ABSTRACT

This research proposes a one-step Bayesian regularized approach to exploratory factor analysis (EFA) with an unknown number of factors. The proposed Bayesian regularized exploratory factor analysis (BREFA) model builds on the idea of bi-level Bayesian sparse group selection and can produce exact zero estimates at both the factor and loading levels. It can distinguish true factors from spurious factors and provide estimations of model and tuning parameters simultaneously. In addition to achieving model simplicity at both the factor and item levels, the approach provides interval estimates that can be used for significance testing, making it capable of addressing both uncorrelated and correlated factors. The Bayesian hierarchical formulation is implemented using Markov chain Monte Carlo estimation with the multivariate spike and slab priors and posterior median estimator. Based on simulated and real data analysis, BREFA demonstrates clear advantages or flexibility compared with traditional and Bayesian EFA, in terms of factor extraction, parameter estimation, and model interpretation.

摘要

这项研究提出了一种一步贝叶斯正则化方法，用于探索性因素分析 (EFA)，其中包含未知数量的因素。提议的贝叶斯正则化探索性因子分析 (BREFA) 模型建立在双层贝叶斯稀疏组选择的思想之上，并且可以在因子和负载水平上产生精确的零估计。它可以区分真实因素和虚假因素，并同时提供模型和调整参数的估计。除了在因子和项目级别实现模型简单性之外，该方法还提供可用于显着性检验的区间估计，使其能够处理不相关和相关的因素。贝叶斯分层公式是使用马尔可夫链蒙特卡罗估计与多元尖峰和平板先验以及后中位数估计器实现的。基于模拟和真实数据分析，BREFA 在因子提取、参数估计和模型解释方面与传统和贝叶斯 EFA 相比具有明显的优势或灵活性。