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The Directional Identification Problem in Bayesian Factor Analysis: An Ex-Post Approach

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  • Christian Aßmann
  • Jens Boysen-Hogrefe
  • Markus Pape

Abstract

Due to their well-known indeterminacies, factor models require identifying assumptions to guarantee unique parameter estimates. For Bayesian estimation, these identifying assumptions are usually implemented by imposing constraints on certain model parameters. This strategy, however, may result in posterior distributions with shapes that depend on the ordering of cross-sections in the data set. We propose an alternative approach, which relies on a sampler without the usual identifying constraints. Identification is reached ex-post based on a Procrustes transformation. Resulting posterior estimates are ordering invariant and show favorable properties with respect to convergence and statistical as well as numerical accuracy

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Bibliographic Info

Paper provided by Kiel Institute for the World Economy in its series Kiel Working Papers with number 1799.

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Length: 42 pages
Date of creation: Oct 2012
Date of revision:
Handle: RePEc:kie:kieliw:1799

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Keywords: Bayesian Estimation; Factor Models; Multimodality; Ordering; Orthogonal Transformation;

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  1. Jean Boivin & Serena Ng, 2003. "Are More Data Always Better for Factor Analysis?," NBER Working Papers 9829, National Bureau of Economic Research, Inc.
  2. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
  3. Donald Rubin & Dorothy Thayer, 1982. "EM algorithms for ML factor analysis," Psychometrika, Springer, vol. 47(1), pages 69-76, March.
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