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The investigation used copulas in computer simulations of performance assessment batteries with varying combinations of item characteristics within Muraki\u0026amp;amp;#39;s 3enera1ized Partial Credit Model. Only two of the significant contrasts that were detected were of practical importance. The results appear to indicate that the expected reduction in information due to the collapsing of categories is not affected by any of the testing conditions simulated in this study. Consequently, a practitioner may combine low-frequency categories with adjacent categories without any significant adverse effect on the information provided by the test items. 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The investigation used copulas in computer simulations of performance assessment batteries with varying combinations of item characteristics within Muraki\u0026#39;s 3enera1ized Partial Credit Model. Only two of the significant contrasts that were detected were of practical importance. The results appear to indicate that the expected reduction in information due to the collapsing of categories is not affected by any of the testing conditions simulated in this study. Consequently, a practitioner may combine low-frequency categories with adjacent categories without any significant adverse effect on the information provided by the test items. (Contains 1 figure, 9 table...","ai_title_tag":"Impact of Category Collapsing on Item Information","publication_date":"2012,,"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"TITLE How the Collapsing of Categories Impacts the Item Information Function in Polytomous Item Response Theory","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [7565876]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon'; window.userInChina = "false";</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":82230053,"attachmentType":"pdf"}"><img alt="First page of “TITLE How the Collapsing of Categories Impacts the Item Information Function in Polytomous Item Response Theory”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/82230053/mini_magick20220316-5690-1bn6utl.png?1647425114" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">TITLE How the Collapsing of Categories Impacts the Item Information Function in Polytomous Item Response Theory</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="7565876" href="https://independent.academia.edu/DariusLecointe"><img alt="Profile image of Darius Lecointe" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/7565876/4124531/18442138/s65_darius.lecointe.jpg" />Darius Lecointe</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2012</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">27 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 73874129; 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if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">The purpose of this Item Response Theory study was to investigate how the expected reduction in item information, due to the collapsing of response categories in performance assessment data, was affected by varying testing conditions: item difficulty, item discrimination, inter-rater reliability, and direction of collapsing. The investigation used copulas in computer simulations of performance assessment batteries with varying combinations of item characteristics within Muraki&#39;s 3enera1ized Partial Credit Model. Only two of the significant contrasts that were detected were of practical importance. The results appear to indicate that the expected reduction in information due to the collapsing of categories is not affected by any of the testing conditions simulated in this study. Consequently, a practitioner may combine low-frequency categories with adjacent categories without any significant adverse effect on the information provided by the test items. (Contains 1 figure, 9 table...</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":82230053,"attachmentType":"pdf","workUrl":"https://www.academia.edu/73874129/TITLE_How_the_Collapsing_of_Categories_Impacts_the_Item_Information_Function_in_Polytomous_Item_Response_Theory"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":82230053,"attachmentType":"pdf","workUrl":"https://www.academia.edu/73874129/TITLE_How_the_Collapsing_of_Categories_Impacts_the_Item_Information_Function_in_Polytomous_Item_Response_Theory"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div><div class="ds-signup-banner-trigger-container"><div class="ds-signup-banner-trigger ds-signup-banner-trigger-control"></div></div><div class="ds-signup-banner ds-signup-banner-control"><div id="ds-signup-banner-close-button"><button class="ds2-5-button ds2-5-button--secondary ds2-5-button--inverse"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">close</span></button></div><div class="ds-signup-banner-ctas"><img src="//a.academia-assets.com/images/academia-logo-capital-white.svg" /><h4 class="ds2-5-heading-serif-sm">Sign up for access to the world's latest research</h4><button class="ds2-5-button ds2-5-button--inverse ds2-5-button--full-width js-swp-download-button" data-signup-modal="{"location":"signup-banner"}">Sign up for free<span class="material-symbols-outlined" style="font-size: 20px" translate="no">arrow_forward</span></button></div><div class="ds-signup-banner-divider"></div><div class="ds-signup-banner-reasons"><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Get notified about relevant papers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Save papers to use in your research</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Join the discussion with peers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Track your impact</span></div></div></div><script>(() => { // Set up signup banner show/hide behavior: // 1. 