Choosing the link function and accounting for link uncertainty in generalized linear models using Bayes factors

Choosing the link function and accounting for link uncertainty in generalized linear models using... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Statistical Papers Springer Journals

Choosing the link function and accounting for link uncertainty in generalized linear models using Bayes factors

Statistical Papers, Volume 47 (3) – Oct 9, 2006

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Publisher
Springer Journals
Copyright
Copyright © 2006 by Springer-Verlag
Subject
Statistics; Statistics for Business/Economics/Mathematical Finance/Insurance; Probability Theory and Stochastic Processes; Economic Theory/Quantitative Economics/Mathematical Methods; Operation Research/Decision Theory
ISSN
0932-5026
eISSN
1613-9798
DOI
10.1007/s00362-006-0296-9
Publisher site
See Article on Publisher Site

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.

Journal

Statistical PapersSpringer Journals

Published: Oct 9, 2006

References

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