Joint Maximum Likelihood Estimation for Diagnostic Classification Models
Joint maximum likelihood estimation (JMLE) is developed for diagnostic classification models (DCMs). JMLE has been barely used in Psychometrics because JMLE parameter estimators typically lack statistical consistency. The JMLE procedure presented here resolves the consistency issue by incorporating...
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| Veröffentlicht in: | Psychometrika 2016-12, Vol.81 (4), p.1069-1092 |
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| creator | Chiu, Chia-Yi Köhn, Hans-Friedrich Zheng, Yi Henson, Robert |
| description | Joint maximum likelihood estimation (JMLE) is developed for diagnostic classification models (DCMs). JMLE has been barely used in Psychometrics because JMLE parameter estimators typically lack statistical consistency. The JMLE procedure presented here resolves the consistency issue by incorporating an external, statistically consistent estimator of examinees’ proficiency class membership into the joint likelihood function, which subsequently allows for the construction of item parameter estimators that also have the consistency property. Consistency of the JMLE parameter estimators is established within the framework of general DCMs: The JMLE parameter estimators are derived for the Loglinear Cognitive Diagnosis Model (LCDM). Two consistency theorems are proven for the LCDM. Using the framework of general DCMs makes the results and proofs also applicable to DCMs that can be expressed as submodels of the LCDM. Simulation studies are reported for evaluating the performance of JMLE when used with tests of varying length and different numbers of attributes. As a practical application, JMLE is also used with “real world” educational data collected with a language proficiency test. |
| doi_str_mv | 10.1007/s11336-016-9534-9 |
| format | Article |
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JMLE has been barely used in Psychometrics because JMLE parameter estimators typically lack statistical consistency. The JMLE procedure presented here resolves the consistency issue by incorporating an external, statistically consistent estimator of examinees’ proficiency class membership into the joint likelihood function, which subsequently allows for the construction of item parameter estimators that also have the consistency property. Consistency of the JMLE parameter estimators is established within the framework of general DCMs: The JMLE parameter estimators are derived for the Loglinear Cognitive Diagnosis Model (LCDM). Two consistency theorems are proven for the LCDM. Using the framework of general DCMs makes the results and proofs also applicable to DCMs that can be expressed as submodels of the LCDM. Simulation studies are reported for evaluating the performance of JMLE when used with tests of varying length and different numbers of attributes. 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methods</topic><topic>Statistical Theory and Methods</topic><topic>Statistics for Social Sciences</topic><topic>Statistics, Nonparametric</topic><topic>Testing and Evaluation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chiu, Chia-Yi</creatorcontrib><creatorcontrib>Köhn, Hans-Friedrich</creatorcontrib><creatorcontrib>Zheng, Yi</creatorcontrib><creatorcontrib>Henson, Robert</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>ProQuest Social Sciences Premium Collection【Remote access available】</collection><collection>ProQuest Central (Corporate)</collection><collection>Neurosciences Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>Health Medical collection</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection</collection><collection>Education Database (Alumni Edition)</collection><collection>Medical Database (Alumni Edition)</collection><collection>Psychology Database (Alumni)</collection><collection>ProQuest Pharma Collection</collection><collection>Hospital Premium Collection</collection><collection>Hospital Premium Collection (Alumni Edition)</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Social Science Premium Collection (Proquest) (PQ_SDU_P3)</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>ProQuest Business Premium Collection</collection><collection>ProQuest One Community College</collection><collection>Education Collection</collection><collection>ProQuest Central</collection><collection>Business Premium Collection (Alumni)</collection><collection>Health Research Premium Collection</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>Health Research Premium Collection (Alumni)</collection><collection>ProQuest Central Student</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ABI/INFORM Global (ProQuest)</collection><collection>ProQuest Education Journals</collection><collection>Health & Medical Collection (Alumni Edition)</collection><collection>Medical Database</collection><collection>Psychology Database</collection><collection>One Business (ProQuest)</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Education</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>ProQuest One Psychology</collection><collection>ProQuest Central Basic</collection><collection>MEDLINE - Academic</collection><jtitle>Psychometrika</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chiu, Chia-Yi</au><au>Köhn, Hans-Friedrich</au><au>Zheng, Yi</au><au>Henson, Robert</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Joint Maximum Likelihood Estimation for Diagnostic Classification Models</atitle><jtitle>Psychometrika</jtitle><stitle>Psychometrika</stitle><addtitle>Psychometrika</addtitle><date>2016-12-01</date><risdate>2016</risdate><volume>81</volume><issue>4</issue><spage>1069</spage><epage>1092</epage><pages>1069-1092</pages><issn>0033-3123</issn><eissn>1860-0980</eissn><abstract>Joint maximum likelihood estimation (JMLE) is developed for diagnostic classification models (DCMs). JMLE has been barely used in Psychometrics because JMLE parameter estimators typically lack statistical consistency. The JMLE procedure presented here resolves the consistency issue by incorporating an external, statistically consistent estimator of examinees’ proficiency class membership into the joint likelihood function, which subsequently allows for the construction of item parameter estimators that also have the consistency property. Consistency of the JMLE parameter estimators is established within the framework of general DCMs: The JMLE parameter estimators are derived for the Loglinear Cognitive Diagnosis Model (LCDM). Two consistency theorems are proven for the LCDM. Using the framework of general DCMs makes the results and proofs also applicable to DCMs that can be expressed as submodels of the LCDM. Simulation studies are reported for evaluating the performance of JMLE when used with tests of varying length and different numbers of attributes. As a practical application, JMLE is also used with “real world” educational data collected with a language proficiency test.</abstract><cop>New York</cop><pub>Springer US</pub><pmid>27734298</pmid><doi>10.1007/s11336-016-9534-9</doi><tpages>24</tpages></addata></record> |
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| subjects | Ability Identification Algorithms Assessment Behavioral Science and Psychology Clinical Decision-Making Computer Simulation Data Interpretation, Statistical Datasets as Topic Educational evaluation Educational Testing Humanities Humans Language Tests Law Likelihood Functions Linear Models Markov Processes Maximum Likelihood Statistics Psychology Psychometrics Psychometrics - methods Statistical Theory and Methods Statistics for Social Sciences Statistics, Nonparametric Testing and Evaluation |
| title | Joint Maximum Likelihood Estimation for Diagnostic Classification Models |
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