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Variable selection in finite mixture of regression models with an unknown number of components

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  • Lee, Kuo-Jung
  • Feldkircher, Martin
  • Chen, Yi-Chi

Abstract

A Bayesian framework for finite mixture models to deal with model selection and the selection of the number of mixture components simultaneously is presented. For that purpose, a feasible reversible jump Markov Chain Monte Carlo algorithm is proposed to model each component as a sparse regression model. This approach is made robust to outliers by using a prior that induces heavy tails and works well under multicollinearity and with high-dimensional data. Finally, the framework is applied to cross-sectional data investigating early warning indicators. The results reveal two distinct country groups for which estimated effects of vulnerability indicators vary considerably.

Suggested Citation

  • Lee, Kuo-Jung & Feldkircher, Martin & Chen, Yi-Chi, 2021. "Variable selection in finite mixture of regression models with an unknown number of components," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:csdana:v:158:y:2021:i:c:s0167947321000141
    DOI: 10.1016/j.csda.2021.107180
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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Berkmen, S. Pelin & Gelos, Gaston & Rennhack, Robert & Walsh, James P., 2012. "The global financial crisis: Explaining cross-country differences in the output impact," Journal of International Money and Finance, Elsevier, vol. 31(1), pages 42-59.
    3. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    4. Feldkircher, Martin, 2014. "The determinants of vulnerability to the global financial crisis 2008 to 2009: Credit growth and other sources of risk," Journal of International Money and Finance, Elsevier, vol. 43(C), pages 19-49.
    5. Cozzini, Alberto & Jasra, Ajay & Montana, Giovanni & Persing, Adam, 2014. "A Bayesian mixture of lasso regressions with t-errors," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 84-97.
    6. 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.
    7. Martin Feldkircher & Thomas Gruber & Isabella Moder, 2014. "Using a Threshold Approach to Flag Vulnerabilities in CESEE Economies," Focus on European Economic Integration, Oesterreichische Nationalbank (Austrian Central Bank), issue 3, pages 8-30.
    8. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    9. Gupta, Mayetri & Ibrahim, Joseph G., 2007. "Variable Selection in Regression Mixture Modeling for the Discovery of Gene Regulatory Networks," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 867-880, September.
    10. Sala-i-Martin, Xavier, 1997. "I Just Ran Two Million Regressions," American Economic Review, American Economic Association, vol. 87(2), pages 178-183, May.
    11. Abbas Khalili & Shili Lin, 2013. "Regularization in Finite Mixture of Regression Models with Diverging Number of Parameters," Biometrics, The International Biometric Society, vol. 69(2), pages 436-446, June.
    12. Jan-Michael Becker & Christian Ringle & Marko Sarstedt & Franziska Völckner, 2015. "How collinearity affects mixture regression results," Marketing Letters, Springer, vol. 26(4), pages 643-659, December.
    13. Joyee Ghosh & Andrew E. Ghattas, 2015. "Bayesian Variable Selection Under Collinearity," The American Statistician, Taylor & Francis Journals, vol. 69(3), pages 165-173, August.
    14. Dunson, David B. & Herring, Amy H. & Engel, Stephanie M., 2008. "Bayesian Selection and Clustering of Polymorphisms in Functionally Related Genes," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 534-546, June.
    15. Li, Pengfei & Chen, Jiahua, 2010. "Testing the Order of a Finite Mixture," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1084-1092.
    16. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 19-40, Suppl. De.
    17. Jian Zhang, 2017. "Screening and clustering of sparse regressions with finite non-Gaussian mixtures," Biometrics, The International Biometric Society, vol. 73(2), pages 540-550, June.
    18. Jesús Crespo Cuaresma & Martin Feldkircher, 2012. "Drivers of Output Loss during the 2008–09 Crisis: A Focus on Emerging Europe," Focus on European Economic Integration, Oesterreichische Nationalbank (Austrian Central Bank), issue 2, pages 46-64.
    19. 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.
    20. Tadesse, Mahlet G. & Sha, Naijun & Vannucci, Marina, 2005. "Bayesian Variable Selection in Clustering High-Dimensional Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 602-617, June.
    21. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    22. Khalili, Abbas & Chen, Jiahua, 2007. "Variable Selection in Finite Mixture of Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1025-1038, September.
    Full references (including those not matched with items on IDEAS)

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