{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/92689"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/92689","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Pseudo-likelihood estimation of multidimensional polytomous item response theory models","abstract":"This Dissertation was approved for publication on 2016-06-24 at 13:03.","abstract_html":"This Dissertation was approved for publication on 2016-06-24 at 13:03.","abstract_has_math":false,"creators":["Paek, Youngshil"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Educational Psychology","degree_department":null,"school":null,"contributors":["Anderson, Carolyn J.","Douglas, Jeffrey A.","Zhang, Jinming","Culpepper, Steven"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-11-10T17:49:20Z","date_published":"2016-11-10T17:49:20Z","updated_at":"2026-07-22T22:26:35Z","subjects":["item parameter","estimation","log-multiplicative association","item response theory","multidimensional","polytomous"],"languages":["en"],"rights":["Copyright 2016 Youngshil Paek"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/92689","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Anderson, Carolyn J.","Douglas, Jeffrey A.","Zhang, Jinming","Culpepper, Steven"]},{"key":"dc:creator","label":"Author","values":["Paek, Youngshil"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2016-11-10T17:49:20Z","2016-06-24","2016-08"]},{"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":["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":["item parameter","estimation","log-multiplicative association","item response theory","multidimensional","polytomous"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2016 Youngshil Paek"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/92689"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This Dissertation was approved for publication on 2016-06-24 at 13:03.","DSpace SAF Submission Ingestion Package generated from Vireo submission #9490 on 2016-11-09 at 10:19:17","Log-multiplicative association (LMA) models, special cases of log-linear models, can be used as multidimensional item response theory (MIRT) models for polytomous items (Anderson, Verkuilen and Peyton, 2010; Anderson, 2013). LMA models do not require numerical integration for their estimation nor do they require assumptions regarding the marginal distribution of the latent variables. However, maximum likelihood estimation (MLE) of LMA models requires iteratively computing fitted values for all possible response patterns. Standard estimation methods for large numbers of items fail because the number of possible response patterns increases exponentially as the number of items and response options per item increase. In this study, a new algorithm is proposed to solve this estimation problem. Anderson, Li and Vermunt (2007) proposed using pseudo-likelihood estimation (PLE); however, their solution only applies to models in the Rasch family, which exploits the relationship between log-linear and logistic regression models. Their method is extended to more general models by adding an additional step that estimates slope (item discrimination) parameters for the latent variables. The new algorithm has two basic steps and simplifies for special cases. In Step 1, a (multinomial) logistic regression model is fit by MLE to one item using rest-scores as an explanatory variable to get new estimates of item slopes that are used in the rest-score for the next item. This process is repeated for each item until all item slopes have been up-dated. Step 2 involves fitting a single conditional logistic regression model for a data set formed by stacking the conditional logistic regressions for each item. This yields new estimates of location (item difficulty) parameters and the covariance matrix for the latent variables. Steps 1 and 2 are repeated until all parameter estimates converge. The results of simulation and empirical studies with real data show that the proposed algorithm successfully estimates parameters in more general LMA models with both location and slope parameters as MIRT models.","Submission original under an indefinite embargo labeled 'Open Access'. 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LMA models do not require numerical integration for their estimation nor do they require assumptions regarding the marginal distribution of the latent variables. However, maximum likelihood estimation (MLE) of LMA models requires iteratively computing fitted values for all possible response patterns. Standard estimation methods for large numbers of items fail because the number of possible response patterns increases exponentially as the number of items and response options per item increase. In this study, a new algorithm is proposed to solve this estimation problem. Anderson, Li and Vermunt (2007) proposed using pseudo-likelihood estimation (PLE); however, their solution only applies to models in the Rasch family, which exploits the relationship between log-linear and logistic regression models. Their method is extended to more general models by adding an additional step that estimates slope (item discrimination) parameters for the latent variables. The new algorithm has two basic steps and simplifies for special cases. In Step 1, a (multinomial) logistic regression model is fit by MLE to one item using rest-scores as an explanatory variable to get new estimates of item slopes that are used in the rest-score for the next item. This process is repeated for each item until all item slopes have been up-dated. Step 2 involves fitting a single conditional logistic regression model for a data set formed by stacking the conditional logistic regressions for each item. This yields new estimates of location (item difficulty) parameters and the covariance matrix for the latent variables. Steps 1 and 2 are repeated until all parameter estimates converge. The results of simulation and empirical studies with real data show that the proposed algorithm successfully estimates parameters in more general LMA models with both location and slope parameters as MIRT models.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2016-11-09 without embargo terms","The student, Youngshil Paek, accepted the attached license on 2016-04-27 at 08:21.","The student, Youngshil Paek, submitted this Dissertation for approval on 2016-04-27 at 09:14.","Made available in DSpace on 2016-11-10T17:49:20Z (GMT). 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