayesian approach based on a generalization of the Metropolis–Hastings algorithm of Cepeda [E.C. Cepeda, Variability modeling in generalized linear models, Unpublished Ph.D. Thesis, Mathematics Institute, Universidade Federal do Rio de Janeiro, 2001]. Finally, we illustrate the proposed methodology by analysing one example, the cattle data set, that is used to study cattle growth.

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