IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v100y2009i8p1717-1726.html
   My bibliography  Save this article

Bayesian factor analysis with fat-tailed factors and its exact marginal likelihood

Author

Listed:
  • Ando, Tomohiro

Abstract

The traditional Bayesian factor analysis method is extended. In contrast to the case for previous studies, the matrix variate t-distribution is utilized to provide a prior density on the latent factors. This is a natural extension of the traditional model and yields many advantages. The crucial issue is the selection of the number of factors. The marginal likelihood, constructed by asymptotic and computational approaches, is generally utilized for this problem. However, both theoretical and computational problems have arisen. In this paper, the exact marginal likelihood is derived. It enables us to evaluate posterior model probabilities without inducing the above problems. Monte Carlo experiments were conducted to examine the performance of the proposed Bayesian factor analysis modelling methodology. The simulation results show that the proposed methodology performs well.

Suggested Citation

  • Ando, Tomohiro, 2009. "Bayesian factor analysis with fat-tailed factors and its exact marginal likelihood," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1717-1726, September.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:8:p:1717-1726
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(09)00039-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sik-Yum Lee & Ye-Mao Xia, 2006. "Maximum Likelihood Methods in Treating Outliers and Symmetrically Heavy-Tailed Distributions for Nonlinear Structural Equation Models with Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 71(3), pages 565-585, September.
    2. Rossi P. E & Gilula Z. & Allenby G. M, 2001. "Overcoming Scale Usage Heterogeneity: A Bayesian Hierarchical Approach," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 20-31, March.
    3. Sik-Yum Lee, 2006. "Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 71(3), pages 541-564, September.
    4. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    5. Tomohiro Ando, 2007. "Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models," Biometrika, Biometrika Trust, vol. 94(2), pages 443-458.
    6. 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 557-587.
    7. Sadanori Konishi, 2004. "Bayesian information criteria and smoothing parameter selection in radial basis function networks," Biometrika, Biometrika Trust, vol. 91(1), pages 27-43, March.
    8. Aguilar, Omar & West, Mike, 2000. "Bayesian Dynamic Factor Models and Portfolio Allocation," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 338-357, July.
    9. Ledyard Tucker, 1940. "The role of correlated factors in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 5(2), pages 141-152, June.
    10. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    11. Phillips, P. C. B., 1985. "The distribution of matrix quotients," Journal of Multivariate Analysis, Elsevier, vol. 16(1), pages 157-161, February.
    12. Hirotugu Akaike, 1987. "Factor analysis and AIC," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 317-332, September.
    13. Sock-Cheng Lewin-Koh, 2003. "Heteroscedastic factor analysis," Biometrika, Biometrika Trust, vol. 90(1), pages 85-97, March.
    14. Sik-Yum Lee & Ye-Mao Xia, 2008. "A Robust Bayesian Approach for Structural Equation Models with Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 73(3), pages 343-364, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jaejoon Lee & Seongil Jo & Jaeyong Lee, 2022. "Robust sparse Bayesian infinite factor models," Computational Statistics, Springer, vol. 37(5), pages 2693-2715, November.
    2. Mohsen Maleki & Darren Wraith, 2019. "Mixtures of multivariate restricted skew-normal factor analyzer models in a Bayesian framework," Computational Statistics, Springer, vol. 34(3), pages 1039-1053, September.
    3. Tsay, Ruey S. & Ando, Tomohiro, 2012. "Bayesian panel data analysis for exploring the impact of subprime financial crisis on the US stock market," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3345-3365.
