A Partially Confirmatory Approach to Scale Development With the Bayesian Lasso

Abstract

The exploratory and confirmatory approaches of factor analysis lie on two ends of a continuum of substantive input for scale development. Recent advancements in Bayesian regularization methods enable more flexibility in covering a wide range of the substantive continuum. Based on the Bayesian Lasso (least absolute shrinkage and selection operator) methods for the regression model and covariance matrix, this research proposes a partially confirmatory approach to address the loading and residual structures at the same time. With at least one specified loading per item, a one-step procedure can be applied to figure out both structures simultaneously. With a few specified loadings per factor, a two-step procedure is preferred to capture the model configuration correctly. In both cases, the Bayesian hierarchical formulation is implemented using Markov Chain Monte Carlo estimation with different Lasso or regular priors. Both simulated and real data sets were analyzed to evaluate the validity, robustness, and practical usefulness of the proposed approach across different situations.