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

Man, Albert

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https://hdl.handle.net/2142/106240 Copy

Description

Title

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

Author(s)

Man, Albert

Issue Date

2019-12-04

Director of Research (if dissertation) or Advisor (if thesis)

Culpepper, Steven A.

Doctoral Committee Chair(s)

Culpepper, Steven A.

Committee Member(s)

• Douglas, Jeff
• Liang, Feng
• Park, Trevor

Department of Study

Statistics

Discipline

Statistics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2019-12

Type of Resource

text

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

Copyright and License Information

Copyright 2019 Albert Man

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