Mixtures of g-priors for Bayesian model averaging with economic applications
By E. Ley, Mark F. J. Steel. 2010
156 citations recorded by the source corpus.
We examine the issue of variable selection in linear regression modeling, where we have a potentially large amount of possible covariates and economic theory offers insufficient guidance on how to select the appropriate subset. In this context, Bayesian Model Averaging presents a formal Bayesian solution to dealing with model uncertainty. Our main interest here is the effect of the prior on the results, such as posterior inclusion probabilities of regressors and predictive performance. We combine a Binomial-Beta prior on model size with a g-prior on the coefficients of each model. In addition, we assign a hyperprior to g, as the choice of g has been found to have a large impact on the results. For the prior on g, we examine the Zellner-Siow prior and a class of Beta shrinkage priors, which covers most choices in the recent literature. We propose a benchmark Beta prior, inspired by earlier findings with fixed g, and show it leads to consistent model selection. The effect of this prior structure on penalties for complexity and lack of fit is described in some detail. Inference is conducted through a Markov chain Monte Carlo sampler over model space and g. We examine the performance of the various priors in the context of simulated and real data. For the latter, we consider two important applications in economics, namely cross-country growth regression and returns to schooling. Recommendations to applied users are provided.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/8206c244a07d08829a72de23f6de66893c8c89b9
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Citations in the corpus
- Mixtures of g-Priors in Generalized Linear Models (2015, background): “Similar to the findings of Ley and Steel (2012) in linear models, we also recommend the benchmark and hyper-g/n priors for general practitioners, due to their balanced performance in selection and prediction.”
- Benchmark Priors Revisited: On Adaptive Shrinkage and the Supermodel Effect in Bayesian Model Averaging (2009, unknown): “The contribution by Liang et al. (2008) differs in providing a closedform solution – which is so computationally demanding that they implement it via analytical approximations.”
- Forecasting the European carbon market (2013, methodology): “In regression problems with many potential explanatory variables, BMA has been a common response to such worries (see, among many others, Raftery et al. (1997), Fernandez et al. (2001a, b), Sala-i-Martin et al. (2004), Eicher et al. (2010) and Ley and Steel (2010)).”
- Model Averaging and Its Use in Economics (2017, methodology): “Ley and Steel (2012) consider the more general class of beta priors on the shrinkage factor where a Beta(b, c) prior on δ induces the following prior on g: p(g) = Γ(b+ c) Γ(b)Γ(c) gb−1(1 + g)−(b+c).”