TY - JOUR
T1 - A Mode-Jumping Algorithm for Bayesian Factor Analysis
AU - Man, Albert Xingyi
AU - Culpepper, Steven Andrew
N1 - Funding Information:
We would like to thank two anonymous reviewers and the associate editor for their helpful comments and thoughtful suggestions. We would also like to thank Christian Aßmann, Jens Boysen-Hogrefe, and Markus Pape for providing their code. This work made use of the Illinois Campus Cluster, a computing resource that is operated by the Illinois Campus Cluster Program (ICCP) in conjunction with the National Center for Supercomputing Applications (NCSA) and which is supported by funds from the University of Illinois at Urbana-Champaign.
Publisher Copyright:
© 2020 American Statistical Association.
PY - 2022
Y1 - 2022
N2 - Exploratory factor analysis is a dimension-reduction technique commonly used in psychology, finance, genomics, neuroscience, and economics. Advances in computational power have opened the door for fully Bayesian treatments of factor analysis. One open problem is enforcing rotational identifability of the latent factor loadings, as the loadings are not identified from the likelihood without further restrictions. Nonidentifability of the loadings can cause posterior multimodality, which can produce misleading posterior summaries. The positive-diagonal, lower-triangular (PLT) constraint is the most commonly used restriction to guarantee identifiability, in which the upper m × m submatrix of the loadings is constrained to be a lower-triangular matrix with positive-diagonal elements. The PLT constraint can fail to guarantee identifiability if the constrained submatrix is singular. Furthermore, though the PLT constraint addresses identifiability-related multimodality, it introduces additional mixing issues. We introduce a new Bayesian sampling algorithm that efficiently explores the multimodal posterior surface and addresses issues with PLT-constrained approaches. Supplementary materials for this article are available online.
AB - Exploratory factor analysis is a dimension-reduction technique commonly used in psychology, finance, genomics, neuroscience, and economics. Advances in computational power have opened the door for fully Bayesian treatments of factor analysis. One open problem is enforcing rotational identifability of the latent factor loadings, as the loadings are not identified from the likelihood without further restrictions. Nonidentifability of the loadings can cause posterior multimodality, which can produce misleading posterior summaries. The positive-diagonal, lower-triangular (PLT) constraint is the most commonly used restriction to guarantee identifiability, in which the upper m × m submatrix of the loadings is constrained to be a lower-triangular matrix with positive-diagonal elements. The PLT constraint can fail to guarantee identifiability if the constrained submatrix is singular. Furthermore, though the PLT constraint addresses identifiability-related multimodality, it introduces additional mixing issues. We introduce a new Bayesian sampling algorithm that efficiently explores the multimodal posterior surface and addresses issues with PLT-constrained approaches. Supplementary materials for this article are available online.
KW - Factor model
KW - Identifiability
KW - Markov chain Monte Carlo
KW - Mixing
KW - Orthogonal rotation
KW - Posterior multimodality
UR - http://www.scopus.com/inward/record.url?scp=85087629491&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85087629491&partnerID=8YFLogxK
U2 - 10.1080/01621459.2020.1773833
DO - 10.1080/01621459.2020.1773833
M3 - Article
AN - SCOPUS:85087629491
SN - 0162-1459
VL - 117
SP - 277
EP - 290
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 537
ER -