Fully and partially exploratory factor analysis with bi-level Bayesian regularization.

This research introduces the fully and partially exploratory factor analysis (EFA) with bi-level Bayesian regularization. The proposed models enable factor selection with a sparse model by conceptualizing the factor and loading as the group and individual levels, respectively. They offer a series of benefits such as factor extraction and parameter estimation in one step, simultaneous estimation of the model and tuning parameters, and the availability of interval estimates. Moreover, partial knowledge can be incorporated together with unknown number of factors in the partially EFA. Simulation studies and real-data analyses demonstrated that both models performed satisfactorily under reasonable conditions and were robust to interference of local dependence, while the partially EFA with appropriate information can outperform the fully version and work well under more extreme conditions. The proposed models have been implemented in the R package LAWBL.