{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/87406"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/87406","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Methods and Theory for Joint Estimation of Incidental and Structural Parameters in Latent Class Models","abstract":"Marginal maximum likelihood estimation has become the standard for parameter estimation in latent variable models. However, there are instances when alternative estimators that jointly estimate incidental parameters and structural parameters might be easier to implement. A drawback to joint estimation, and joint maximum likelihood estimation in particular, is that little theory has been developed to understand their asymptotic behavior. Here we consider joint estimation of class membership and structural parameters in latent class models for binary responses. An estimator that first utilizes a K-means clustering solution on a statistic that identifies class membership and then maximizes the conditional likelihood of the structural parameters is studied. It is shown that this estimator is consistent and is asymptotically normal. In addition, it is shown that this estimator is identical to the joint maximum likelihood estimator with probability approaching 1 as the sample size and item response vector length both approach infinity, for a special case. An argument is then given that we can also expect this result in more general cases. The small sample properties of the estimator are studied by simulation.","abstract_html":"Marginal maximum likelihood estimation has become the standard for parameter estimation in latent variable models. However, there are instances when alternative estimators that jointly estimate incidental parameters and structural parameters might be easier to implement. A drawback to joint estimation, and joint maximum likelihood estimation in particular, is that little theory has been developed to understand their asymptotic behavior. Here we consider joint estimation of class membership and structural parameters in latent class models for binary responses. An estimator that first utilizes a K-means clustering solution on a statistic that identifies class membership and then maximizes the conditional likelihood of the structural parameters is studied. It is shown that this estimator is consistent and is asymptotically normal. In addition, it is shown that this estimator is identical to the joint maximum likelihood estimator with probability approaching 1 as the sample size and item response vector length both approach infinity, for a special case. An argument is then given that we can also expect this result in more general cases. The small sample properties of the estimator are studied by simulation.","abstract_has_math":false,"creators":["Li, Xiaodong"],"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"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T16:02:44Z","date_published":"2015-09-28T16:02:44Z","updated_at":"2026-07-22T22:26:30Z","subjects":["Statistics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3242917"],"render_values":[{"text":"(MiAaPQ)AAI3242917","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/87406","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Douglas, Jeffrey"]},{"key":"dc:creator","label":"Author","values":["Li, Xiaodong"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T16:02:44Z","10000-01-01","2006"]},{"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":["Statistics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/87406","(MiAaPQ)AAI3242917"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Marginal maximum likelihood estimation has become the standard for parameter estimation in latent variable models. However, there are instances when alternative estimators that jointly estimate incidental parameters and structural parameters might be easier to implement. A drawback to joint estimation, and joint maximum likelihood estimation in particular, is that little theory has been developed to understand their asymptotic behavior. Here we consider joint estimation of class membership and structural parameters in latent class models for binary responses. An estimator that first utilizes a K-means clustering solution on a statistic that identifies class membership and then maximizes the conditional likelihood of the structural parameters is studied. It is shown that this estimator is consistent and is asymptotically normal. In addition, it is shown that this estimator is identical to the joint maximum likelihood estimator with probability approaching 1 as the sample size and item response vector length both approach infinity, for a special case. 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However, there are instances when alternative estimators that jointly estimate incidental parameters and structural parameters might be easier to implement. A drawback to joint estimation, and joint maximum likelihood estimation in particular, is that little theory has been developed to understand their asymptotic behavior. Here we consider joint estimation of class membership and structural parameters in latent class models for binary responses. An estimator that first utilizes a K-means clustering solution on a statistic that identifies class membership and then maximizes the conditional likelihood of the structural parameters is studied. It is shown that this estimator is consistent and is asymptotically normal. In addition, it is shown that this estimator is identical to the joint maximum likelihood estimator with probability approaching 1 as the sample size and item response vector length both approach infinity, for a special case. An argument is then given that we can also expect this result in more general cases. The small sample properties of the estimator are studied by simulation.","Made available in DSpace on 2015-09-28T16:02:44Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3242917.pdf: 1290505 bytes, checksum: 9793eeab6377d03d6256b1087409e17e (MD5) Previous issue date: 2006","Embargo set by: Seth Robbins for item 88687 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","59 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006."],"dc:identifier":["http://hdl.handle.net/2142/87406","(MiAaPQ)AAI3242917"],"dc:language":["eng"],"dc:subject":["Statistics"],"dc:title":["Methods and Theory for Joint Estimation of Incidental and Structural Parameters in Latent Class Models"],"dc:type":["text"],"thesis:degree_discipline":["Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:30Z"}