{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/106240"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/106240","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A mode-jumping algorithm for exploratory factor analysis with continuous and binary responses","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.","abstract_html":"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.","abstract_has_math":true,"creators":["Man, Albert"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Statistics","degree_department":null,"school":null,"contributors":["Culpepper, Steven A.","Douglas, Jeff","Liang, Feng","Park, Trevor"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-12","date_published":"2019-12","updated_at":"2026-07-22T22:24:45Z","subjects":["Bayesian","Factor Analysis","Rotational indeterminacy","MCMC"],"languages":["en"],"rights":["Copyright 2019 Albert Man"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/106240","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Culpepper, Steven A.","Douglas, Jeff","Liang, Feng","Park, Trevor"]},{"key":"dc:creator","label":"Author","values":["Man, Albert"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-12","2020-03-02T21:58:22Z","2019-12-04"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Bayesian","Factor Analysis","Rotational indeterminacy","MCMC"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2019 Albert Man"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/106240"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-02-28 without embargo terms","The student, Albert Man, accepted the attached license on 2019-12-03 at 16:43.","The student, Albert Man, submitted this Dissertation for approval on 2019-12-03 at 16:48.","This Dissertation was approved for publication on 2019-12-04 at 15:42.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14677 on 2020-02-28 at 17:15:04","Made available in DSpace on 2020-03-02T21:58:22Z (GMT). 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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.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-02-28 without embargo terms","The student, Albert Man, accepted the attached license on 2019-12-03 at 16:43.","The student, Albert Man, submitted this Dissertation for approval on 2019-12-03 at 16:48.","This Dissertation was approved for publication on 2019-12-04 at 15:42.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14677 on 2020-02-28 at 17:15:04","Made available in DSpace on 2020-03-02T21:58:22Z (GMT). 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