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Revista Colombiana de Estadística

versão impressa ISSN 0120-1751

Rev.Colomb.Estad. vol.42 no.1 Bogotá jan./jun. 2019  Epub 23-Maio-2019 

Artículos originales de investigación

A Bayesian Approach to Mixed Gamma Regression Models

Un enfoque bayesiano para modelos mixtos de regresión Gamma

Martha Lucía Corrales-Bossioa  , Edilberto Cepeda-Cuervob 

a Escuela de Matemáticas, Universidad Sergio Arboleda, Bogotá, Colombia.

b Departamento de Estadística, Facultad de Ciencias, Universidad Nacional de Colombia, Bogotá, Colombia.


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.

Key words: Bayesian analysis; Gamma distribution; Gamma regression; Mixed models


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).

Palabras-clave: Análisis bayesiano; Distribución Gamma; Regresión Gamma; Modelos mixtos

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Albert, J. H. & Chib, S. (1993), 'Bayesian analysis of binary and polychotomous response data', Journal of the American statistical Association 88(422), 669-679. [ Links ]

Besag, J., Green, P., Higdon, D. & Mengersen, K. (1995), 'Bayesian computation and stochastic systems', Statistical science pp. 3-41. [ Links ]

Brooks, S. P. & Gelman, A. (1998), 'General methods for monitoring convergence of iterative simulations', Journal of computational and graphical statistics 7(4), 434-455. [ Links ]

Brown, H. & Prescott, R. (2014), Applied mixed models in medicine, John Wiley & Sons. [ Links ]

Cepeda-Cuervo, E., Migon, H. S., Garrido, L. & Achcar, J. A. (2014), 'Generalized linear models with random effects in the two-parameter exponential family', Journal of Statistical Computation and Simulation 84(3), 513-525. [ Links ]

Cepeda, E. (2001), Modelagem da variabilidade em modelos lineares generalizados, Ph.D. tesis, Universidade Federal do Rio do Janeiro. [ Links ]

Cepeda, E. C. & Gamerman, D. (2004), 'Bayesian modeling of joint regressions for the mean and covariance matrix', Biometrical journal 46(4), 430-440. [ Links ]

Cepeda, E. & Gamerman, D. (2005), 'Bayesian methodology for modeling parameters in the two parameter exponential family', Revista Estadistica 57(168-169), 93-105. [ Links ]

Cox, D. R. & Reid, N. (1987), 'Parameter orthogonality and approximate conditional inference', Journal of the Royal Statistical Society. Series B (Methodological) pp. 1-39. [ Links ]

De Jong, P., Heller, G. Z. et al. (2008), Generalized linear models for insurance data, Vol. 10, Cambridge University Press Cambridge. [ Links ]

Demidenko, E. (2013), Mixed models: theory and applications with R, John Wiley & Sons. [ Links ]

Figueroa-Zúñiga, J. I., Arellano-Valle, R. B. & Ferrari, S. L. (2013), 'Mixed beta regression: A bayesian perspective', Computational Statistics & Data Analysis 61, 137-147. [ Links ]

Fong, Y., Rue, H. & Wakefield, J. (2010), 'Bayesian inference for generalized linear mixed models', Biostatistics 11(3), 397-412. [ Links ]

Fonseca, T. C., Ferreira, M. A. & Migon, H. S. (2008), 'Objective Bayesian analysis for the Student-t regression model', Biometrika 95(2), 325-333. [ Links ]

Geweke, J. (1992), 'Evaluating the accuracy of sampling-based approaches to calculation of moments (with discussion)', Bayesian Statistics 4, 169-193. [ Links ]

Heidelberger, P. & Welch, P. D. (1981), 'A spectral method for confidence interval generation and run length control in simulations', Communications of the ACM 24(4), 233-245. [ Links ]

McCullagh, P. & Nelder, J. A. (1989), Generalized Linear Models, Chapman & Hall. [ Links ]

Plummer, M., Best, N., Cowles, K. & Vines, K. (2006), 'CODA: convergence diagnosis and output analysis for MCMC', R news 6(1), 7-11. [ Links ]

R Core Team (2017), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. [ Links ]

Raffery, A. & Lewis, S. (1992), 'One long run with diagnostics: Implementation strategies for markov chain monte carlo', Statist. Sci 7, 493-497. [ Links ]

Ronquist, F. & Huelsenbeck, J. P. (2003), 'Mrbayes 3: Bayesian phylogenetic inference under mixed models', Bioinformatics 19(12), 1572-1574. [ Links ]

Thomas, A. (2006), 'Making bugs open', R news 6, 12-17. [ Links ]

Vonesh, E. F. (2006), 'Mixed models: Theory and applications'. [ Links ]

Recebido: Dezembro de 2017; Aceito: Novembro de 2018

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