A Bayesian Approach to Mixed Gamma Regression Models

• Autores: Martha Corrales Bossio, Edilberto Cepeda Cuervo
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 42, Nº. 1, 2019, págs. 81-99
• Idioma: inglés
• DOI: 10.15446/rce.v42n1.69334
• Títulos paralelos:
  • Un enfoque bayesiano para modelos mixtos de regresión Gamma
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen Los modelos de regresión gamma son una opción adecuada para modelar variables continuas que toman valores reales positivos. Este artículo presenta un modelo de regresión gamma con efectos mixtos desde un enfoque bayesiano. Utilizamos la parametrización de la distribución gamma en términos de la media y el parámetro de forma, los cuales se modelan a través de estructuras de regresión que pueden involucrar efectos fijos y aleatorios. Se proporciona una implementación computacional a través del muestreo de Gibbs y se presentan ejemplos ilustrativos (datos simulados y reales).

  • English

    Abstract Gamma regression models are a suitable choice to model continuous variables that take positive real values. This paper presents a gamma regression model with mixed effects from a Bayesian approach. We use the parametrization of the gamma distribution in terms of the mean and the shape parameter, both of which are modelled through regression structures that may involve fixed and random effects. A computational implementation via Gibbs sampling is provided and illustrative examples (simulated and real data) are presented.

• Referencias bibliográficas
  • Albert, J. H.,Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American statistical Association....
  • Besag, J.,Green, P.,Higdon, D.,Mengersen, K. (1995). Bayesian computation and stochastic systems. Statistical science. 3-41
  • Brooks, S. P.,Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical...
  • Brown, H.,Prescott, R. (2014). Applied mixed models in medicine. John Wiley & Sons.
  • Cepeda-Cuervo, E.,Migon, H. S.,Garrido, L.,Achcar, J. A. (2014). Generalized linear models with random effects in the two-parameter exponential...
  • Cepeda, E. (2001). Modelagem da variabilidade em modelos lineares generalizados. Universidade Federal do Rio do Janeiro.
  • Cepeda, E. C.,Gamerman, D. (2004). Bayesian modeling of joint regressions for the mean and covariance matrix. Biometrical journal. 46. 430
  • Cepeda, E.,Gamerman, D. (2005). Bayesian methodology for modeling parameters in the two parameter exponential family. Revista Estadistica....
  • Cox, D. R.,Reid, N. (1987). Parameter orthogonality and approximate conditional inference. Journal of the Royal Statistical Society. 1-39
  • De Jong, P.,Heller, G. Z.. (2008). Generalized linear models for insurance data. Cambridge University Press Cambridge.
  • Demidenko, E. (2013). Mixed models: theory and applications with R. John Wiley & Sons.
  • Figueroa-Zúñiga, J. I.,Arellano-Valle, R. B.,Ferrari, S. L. (2013). Mixed beta regression: A bayesian perspective. Computational Statistics...
  • Fong, Y.,Rue, H.,Wakefield, J. (2010). Bayesian inference for generalized linear mixed models. Biostatistics. 11. 397-412
  • Fonseca, T. C.,Ferreira, M. A.,Migon, H. S. (2008). Objective Bayesian analysis for the Student-t regression model. Biometrika. 95. 325
  • Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to calculation of moments (with discussion). Bayesian Statistics....
  • Heidelberger, P.,Welch, P. D. (1981). A spectral method for confidence interval generation and run length control in simulations. Communications...
  • McCullagh, P.,Nelder, J. A. (1989). Generalized Linear Models. Chapman & Hall.
  • Plummer, M.,Best, N.,Cowles, K.,Vines, K. (2006). CODA: convergence diagnosis and output analysis for MCMC. R news. 6. 7-11
  • (2017). R Core Team. R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria.
  • Raffery, A.,Lewis, S. (1992). One long run with diagnostics: Implementation strategies for markov chain monte carlo. Statist. Sci. 7. 493
  • Ronquist, F.,Huelsenbeck, J. P. (2003). Mrbayes 3: Bayesian phylogenetic inference under mixed models. Bioinformatics. 19. 1572
  • Thomas, A. (2006). Making bugs open. 12
  • Vonesh, E. F. (2006). Mixed models: Theory and applications.