Bayesian Statistical Inference for Factor Analysis Models with Clustered Data

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.

Keywords

• clustered data
• factor analysis
• MCMC method
• Gibbs sampling
• influence diagnosis
• Bayesian case-deletion model