Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance,
will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly
indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using
Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable
insight for the researcher about its experimental results.
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Bayesian data analysis;
Markov Chain Monte Carlo;
generalized linear models;
Document Type: Research Article
Departamento de Estatística,Universidade de Brasília, ICC centro, subsolo, módulo 15, CEP70910-900BrasíliaDF, Brazil
Departamento de Ciências Exatas,Universidade de São Paulo – ESALQ, Av. Pádua Dias 11, CP 9, CEP13418-900PiracicabaSP, Brazil
I-BioStat,Universiteit Hasselt and Katholieke Universiteit Leuven, Agoralaan 13590Diepenbeek, Belgium
August 1, 2011