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 Title: A mode-jumping algorithm for exploratory factor analysis with continuous and binary responses Author(s): Man, Albert Director of Research: Culpepper, Steven A. Doctoral Committee Chair(s): Culpepper, Steven A. Doctoral Committee Member(s): Douglas, Jeff; Liang, Feng; Park, Trevor Department / Program: Statistics Discipline: Statistics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Bayesian Factor Analysis Rotational indeterminacy MCMC Abstract: 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. Issue Date: 2019-12-04 Type: Text URI: http://hdl.handle.net/2142/106240 Rights Information: Copyright 2019 Albert Man Date Available in IDEALS: 2020-03-02 Date Deposited: 2019-12
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