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Czado, Claudia and Raftery, A. E. (2001): Choosing the Link Function and Accounting for Link Uncertainty in Generalized Linear Models using Bayes Factors. Collaborative Research Center 386, Discussion Paper 262
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Abstract

One important component of model selection using generalized linear models (GLM) is the choice of a link function. Approximate Bayes factors are used to assess the improvement in fit over a GLM with canonical link when a parametric link family is used. For this approximate Bayes factors are calculated using the approximations given in Raftery (1996), together with a reference set of prior distributions. This methodology can also be used to differentiate between different parametric link families, as well as allowing one to jointly select the link family and the independent variables. This involves comparing nonnested models. This is illustrated using parametric link families studied in Czado (1997) for two data sets involving binomial responses.