Bayesian Factor Analysis as a Variable-Selection Problem: Alternative Priors and Consequences.
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.
a Department of Human Development and Family Studies , Pennsylvania State University.
Zhao-Hua
ZH
Lu
a Department of Human Development and Family Studies , Pennsylvania State University.
Sy-Miin
SM
Chow
a Department of Human Development and Family Studies , Pennsylvania State University.
Eric
E
Loken
D000465:Algorithms; D001499:Bayes Theorem; D003198:Computer Simulation; D003657:Decision Making; D004651:Employment / Q000523:psychology; D005163:Factor Analysis, Statistical; D006801:Humans; D015233:Models, Statistical; D009010:Monte Carlo Method; D010379:Peer Group; D012372:ROC Curve; D012044:Regression Analysis; D000070777:School Teachers / Q000523:psychology; D012944:Social Support; D013315:Stress, Psychological
Bayesian structural equation modeling; Factor analysis; Markov chain Monte Carlo algorithms; variable selection