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Bayesian hierarchical robust factor analysis models for partially observed sample-selection data

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  • Kim, Hea-Jung

Abstract

This paper introduces a class of scale mixtures of normal selection factor (SMNSF) analysis models which are robust against departures from normality and designed to correct sample-selection bias. Various properties of this class of models are established, including a stochastic representation, a distributional hierarchy, and a quantification of sample-selection bias. A hierarchical Bayesian methodology is also developed for estimation purposes. It involves a simple and computationally feasible Markov Chain Monte Carlo algorithm that avoids analytical or numerical derivatives of the log-likelihood function. Results from simulation studies attest to the good finite-sample performance of the new model in terms of sample-selection bias reduction and robustness against outliers. A data illustration is included.

Suggested Citation

  • Kim, Hea-Jung, 2018. "Bayesian hierarchical robust factor analysis models for partially observed sample-selection data," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 65-82.
    • Handle: RePEc:eee:jmvana:v:164:y:2018:i:c:p:65-82
    DOI: 10.1016/j.jmva.2017.11.003
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    References listed on IDEAS

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    1. Kim, Hyoung-Moon & Maadooliat, Mehdi & Arellano-Valle, Reinaldo B. & Genton, Marc G., 2016. "Skewed factor models using selection mechanisms," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 162-177.
    2. Yiu-Fai Yung, 1997. "Finite mixtures in confirmatory factor-analysis models," Psychometrika, Springer;The Psychometric Society, vol. 62(3), pages 297-330, September.
    3. Arrazola, María & de Hevia, José, 2008. "Three measures of returns to education: An illustration for the case of Spain," Economics of Education Review, Elsevier, vol. 27(3), pages 266-275, June.
    4. Asim Ansari & Kamel Jedidi & Laurette Dube, 2002. "Heterogeneous factor analysis models: A bayesian approach," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 49-77, March.
    5. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    6. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
    7. Wan-Lun Wang & Tsung-I Lin, 2013. "An efficient ECM algorithm for maximum likelihood estimation in mixtures of t-factor analyzers," Computational Statistics, Springer, vol. 28(2), pages 751-769, April.
    8. Kim, Hea-Jung, 2008. "A class of weighted multivariate normal distributions and its properties," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1758-1771, September.
    9. Ding, Peng, 2014. "Bayesian robust inference of sample selection using selection-t models," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 451-464.
    10. Pison, Greet & Rousseeuw, Peter J. & Filzmoser, Peter & Croux, Christophe, 2003. "Robust factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 145-172, January.
    11. Angela Montanari & Cinzia Viroli, 2010. "A skew-normal factor model for the analysis of student satisfaction towards university courses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(3), pages 473-487.
    12. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    13. Tsung-I Lin & Pal Wu & Geoffrey McLachlan & Sharon Lee, 2015. "A robust factor analysis model using the restricted skew- $$t$$ t distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 510-531, September.
    14. McLachlan, G.J. & Bean, R.W. & Ben-Tovim Jones, L., 2007. "Extension of the mixture of factor analyzers model to incorporate the multivariate t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5327-5338, July.
    15. Ming‐Hui Chen, 2005. "Computing marginal likelihoods from a single MCMC output," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(1), pages 16-29, February.
    16. 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.
    17. Yulia V. Marchenko & Marc G. Genton, 2012. "A Heckman Selection- t Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 304-317, March.
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