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The investigation used copulas in computer simulations of performance assessment batteries with varying combinations of item characteristics within Muraki's 3enera1ized Partial Credit Model. Only two of the significant contrasts that were detected were of practical importance. The results appear to indicate that the expected reduction in information due to the collapsing of categories is not affected by any of the testing conditions simulated in this study. Consequently, a practitioner may combine low-frequency categories with adjacent categories without any significant adverse effect on the information provided by the test items. (Contains 1 figure, 9 tables, and 19 references.) (Author)</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"How the Collapsing of Categories Impacts the Item Information Function in Polytomous Item Response Theory","attachmentId":71744978,"attachmentType":"pdf","work_url":"https://www.academia.edu/56282327/How_the_Collapsing_of_Categories_Impacts_the_Item_Information_Function_in_Polytomous_Item_Response_Theory","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/56282327/How_the_Collapsing_of_Categories_Impacts_the_Item_Information_Function_in_Polytomous_Item_Response_Theory"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="102513983" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/102513983/An_Evaluation_of_Different_Statistical_Targets_for_Assembling_Parallel_Forms_in_Item_Response_Theory">An Evaluation of Different Statistical Targets for Assembling Parallel Forms in Item Response Theory</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="271620005" href="https://independent.academia.edu/UsamaAli313">Usama Ali</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Applied Psychological Measurement, 2015</p><p class="ds-related-work--abstract ds2-5-body-sm">Assembly of parallel forms is an important step in the test development process. Therefore, choosing a suitable theoretical framework to generate well-defined test specifications is critical. The performance of different statistical targets of test specifications using the test characteristic curve (TCC) and the test information function (TIF) was investigated. Test length, the number of test forms, and content specifications are considered as well. The TCC target results in forms that are parallel in difficulty, but not necessarily in terms of precision. Vice versa, test forms created using a TIF target are parallel in terms of precision, but not necessarily in terms of difficulty. As sometimes the focus is either on TIF or TCC, differences in either difficulty or precision can arise. Differences in difficulty can be mitigated by equating, but differences in precision cannot. In a series of simulations using a real item bank, the two-parameter logistic model, and mixed integer line...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"An Evaluation of Different Statistical Targets for Assembling Parallel Forms in Item Response Theory","attachmentId":102764059,"attachmentType":"pdf","work_url":"https://www.academia.edu/102513983/An_Evaluation_of_Different_Statistical_Targets_for_Assembling_Parallel_Forms_in_Item_Response_Theory","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/102513983/An_Evaluation_of_Different_Statistical_Targets_for_Assembling_Parallel_Forms_in_Item_Response_Theory"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="7037122" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/7037122/21_Assessing_the_Fit_of_Item_Response_Theory_Models">21 Assessing the Fit of Item Response Theory Models</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="12011412" href="https://uconn.academia.edu/HariharanSwaminathan">Hariharan Swaminathan</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Handbook of Statistics, 2006</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"21 Assessing the Fit of Item Response Theory Models","attachmentId":48624449,"attachmentType":"pdf","work_url":"https://www.academia.edu/7037122/21_Assessing_the_Fit_of_Item_Response_Theory_Models","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/7037122/21_Assessing_the_Fit_of_Item_Response_Theory_Models"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="93489746" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/93489746/A_Monte_Carlo_Study_Investigating_the_Influence_of_Item_Discrimination_Category_Intersection_Parameters_and_Differential_Item_Functioning_in_Polytomous_Items">A Monte Carlo Study Investigating the Influence of Item Discrimination, Category Intersection Parameters, and Differential Item Functioning in Polytomous Items</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="238484304" href="https://independent.academia.edu/ThurmanCarol">Carol Thurman</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2009</p><p class="ds-related-work--abstract ds2-5-body-sm">The increased use of polytomous item formats has led assessment developers to pay greater attention to the detection of differential item functioning (DIF) in these items. DIF occurs when an item performs differently for two contrasting groups of respondents (e.g., males versus females) after controlling for differences in the abilities of the groups. Determining whether the difference in performance on an item between two demographic groups is due to between group differences in ability or some form of unfairness in the item is a more complex task for a polytomous item, because of its many score categories, than for a dichotomous item. Effective DIF detection methods must be able to locate DIF within each of these various score categories. The Mantel, Generalized Mantel Haenszel (GMH), and Logistic Regression (LR) are three