Choosing the link function and accounting for link uncertainty in generalized linear models using Bayes factors |
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Authors: | Claudia Czado Adrian E Raftery |
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Institution: | 1. Zentrum Mathematik, Technische Universit?t München, Boltzmannstr. 3, 85747, Garching bei München, Germany 2. Department of Statistics, Unicersity of Washington, Box 354322, 98195-4322, Seattle, WA, USA
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Abstract: | One important component of model selection using generalized linear models (GLM) is the choice of a link function. We propose
using approximate Bayes factors to assess the improvement in fit over a GLM with canonical link when a parametric link family
is used. The approximate Bayes factors are calculated using the Laplace approximations given in 32], together with a reference
set of prior distributions. This methodology can 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
and so standard significance tests cannot be used. The approach also accounts explicitly for uncertainty about the link function.
The methods are illustrated using parametric link families studied in 12] for two data sets involving binomial responses.
The first author was supported by Sonderforschungsbereich 386 Statistische Analyse Diskreter Strukturen, and the second author by NIH Grant 1R01CA094212-01 and ONR Grant N00014-01-10745. |
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Keywords: | Bayes factors link function GLM model selection reference prior |
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