An evaluation of prior influence on the predictive ability of Bayesian model averaging

Model averaging is gaining popularity among ecologists for making inference and predictions. Methods for combining models include Bayesian model averaging (BMA) and Akaike's Information Criterion (AIC) model averaging. BMA can be implemented with different prior model weights, including the Kullback-Leibler prior associated with AIC model averaging, but it is unclear how the prior model weight affects model results in a predictive context. Here, we implemented BMA using the Bayesian Information Criterion (BIC) approximation to Bayes factors for building predictive models of bird abundance and occurrence in the Chihuahuan Desert of New Mexico. We examined how model predictive ability differed across four prior model weights, and how averaged coefficient estimates, standard errors and coefficients' posterior probabilities varied for 16 bird species. We also compared the predictive ability of BMA models to a best single-model approach. Overall, Occam's prior of parsimony provided the best predictive models. In general, the Kullback-Leibler prior, however, favored complex models of lower predictive ability. BMA performed better than a best single-model approach independently of the prior model weight for 6 out of 16 species. For 6 other species, the choice of the prior model weight affected whether BMA was better than the best single-model approach. Our results demonstrate that parsimonious priors may be favorable over priors that favor complexity for making predictions. The approach we present has direct applications in ecology for better predicting patterns of species' abundance and occurrence.