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

  • Christian Aßmann
  • Jens Boysen-Hogrefe
  • Markus Pape

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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File URL: https://www.ifw-members.ifw-kiel.de/publications/the-directional-identification-problem-in-bayesian-factor-analysis-an-ex-post-approach/KWP_1799.pdf
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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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  1. Carvalho, Carlos M. & Chang, Jeffrey & Lucas, Joseph E. & Nevins, Joseph R. & Wang, Quanli & West, Mike, 2008. "High-Dimensional Sparse Factor Modeling: Applications in Gene Expression Genomics," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1438-1456.
  2. Boivin, Jean & Ng, Serena, 2006. "Are more data always better for factor analysis?," Journal of Econometrics, Elsevier, vol. 132(1), pages 169-194, May.
  3. Geweke, John & Zhou, Guofu, 1996. "Measuring the Pricing Error of the Arbitrage Pricing Theory," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 557-87.
  4. Doz, Catherine & Giannone, Domenico & Reichlin, Lucrezia, 2011. "A two-step estimator for large approximate dynamic factor models based on Kalman filtering," Journal of Econometrics, Elsevier, vol. 164(1), pages 188-205, September.
  5. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
  6. M. Ayhan Kose & Christopher Otrok & Charles H. Whiteman, 2003. "International Business Cycles: World, Region, and Country-Specific Factors," American Economic Review, American Economic Association, vol. 93(4), pages 1216-1239, September.
  7. Otrok, Christopher & Whiteman, Charles H, 1998. "Bayesian Leading Indicators: Measuring and Predicting Economic Conditions in Iowa," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 997-1014, November.
  8. 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.
  9. John F. Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
  10. Donald Rubin & Dorothy Thayer, 1982. "EM algorithms for ML factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 47(1), pages 69-76, March.
  11. repec:hal:journl:peer-00844811 is not listed on IDEAS
  12. Aguilar, Omar & West, Mike, 2000. "Bayesian Dynamic Factor Models and Portfolio Allocation," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 338-57, July.
  13. Donald Rubin & Dorothy Thayer, 1983. "More on EM for ML factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 48(2), pages 253-257, June.
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