A mode-jumping algorithm for exploratory factor analysis with continuous and binary responses

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 $m \times m$ 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 for both continuous and binary responses that efficiently explores the multimodal posterior surface and addresses issues with current approaches.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2019

Author dc:creator

• Man, Albert

Contributors dc:contributor

• Culpepper, Steven A.
• Douglas, Jeff
• Liang, Feng
• Park, Trevor

• Bayesian
• Factor Analysis
• Rotational indeterminacy
• MCMC

Statement dc:rights

• Copyright 2019 Albert Man

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/106240

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/106240