of several DIF detection methods that are able to test for DIF in polytomous items. There have been relatively few studies on the effectiveness of polytomous procedures to detect DIF; and of those studies, only a very small percentage have examined the efficiency of the Mantel, GMH, and LR procedures when item discrimination magnitudes and category intersection parameters vary and when there are different patterns of DIF (e.g., balanced versus constant) within score categories. This Monte Carlo simulation study compared the Type I error and power of the Mantel, GMH, and OLR (LR method for ordinal data) procedures when variation occurred in 1) the item discrimination parameters, 2) category intersection parameters, 3) DIF patterns within score categories, and 4) the average latent traits between the reference and focal groups. Results of this investigation showed that high item discrimination levels were directly related to increased DIF detection rates. The location of the difficulty parameters was also found to have a direct effect on DIF detection rates. Additionally, depending on item difficulty, DIF magnitudes and patterns within score categories were found to impact DIF detection rates and finally, DIF detection power increased as DIF magnitudes became larger. The GMH outperformed the Mantel and OLR and is recommended for use with polytomous data when the item discrimination varies across items.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A Monte Carlo Study Investigating the Influence of Item Discrimination, Category Intersection Parameters, and Differential Item Functioning in Polytomous Items","attachmentId":96213780,"attachmentType":"pdf","work_url":"https://www.academia.edu/93489746/A_Monte_Carlo_Study_Investigating_the_Influence_of_Item_Discrimination_Category_Intersection_Parameters_and_Differential_Item_Functioning_in_Polytomous_Items","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/93489746/A_Monte_Carlo_Study_Investigating_the_Influence_of_Item_Discrimination_Category_Intersection_Parameters_and_Differential_Item_Functioning_in_Polytomous_Items"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="34533345" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/34533345/Computerized_Adaptive_Test_CAT_Applications_and_Item_Response_Theory_Models_for_Polytomous_Items">Computerized Adaptive Test (CAT) Applications and Item Response Theory Models for Polytomous Items</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="393094" href="https://ankara.academia.edu/RDemirtasli">R. Demirtasli</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="7432356" href="https://pamukkale.academia.edu/ErenCanAybek">Eren Can Aybek</a></div><p class="ds-related-work--abstract ds2-5-body-sm">This article aims to provide a theoretical framework for computerized adaptive tests (CAT) and item response theory models for polytomous items. Besides that, it aims to introduce the simulation and live CAT software to the related researchers. Computerized adaptive test algorithm, assumptions of item response theory models, nominal response model, partial credit and generalized partial credit models and graded response model are described carefully to reach that aim. Likewise, item selection methods, such as maximum Fisher information, maximum expected information, minimum expected posterior variance, maximum expected posterior weighted-information, and ability prediction methods, such as expected a posteriori and maximum a posteriori, are expounded as well as stopping rules for the computerized adaptive tests.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Computerized Adaptive Test (CAT) Applications and Item Response Theory Models for Polytomous Items","attachmentId":54399405,"attachmentType":"pdf","work_url":"https://www.academia.edu/34533345/Computerized_Adaptive_Test_CAT_Applications_and_Item_Response_Theory_Models_for_Polytomous_Items","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/34533345/Computerized_Adaptive_Test_CAT_Applications_and_Item_Response_Theory_Models_for_Polytomous_Items"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="76476849" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/76476849/An_Evaluation_of_Item_Response_Theory_Classification_Accuracy_and_Consistency_Indices">An Evaluation of Item Response Theory Classification Accuracy and Consistency Indices</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="14477127" href="https://michigan.academia.edu/ShiqiHao">Shiqi Hao</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Applied Psychological Measurement, 2012</p><p class="ds-related-work--abstract ds2-5-body-sm">This article introduces two new classification consistency indices that can be used when item response theory (IRT) models have been applied. The new indices are shown to be related to Rudner's classification accuracy index and Guo's classification accuracy index. The Rudner-and Guo-based classification accuracy and consistency indices are evaluated and compared with estimates from the more commonly applied IRT-recursive procedure using a simulation study and data from two large-scale assessments. Results from the simulation study and practical examples suggested that the Guo-and Rudner-based indices tended to produce estimates that were closer to the simulated values and exceeded those from the IRT-recursive-based procedure. However, results did suggest that the Rudner-and Guo-based indices can have some undesirable features that are important to keep in mind when applying them in practice. The values of the classification accuracy and consistency indices appeared to be affected by a number of factors including the distribution of examinees, test length, the placement of the cut-scores, and the proficiency estimators applied to estimate examinee ability. Suggestions are made that an important part of investigations evaluating classification accuracy and consistency indices should be the creation of figures that show the value of the classification accuracy and classification consistency for individual examinees across the range of possible scores as these figures can help provide indications into subtle and important differences between indices.