There are many aspects of model choice that are involved in health effect studies of particulate matter and other pollutants. Some of these choices concern which pollutants and confounding variables should be included in the model, what type of lag structure for the covariates should be used, which interactions need to be considered, and how to model nonlinear trends. Because of the large number of potential variables, model selection is often used to find a parsimonious model. Different model selection strategies may lead to very different models and conclusions for the same set of data. As variable selection may involve numerous tests of hypotheses, the resulting significance levels may be called into question, and there is the concern that the positive associations are a result of multiple testing. Bayesian model averaging is an alternative that can be used to combine inferences from multiple models and incorporate model uncertainty. This paper presents objective prior distributions for Bayesian model averaging in generalized linear models so that Bayesian model selection corresponds to standard methods of model selection, such as the Akaike Information Criterion (AIC) or Bayes Information Criterion (BIC), and inferences within a model are based on standard maximum likelihood estimation. These methods allow non-Bayesians to describe the level of uncertainty due to model selection, and can be used to combine inferences by averaging over a wider class of models using readily available summary statistics from standard model fitting programs. Using Bayesian Model Averaging and objective prior distributions, we re-analyze data from Birmingham, AL and illustrate the role of model uncertainty in inferences about the effect of particulate matter on elderly mortality.

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This work was supported by NSF grants DMS-96.26135 and DMS-97.33013, and was completed while the author was a visitor at the National Research Center for Statistics and the Environment, University of Washington. Although the research described in this article has been funded in part by the United States Environmental Protection Agency through agreement CR825173-01-0 to the University of Washington, it has as not been subjected to the Agency's required peer and policy review and therefore does not necessarily reflect the views of the Agency and no official endorsement should be inferred.