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We express the mean and variance terms in a double exponential regressionmodel as additive functions of the predictors and use Bayesian variableselection to determine which predictors enter the model, and whether they enterlinearly or flexibly. When the variance term is null we obtain a generalizedadditive model, which becomes a generalized linear model if the predictorsenter the mean linearly. The model is estimated using Markov chain Monte Carlosimulation and the methodology is illustrated using real and simulated datasets.

Variable Selection and Model Averaging in Semiparametric Overdispersed Generalized Linear Models