{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/117700"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/117700","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Learning models and the double monotone model","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-04-12 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-04-12 without embargo terms","abstract_has_math":false,"creators":["Yu, Albert"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Statistics","degree_department":null,"school":null,"contributors":["Douglas, Jeffrey","Culpepper, Steven","Kern, Justin","Zhang, Susu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-12","date_published":"2022-12","updated_at":"2026-07-22T22:24:56Z","subjects":["Irt","Double Monotone Model","Learning Models"],"languages":["en","eng"],"rights":["Copyright 2022 Albert Yu"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/117700","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Douglas, Jeffrey","Culpepper, Steven","Kern, Justin","Zhang, Susu"]},{"key":"dc:creator","label":"Author","values":["Yu, Albert"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-12","2022-10-14"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"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":["Irt","Double Monotone Model","Learning Models"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2022 Albert Yu"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/117700"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-04-12 without embargo terms","The student, Albert Yu, accepted the attached license on 2022-09-24 at 09:10.","The student, Albert Yu, submitted this Dissertation for approval on 2022-09-24 at 09:13.","This Dissertation was approved for publication on 2022-10-14 at 09:00.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18444 on 2023-04-12 at 07:22:51","The goal of some assessments is to evaluate a person’s ability levels while others aim to teach through an intervention. In Chapter 1, we propose some IRT growth models for learning and estimate their learning parameters under the restrictions of the Linear Logistic Test Model. We also examine the potential benefit of using an adaptive selection method in conjunction with these models which aims to increase the rate of learning. In 1971, Mokken proposed the Double Monotone Model (DMM), a non-parametric item response model which is widely used to assess peoples’ abilities or attitudes. In Chapter 2, we introduce a procedure for estimating the DMM. We study its performance in simulation and use M-estimation to develop an asymptotic theory for estimation of ICCs using isotonic regression. Previous isotonic regression theory showed that the isotonic regression estimator, ˆ Pj , is consistent for Pj when θ is observable. When θ is unknown and estimated by θˆ, we show that the isotonic regression estimator, P˜j , is also consistent for Pj . We perform a real data analysis and illustrate how to select subsets of items to achieve double monotonicity, and we develop a test for double monotonicity with a null hypothesis of double monotonicity. In Chapter 3, we compare the performance of the 1PL to the DMM under various conditions with the constraints of double monotonicity. We found that fitting a 1PL can perform at least as well as the DMM for short exams and small sample sizes, even when the 1PL does not hold. This is due to the requirement of a plug-in estimate of theta for the nonparametric model. We also study the implication for ability estimation and found that nonparametric estimation is quite good. Recommendations are given for when to use or not use the nonparametric DMM."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Learning models and the double monotone model"]}]}],"canonical_facts":{"dc:contributor":["Douglas, Jeffrey","Culpepper, Steven","Kern, Justin","Zhang, Susu"],"dc:creator":["Yu, Albert"],"dc:date":["2022-12","2022-10-14"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-04-12 without embargo terms","The student, Albert Yu, accepted the attached license on 2022-09-24 at 09:10.","The student, Albert Yu, submitted this Dissertation for approval on 2022-09-24 at 09:13.","This Dissertation was approved for publication on 2022-10-14 at 09:00.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18444 on 2023-04-12 at 07:22:51","The goal of some assessments is to evaluate a person’s ability levels while others aim to teach through an intervention. In Chapter 1, we propose some IRT growth models for learning and estimate their learning parameters under the restrictions of the Linear Logistic Test Model. We also examine the potential benefit of using an adaptive selection method in conjunction with these models which aims to increase the rate of learning. In 1971, Mokken proposed the Double Monotone Model (DMM), a non-parametric item response model which is widely used to assess peoples’ abilities or attitudes. In Chapter 2, we introduce a procedure for estimating the DMM. We study its performance in simulation and use M-estimation to develop an asymptotic theory for estimation of ICCs using isotonic regression. Previous isotonic regression theory showed that the isotonic regression estimator, ˆ Pj , is consistent for Pj when θ is observable. When θ is unknown and estimated by θˆ, we show that the isotonic regression estimator, P˜j , is also consistent for Pj . We perform a real data analysis and illustrate how to select subsets of items to achieve double monotonicity, and we develop a test for double monotonicity with a null hypothesis of double monotonicity. In Chapter 3, we compare the performance of the 1PL to the DMM under various conditions with the constraints of double monotonicity. We found that fitting a 1PL can perform at least as well as the DMM for short exams and small sample sizes, even when the 1PL does not hold. This is due to the requirement of a plug-in estimate of theta for the nonparametric model. We also study the implication for ability estimation and found that nonparametric estimation is quite good. Recommendations are given for when to use or not use the nonparametric DMM."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/117700"],"dc:language":["en","eng"],"dc:rights":["Copyright 2022 Albert Yu"],"dc:subject":["Irt","Double Monotone Model","Learning Models"],"dc:title":["Learning models and the double monotone model"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:56Z"}