Choosing the Link Function and Accounting for Link Uncertainty in Generalized Linear Models using Bayes Factors

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.