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Variational Bayesian analysis for two-part latent variable model

Author

Listed:
  • Yemao Xia

    (Nanjing Forestry University)

  • Jinye Chen

    (Nanjing Forestry University)

  • Depeng Jiang

    (University of Manitoba)

Abstract

It is recommended to use two-part models for analyzing zero-inflated data that exhibit a spike at zero or have a large proportion of participants with zero values. This paper presents a variational Bayesian inference procedure for the analysis of a two-part latent variable model. We take advantage of the Pólya Gamma stochastic representation to approximate the posterior distribution via a mean-field variational method. We propose a scheme to update the variational parameters using the coordinate ascent inference algorithm and develop a variational Bayes based procedure for the variable selection and model assessment. We conduct simulation studies to assess the performance of our proposed method and compare it with the Markov Chains Monte Carlo sampling method. Our results show that the proposed variational Bayesian approach achieves computational efficiency without sacrificing estimation accuracy. We further illustrate the practical merits of the proposed approach by analyzing household finance survey data.

Suggested Citation

  • Yemao Xia & Jinye Chen & Depeng Jiang, 2024. "Variational Bayesian analysis for two-part latent variable model," Computational Statistics, Springer, vol. 39(4), pages 2259-2290, June.
  • Handle: RePEc:spr:compst:v:39:y:2024:i:4:d:10.1007_s00180-023-01417-6
    DOI: 10.1007/s00180-023-01417-6
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    References listed on IDEAS

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    1. van Rooij, Maarten & Lusardi, Annamaria & Alessie, Rob, 2011. "Financial literacy and stock market participation," Journal of Financial Economics, Elsevier, vol. 101(2), pages 449-472, August.
    2. Yixin Wang & David M. Blei, 2019. "Frequentist Consistency of Variational Bayes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1147-1161, July.
    3. 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.
    4. 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.
    5. David M. Blei & Alp Kucukelbir & Jon D. McAuliffe, 2017. "Variational Inference: A Review for Statisticians," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 859-877, April.
    6. 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.
    7. 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.
    8. Ming-Hui Chen, 2004. "Bayesian criterion based model assessment for categorical data," Biometrika, Biometrika Trust, vol. 91(1), pages 45-63, March.
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