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

Zhaohua Lu

doi:10.1080/00273171.2016.1168279

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

2016-06-17

Zhaohua Lu *

Sy‐Miin Chow

Eric Loken

DOI：10.1080/00273171.2016.1168279

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Abstract

En 中文

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, Muthen & 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 Muthen 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.

Keywords:

Factor analysis

Bayesian structural equation modeling

variable selection

Markov chain Monte Carlo algorithms

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