EconPapers    
Economics at your fingertips  
 

Dealing with Reflection Invariance in Bayesian Factor Analysis

Elena A. Erosheva () and S. McKay Curtis ()
Additional contact information
Elena A. Erosheva: University of Washington
S. McKay Curtis: University of Washington

Psychometrika, 2017, vol. 82, issue 2, No 2, 295-307

Abstract: Abstract This paper considers the reflection unidentifiability problem in confirmatory factor analysis (CFA) and the associated implications for Bayesian estimation. We note a direct analogy between the multimodality in CFA models that is due to all possible column sign changes in the matrix of loadings and the multimodality in finite mixture models that is due to all possible relabelings of the mixture components. Drawing on this analogy, we derive and present a simple approach for dealing with reflection in variance in Bayesian factor analysis. We recommend fitting Bayesian factor analysis models without rotational constraints on the loadings—allowing Markov chain Monte Carlo algorithms to explore the full posterior distribution—and then using a relabeling algorithm to pick a factor solution that corresponds to one mode. We demonstrate our approach on the case of a bifactor model; however, the relabeling algorithm is straightforward to generalize for handling multimodalities due to sign invariance in the likelihood in other factor analysis models.

Keywords: identifiability constraints; label-switching; Markov chain Monte Carlo; relabeling; rotation; rotational invariance (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s11336-017-9564-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:psycho:v:82:y:2017:i:2:d:10.1007_s11336-017-9564-y

Ordering information: This journal article can be ordered from
http://www.springer. ... gy/journal/11336/PS2

DOI: 10.1007/s11336-017-9564-y

Access Statistics for this article

Psychometrika is currently edited by Irini Moustaki

More articles in Psychometrika from Springer, The Psychometric Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().

 
Page updated 2025-03-20
Handle: RePEc:spr:psycho:v:82:y:2017:i:2:d:10.1007_s11336-017-9564-y