{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/101297"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/101297","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"From expectation-3-maximization to bayesian expectation-3-maximization: A latent mixture modeling-based bayesian algorithm for the 4-parameter logistic model","abstract":"There is renewed interest in the four-parameter logistic model (4PLM), but the lack of a user-friendly calibration method constitutes a major barrier to its widespread application. In the present study, this researcher reformulated the 4PLM from a latent mixture modeling view and developed the Expectation-Maximization-Maximization-Maximization (EMMM) method. Combining the EMMM with the Bayesian approach, allowed the Bayesian Expectation-Maximization-Maximization-Maximization (BEMMM) algorithm to be proposed. First, the author compared the EMMM with BEMMM to confirm that the BEMMM method reduced the number of implausible estimates in EMMM. Next, when comparing the BEMMM with the Markov Chain Monte Carlo method (Culpepper, 2016) and Bayesian Modal Estimation (Waller & Feuerstahler, 2017), the results from a simulation study and a real-world data calibration indicated that the BEMMM and the MCMC are more accurate than the BME, while the BEMMM is much faster than the MCMC.","abstract_html":"There is renewed interest in the four-parameter logistic model (4PLM), but the lack of a user-friendly calibration method constitutes a major barrier to its widespread application. In the present study, this researcher reformulated the 4PLM from a latent mixture modeling view and developed the Expectation-Maximization-Maximization-Maximization (EMMM) method. Combining the EMMM with the Bayesian approach, allowed the Bayesian Expectation-Maximization-Maximization-Maximization (BEMMM) algorithm to be proposed. First, the author compared the EMMM with BEMMM to confirm that the BEMMM method reduced the number of implausible estimates in EMMM. Next, when comparing the BEMMM with the Markov Chain Monte Carlo method (Culpepper, 2016) and Bayesian Modal Estimation (Waller & Feuerstahler, 2017), the results from a simulation study and a real-world data calibration indicated that the BEMMM and the MCMC are more accurate than the BME, while the BEMMM is much faster than the MCMC.","abstract_has_math":false,"creators":["Zhang, Ci"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Educational Psychology","degree_department":null,"school":null,"contributors":["Zhang, Jinming","Chang, Hua-Hua","Anderson, Carolyn J."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-09-04T20:47:03Z","date_published":"2018-09-04T20:47:03Z","updated_at":"2026-07-22T22:24:38Z","subjects":["Item response theory (IRT), 4PLM, EMMM, BEMMM"],"languages":["en"],"rights":["Copyright 2018 Ci Zhang"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/101297","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Zhang, Jinming","Chang, Hua-Hua","Anderson, Carolyn J."]},{"key":"dc:creator","label":"Author","values":["Zhang, Ci"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-09-04T20:47:03Z","2020-09-05T09:15:09Z","2018-04-13","2018-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Educational Psychology"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"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":["Item response theory (IRT), 4PLM, EMMM, BEMMM"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2018 Ci Zhang"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/101297"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["There is renewed interest in the four-parameter logistic model (4PLM), but the lack of a user-friendly calibration method constitutes a major barrier to its widespread application. In the present study, this researcher reformulated the 4PLM from a latent mixture modeling view and developed the Expectation-Maximization-Maximization-Maximization (EMMM) method. Combining the EMMM with the Bayesian approach, allowed the Bayesian Expectation-Maximization-Maximization-Maximization (BEMMM) algorithm to be proposed. First, the author compared the EMMM with BEMMM to confirm that the BEMMM method reduced the number of implausible estimates in EMMM. Next, when comparing the BEMMM with the Markov Chain Monte Carlo method (Culpepper, 2016) and Bayesian Modal Estimation (Waller & Feuerstahler, 2017), the results from a simulation study and a real-world data calibration indicated that the BEMMM and the MCMC are more accurate than the BME, while the BEMMM is much faster than the MCMC.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2020-05-01","The student, Ci Zhang, accepted the attached license on 2018-04-11 at 15:29.","The student, Ci Zhang, submitted this Thesis for approval on 2018-04-11 at 15:36.","This Thesis was approved for publication on 2018-04-13 at 11:03.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12194 on 2018-08-31 at 17:27:19","Made available in DSpace on 2018-09-04T20:47:03Z (GMT). No. of bitstreams: 2 ZHANG-THESIS-2018.pdf: 1851527 bytes, checksum: 95a341e0aad4bb76bbe6e691b461868d (MD5) LICENSE.txt: 4205 bytes, checksum: f735a60aef4d3c0daa0576cb5a4301d6 (MD5) Previous issue date: 2018-04-13","Embargo set by: Seth Robbins for item 107382 Lift date: 2020-09-04T20:47:38Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Embargo set by: Seth Robbins for item 107382 Lift date: 2020-09-04T20:50:11Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Limited Restriction Lifted for Item 107382 on 2020-09-05T09:15:09Z."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["From expectation-3-maximization to bayesian expectation-3-maximization: A latent mixture modeling-based bayesian algorithm for the 4-parameter logistic model"]}]}],"canonical_facts":{"dc:contributor":["Zhang, Jinming","Chang, Hua-Hua","Anderson, Carolyn J."],"dc:creator":["Zhang, Ci"],"dc:date":["2018-09-04T20:47:03Z","2020-09-05T09:15:09Z","2018-04-13","2018-05"],"dc:description":["There is renewed interest in the four-parameter logistic model (4PLM), but the lack of a user-friendly calibration method constitutes a major barrier to its widespread application. In the present study, this researcher reformulated the 4PLM from a latent mixture modeling view and developed the Expectation-Maximization-Maximization-Maximization (EMMM) method. Combining the EMMM with the Bayesian approach, allowed the Bayesian Expectation-Maximization-Maximization-Maximization (BEMMM) algorithm to be proposed. First, the author compared the EMMM with BEMMM to confirm that the BEMMM method reduced the number of implausible estimates in EMMM. Next, when comparing the BEMMM with the Markov Chain Monte Carlo method (Culpepper, 2016) and Bayesian Modal Estimation (Waller & Feuerstahler, 2017), the results from a simulation study and a real-world data calibration indicated that the BEMMM and the MCMC are more accurate than the BME, while the BEMMM is much faster than the MCMC.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2020-05-01","The student, Ci Zhang, accepted the attached license on 2018-04-11 at 15:29.","The student, Ci Zhang, submitted this Thesis for approval on 2018-04-11 at 15:36.","This Thesis was approved for publication on 2018-04-13 at 11:03.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12194 on 2018-08-31 at 17:27:19","Made available in DSpace on 2018-09-04T20:47:03Z (GMT). No. of bitstreams: 2 ZHANG-THESIS-2018.pdf: 1851527 bytes, checksum: 95a341e0aad4bb76bbe6e691b461868d (MD5) LICENSE.txt: 4205 bytes, checksum: f735a60aef4d3c0daa0576cb5a4301d6 (MD5) Previous issue date: 2018-04-13","Embargo set by: Seth Robbins for item 107382 Lift date: 2020-09-04T20:47:38Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Embargo set by: Seth Robbins for item 107382 Lift date: 2020-09-04T20:50:11Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Limited Restriction Lifted for Item 107382 on 2020-09-05T09:15:09Z."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/101297"],"dc:language":["en"],"dc:rights":["Copyright 2018 Ci Zhang"],"dc:subject":["Item response theory (IRT), 4PLM, EMMM, BEMMM"],"dc:title":["From expectation-3-maximization to bayesian expectation-3-maximization: A latent mixture modeling-based bayesian algorithm for the 4-parameter logistic model"],"dc:type":["text"],"thesis:degree_discipline":["Educational Psychology"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:38Z"}