Bayesian Factor Analysis as a Variable-Selection Problem: Alternative Priors and Consequences. (3rd July 2016)

• Record Type: Journal Article
• Authors: Lu, Zhao-Hua; Chow, Sy-Miin; Loken, Eric
• Is Part Of: Multivariate behavioral research. Volume 51:Number 4(2016)
• Page Start: 519
• Page End: 539
• Publication Date: 2016-07-03
• Subjects: Factor analysis -- Bayesian structural equation modeling -- variable selection -- Markov chain Monte Carlo algorithms; Psychometrics -- Periodicals; Psychology, Experimental -- Periodicals; Psychology, Experimental; Psychometrics; Periodicals; 150.15195
• DOI: 10.1080/00273171.2016.1168279
• Languages: English
• ISSNs: 0027-3171

Abstract

ABSTRACT: Factor analysis is a popular statistical technique for multivariate data analysis. Developments in the structural equation modeling framework have enabled the use of hybrid confirmatory/exploratory approaches in which factor-loading structures can be explored relatively flexibly within a confirmatory factor analysis (CFA) framework. Recently, Muthén & Asparouhov proposed a Bayesian structural equation modeling (BSEM) approach to explore the presence of cross loadings in CFA models. We show that the issue of determining factor-loading patterns may be formulated as a Bayesian variable selection problem in which Muthén and Asparouhov's approach can be regarded as a BSEM approach with ridge regression prior (BSEM-RP). We propose another Bayesian approach, denoted herein as the Bayesian structural equation modeling with spike-and-slab prior (BSEM-SSP), which serves as a one-stage alternative to the BSEM-RP. We review the theoretical advantages and disadvantages of both approaches and compare their empirical performance relative to two modification indices-based approaches and exploratory factor analysis with target rotation. A teacher stress scale data set is used to demonstrate our approach.