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Bayesian variable selection for correlated covariates via colored cliques

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  • Stefano Monni

Abstract

We propose a Bayesian method to select groups of correlated explanatory variables in a linear regression framework. We do this by introducing in the prior distribution assigned to the regression coefficients a random matrix $$G$$ G that encodes the group structure. The groups can thus be inferred by sampling from the posterior distribution of $$G$$ G . We then give a graph-theoretic interpretation of this random matrix $$G$$ G as the adjacency matrix of cliques. We discuss the extension of the groups from cliques to more general random graphs, so that the proposed approach can be viewed as a method to find networks of correlated covariates that are associated with the response. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Stefano Monni, 2014. "Bayesian variable selection for correlated covariates via colored cliques," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 143-163, April.
    • Handle: RePEc:spr:alstar:v:98:y:2014:i:2:p:143-163
    DOI: 10.1007/s10182-013-0218-9
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    References listed on IDEAS

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    5. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
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    Keywords

    Variable selection; Graphs;

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