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Bayesian Feature Extraction for Two-Part Latent Variable Model with Polytomous Manifestations

Author

Listed:
  • Qi Zhang

    (School of Science, Nanjing Forestry University, Nanjing 210037, China)

  • Yihui Zhang

    (School of Computer Science, China University of Geosciences, Wuhan 430074, China)

  • Yemao Xia

    (School of Science, Nanjing Forestry University, Nanjing 210037, China)

Abstract

Semi-continuous data are very common in social sciences and economics. In this paper, a Bayesian variable selection procedure is developed to assess the influence of observed and/or unobserved exogenous factors on semi-continuous data. Our formulation is based on a two-part latent variable model with polytomous responses. We consider two schemes for the penalties of regression coefficients and factor loadings: a Bayesian spike and slab bimodal prior and a Bayesian lasso prior. Within the Bayesian framework, we implement a Markov chain Monte Carlo sampling method to conduct posterior inference. To facilitate posterior sampling, we recast the logistic model from Part One as a norm-type mixture model. A Gibbs sampler is designed to draw observations from the posterior. Our empirical results show that with suitable values of hyperparameters, the spike and slab bimodal method slightly outperforms Bayesian lasso in the current analysis. Finally, a real example related to the Chinese Household Financial Survey is analyzed to illustrate application of the methodology.

Suggested Citation

  • Qi Zhang & Yihui Zhang & Yemao Xia, 2024. "Bayesian Feature Extraction for Two-Part Latent Variable Model with Polytomous Manifestations," Mathematics, MDPI, vol. 12(5), pages 1-23, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:783-:d:1352503
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    References listed on IDEAS

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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. Veronika Ročková & Edward I. George, 2014. "EMVS: The EM Approach to Bayesian Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 828-846, June.
    3. Xinyuan Song & Yemao Xia & Hongtu Zhu, 2017. "Hidden Markov latent variable models with multivariate longitudinal data," Biometrics, The International Biometric Society, vol. 73(1), pages 313-323, March.
    4. Nicholas G. Polson & James G. Scott & Jesse Windle, 2013. "Bayesian Inference for Logistic Models Using Pólya--Gamma Latent Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1339-1349, December.
    5. Wei Zhang & Takayo Ota & Viji Shridhar & Jeremy Chien & Baolin Wu & Rui Kuang, 2013. "Network-based Survival Analysis Reveals Subnetwork Signatures for Predicting Outcomes of Ovarian Cancer Treatment," PLOS Computational Biology, Public Library of Science, vol. 9(3), pages 1-16, March.
    6. Cragg, John G, 1971. "Some Statistical Models for Limited Dependent Variables with Application to the Demand for Durable Goods," Econometrica, Econometric Society, vol. 39(5), pages 829-844, September.
    7. 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.
    8. Ishwaran, Hemant & Rao, J. Sunil, 2005. "Spike and Slab Gene Selection for Multigroup Microarray Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 764-780, September.
    9. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    10. Partha Deb & Murat K. Munkin & Pravin K. Trivedi, 2006. "Bayesian analysis of the two‐part model with endogeneity: application to health care expenditure," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(7), pages 1081-1099, November.
    11. Duan, Naihua, et al, 1983. "A Comparison of Alternative Models for the Demand for Medical Care," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 115-126, April.
    12. 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.
    13. Xia, Ye-Mao & Tang, Nian-Sheng, 2019. "Bayesian analysis for mixture of latent variable hidden Markov models with multivariate longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 190-211.
    14. Naijun Sha & Benard Owusu Dechi, 2019. "A Bayes Inference for Ordinal Response with Latent Variable Approach," Stats, MDPI, vol. 2(2), pages 1-11, June.
    15. 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.
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