A Generalized Partially Confirmatory Factor Analysis Framework with Mixed Bayesian Lasso Methods

This research extends the partially confirmatory approach to accommodate mixed types of data and missingness in a unified framework that can address a wide range of the confirmatory-exploratory continuum in factor analysis. A mix of Bayesian adaptive and covariance Lasso procedures was developed to estimate model parameters and regularize the loading structure and local dependence simultaneously. Several model variants were offered with different constraints for identification. The less-constrained variant can achieve sufficient condition for the more-powerful variant, although loading estimates associated with local dependence can be inflated. Parameter recovery was satisfactory, but the information on local dependence was partially lost with categorical data or missingness. A real-life example illustrated how the models can be used to obtain a more discernible loading pattern and to identify items that do not measure what they are supposed to measure. The proposed methodology has been implemented in the R package LAWBL.