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Bayesian Statistical Inference for Factor Analysis Models with Clustered Data

Author

Listed:
  • Bowen Chen

    (College of Mathematics, Yunnan Normal University, Kunming 650500, China)

  • Na He

    (College of Life Sciences, Yunnan Normal University, Kunming 650500, China)

  • Xingping Li

    (College of Mathematics, Yunnan Normal University, Kunming 650500, China)

Abstract

Clustered data are a complex and frequently used type of data. Traditional factor analysis methods are effective for non-clustered data, but they do not adequately capture correlations between multiple observed individuals or variables in clustered data. This paper proposes a Bayesian approach utilizing MCMC and Gibbs sampling algorithms to accurately estimate parameters of interest within the clustered factor analysis model. The mean traversal graph of parameters ensures that the Markov chain converges, and the Bayesian case-deletion model is used to analyze the model’s impact and identify outliers in clustered data using Cook’s posterior mean distance. The applicability and validity of the principal-component-method-based factor analysis model for clustered data are demonstrated by comparing the parameter estimation of this method with the principal component method, the clustered data with and without internal relationships are compared by example analysis, and the anomalous groups are identified by the Cook’s posterior mean distance.

Suggested Citation

  • Bowen Chen & Na He & Xingping Li, 2024. "Bayesian Statistical Inference for Factor Analysis Models with Clustered Data," Mathematics, MDPI, vol. 12(13), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:1949-:d:1420664
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    References listed on IDEAS

    as
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    2. Greenwald, Bruce C., 1983. "A general analysis of bias in the estimated standard errors of least squares coefficients," Journal of Econometrics, Elsevier, vol. 22(3), pages 323-338, August.
    3. Moulton, Brent R., 1986. "Random group effects and the precision of regression estimates," Journal of Econometrics, Elsevier, vol. 32(3), pages 385-397, August.
    4. Chen, Kani & Jin, Zhezhen, 2006. "Partial Linear Regression Models for Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 195-204, March.
    5. Badi H. Baltagi & James M. Griffin & Weiwen Xiong, 2000. "To Pool Or Not To Pool: Homogeneous Versus Hetergeneous Estimations Applied to Cigarette Demand," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 117-126, February.
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