    4. Leung, Dennis & Drton, Mathias, 2016. "Order-invariant prior specification in Bayesian factor analysis," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 60-66.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bai, Jushan & Ando, Tomohiro, 2013. "Multifactor asset pricing with a large number of observable risk factors and unobservable common and group-specific factors," MPRA Paper 52785, University Library of Munich, Germany, revised Dec 2013.
    2. Aßmann, Christian & Boysen-Hogrefe, Jens & Pape, Markus, 2012. "The directional identification problem in Bayesian factor analysis: An ex-post approach," Kiel Working Papers 1799, Kiel Institute for the World Economy (IfW Kiel).
    3. Necati Tekatli, 2007. "Generalized Factor Models: A Bayesian Approach," Working Papers 334, Barcelona School of Economics.
    4. Necati Tekatli, 2010. "A Bayesian Generalized Factor Model with Comparative Analysis (Genellestirilmis Faktor Modellerinin Bayesyen Yaklasimi ve Karsilastirmali Analizi)," Working Papers 1018, Research and Monetary Policy Department, Central Bank of the Republic of Turkey.
    5. Aßmann, Christian & Boysen-Hogrefe, Jens & Pape, Markus, 2016. "Bayesian analysis of static and dynamic factor models: An ex-post approach towards the rotation problem," Journal of Econometrics, Elsevier, vol. 192(1), pages 190-206.
    6. Chadwick, Meltem, 2010. "Performance of Bayesian Latent Factor Models in Measuring Pricing Errors," MPRA Paper 79060, University Library of Munich, Germany.
    7. Bork, Lasse, 2009. "Estimating US Monetary Policy Shocks Using a Factor-Augmented Vector Autoregression: An EM Algorithm Approach," Finance Research Group Working Papers F-2009-03, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    8. Tsay, Ruey S. & Ando, Tomohiro, 2012. "Bayesian panel data analysis for exploring the impact of subprime financial crisis on the US stock market," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3345-3365.
    9. Sylvia Kaufmann & Christian Schumacher, 2013. "Bayesian estimation of sparse dynamic factor models with order-independent identification," Working Papers 13.04, Swiss National Bank, Study Center Gerzensee.
    10. S. J. Koopman & G. Mesters, 2017. "Empirical Bayes Methods for Dynamic Factor Models," The Review of Economics and Statistics, MIT Press, vol. 99(3), pages 486-498, July.
    11. Calzolari, Giorgio & Halbleib, Roxana, 2018. "Estimating stable latent factor models by indirect inference," Journal of Econometrics, Elsevier, vol. 205(1), pages 280-301.
    12. Ke-Hai Yuan & Zhiyong Zhang, 2012. "Robust Structural Equation Modeling with Missing Data and Auxiliary Variables," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 803-826, October.
    13. Tomohiro Ando & Ruey S. Tsay, 2009. "Model selection for generalized linear models with factor‐augmented predictors," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 207-235, May.
    14. Daniela Andreini & Diego Rinallo & Giuseppe Pedeliento & Mara Bergamaschi, 2017. "Brands and Religion in the Secularized Marketplace and Workplace: Insights from the Case of an Italian Hospital Renamed After a Roman Catholic Pope," Journal of Business Ethics, Springer, vol. 141(3), pages 529-550, March.
    15. Byrd, T. A. & Marshall, T. E., 1997. "Relating information technology investment to organizational performance: a causal model analysis," Omega, Elsevier, vol. 25(1), pages 43-56, February.
    16. Kastner, Gregor, 2019. "Sparse Bayesian time-varying covariance estimation in many dimensions," Journal of Econometrics, Elsevier, vol. 210(1), pages 98-115.
    17. Filippo Ferroni & Benjamin Klaus, 2015. "Euro Area business cycles in turbulent times: convergence or decoupling?," Applied Economics, Taylor & Francis Journals, vol. 47(34-35), pages 3791-3815, July.
    18. Zhang, Yixiao & Yu, Cindy L. & Li, Haitao, 2022. "Nowcasting GDP Using Dynamic Factor Model with Unknown Number of Factors and Stochastic Volatility: A Bayesian Approach," Econometrics and Statistics, Elsevier, vol. 24(C), pages 75-93.
    19. Gabriele Fiorentini & Enrique Sentana & Neil Shephard, 2004. "Likelihood-Based Estimation of Latent Generalized ARCH Structures," Econometrica, Econometric Society, vol. 72(5), pages 1481-1517, September.
    20. Conti, Gabriella & Frühwirth-Schnatter, Sylvia & Heckman, James J. & Piatek, Rémi, 2014. "Bayesian exploratory factor analysis," Journal of Econometrics, Elsevier, vol. 183(1), pages 31-57.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:100:y:2009:i:8:p:1717-1726. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.