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METRON

, Volume 72, Issue 2, pp 217–229 | Cite as

Negotiating multicollinearity with spike-and-slab priors

  • Veronika Ročková
  • Edward I. George
Article

Abstract

In multiple regression under the normal linear model, the presence of multicollinearity is well known to lead to unreliable and unstable maximum likelihood estimates. This can be particularly troublesome for the problem of variable selection where it becomes more difficult to distinguish between subset models. Here we show how adding a spike-and-slab prior mitigates this difficulty by filtering the likelihood surface into a posterior distribution that allocates the relevant likelihood information to each of the subset model modes. For identification of promising high posterior models in this setting, we consider three EM algorithms, the fast closed form EMVS version of Rockova and George (J Am Stat Assoc, 2014) and two new versions designed for variants of the spike-and-slab formulation. For a multimodal posterior under multicollinearity, we compare the regions of convergence of these three algorithms. Deterministic annealing versions of the EMVS algorithm are seen to substantially mitigate this multimodality. A single simple running example is used for illustration throughout.

Keywords

Deterministic annealing EM algorithm EMVS \(g\)-prior Variable selection 

Mathematics Subject Classification

62F15 62J05 

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Copyright information

© Sapienza Università di Roma 2014

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of PennsylvaniaPhiladelphiaUSA

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