Partially Confirmatory Approach to Factor Analysis with Bayesian Learning: A LAWBL Tutorial

Abstract

Different from traditional practice that considers factor analysis as either exploratory or confirmatory, different amounts of substantive information can be available in between the confirmatory and exploratory extremes under the partially confirmatory approach. Based on Bayesian Lasso methods, three models were recently proposed for various types of data under the new approach: the partially confirmatory factor analysis (PCFA), generalized PCFA, and partially confirmatory item response model. All models with related variants can be implemented in the R package LAWBL, which is available free of charge. This article introduces the theoretical and statistical foundation of the three models in a unified framework, including model formulation, identification, variants, and Bayesian inference and estimation with regularizations. Didactic examples covering different scenarios are employed to illustrate the implementation of the models and their variants in LAWBL step by step. Guidelines and suggestions are given to researchers and practitioners in a discussion.