Bayesian Factor Analysis as a Variable-Selection Problem: Alternative Priors and Consequences

Zhao Hua Lu, Sy Miin Chow, Eric Loken

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)519-539
Number of pages21
JournalMultivariate Behavioral Research
Issue number4
StatePublished - Jul 3 2016

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Experimental and Cognitive Psychology
  • Arts and Humanities (miscellaneous)


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