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"An Evaluation of Item Response Theory Classification Accuracy and Consistency Indices","attachmentId":84173425,"attachmentType":"pdf","work_url":"https://www.academia.edu/76476849/An_Evaluation_of_Item_Response_Theory_Classification_Accuracy_and_Consistency_Indices","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/76476849/An_Evaluation_of_Item_Response_Theory_Classification_Accuracy_and_Consistency_Indices"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="74375611" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/74375611/Item_response_theory_A_first_approach">Item response theory – A first approach</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="638875" href="https://independent.academia.edu/TOliveira">Teresa Oliveira</a></div><p class="ds-related-work--abstract ds2-5-body-sm">The Item Response Theory (IRT) has become one of the most popular scoring frameworks for measurement data, frequently used in computerized adaptive testing, cognitively diagnostic assessment and test equating. According to Andrade et al. (2000), IRT can be defined as a set of mathematical models (Item Response Models-IRM) constructed to represent the probability of an individual giving the right answer to an item of a particular test. The number of Item Responsible Models available to measurement analysis has increased considerably in the last fifteen years due to increasing computer power and due to a demand for accuracy and more meaningful inferences grounded in complex data. The developments in modeling with Item Response Theory were related with developments in estimation theory, most remarkably Bayesian estimation with Markov chain Monte Carlo algorithms (Patz & Junker, 1999). The popularity of Item Response Theory has also implied numerous overviews in books and journals, and many connections between IRT and other statistical estimation procedures, such as factor analysis and structural equation modeling, have been made repeatedly (Van der Lindem & Hambleton, 1997).As stated before the Item Response Theory covers a variety of measurement models, ranging from basic one-dimensional models for dichotomously and polytomously scored items and their multidimensional analogues to models that incorporate information about cognitive sub-processes which influence the overall item response process. The aim of this work is to introduce the main concepts associated with onedimensional models of Item Response Theory, to specify the logistic models with one, two and three parameters, to discuss some properties of these models and to present the main estimation procedures.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Item response theory – A first approach","attachmentId":82551211,"attachmentType":"pdf","work_url":"https://www.academia.edu/74375611/Item_response_theory_A_first_approach","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/74375611/Item_response_theory_A_first_approach"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="70518957" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/70518957/The_Applicability_of_Item_Response_Theory_Based_Statistics_to_Detect_Differential_Item_Functioning_in_Polytomous_Tests">The Applicability of Item Response Theory Based Statistics to Detect Differential Item Functioning in Polytomous Tests</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="15592909" href="https://oauife.academia.edu/AbdulWahabIbrahimAfejigba">Abdul-Wahab Ibrahim</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Randwick International of Education and Linguistics Science Journal</p><p class="ds-related-work--abstract ds2-5-body-sm">The study used statistical procedures based on Item Response Theory to detect Differential Item Functioning (DIF) in polytomous tests. These were with a view to improving the quality of test items construction. The sample consisted of an intact class of 513 Part 3 undergraduate students who registered for the course EDU 304: Tests and Measurement at Sule Lamido University during 2017/2018 Second Semester. A self-developed polytomous research instrument was used to collect data. Data collected were analysed using Generalized Mantel Haenszel, Simultaneous Item Bias Test, and Logistic Discriminant Function Analysis. The results showed that there was no significant relationship between the proportions of test items that function differentially in the polytomous test when the different statistical methods are used. Further, the three parametric and non-parametric methods complement each other in their ability to detect DIF in the polytomous test format as all of them have capacity to de...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The Applicability of Item Response Theory Based Statistics to Detect Differential Item Functioning in Polytomous Tests","attachmentId":80239283,"attachmentType":"pdf","work_url":"https://www.academia.edu/70518957/The_Applicability_of_Item_Response_Theory_Based_Statistics_to_Detect_Differential_Item_Functioning_in_Polytomous_Tests","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/70518957/The_Applicability_of_Item_Response_Theory_Based_Statistics_to_Detect_Differential_Item_Functioning_in_Polytomous_Tests"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="60387463" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/60387463/Some_Applications_of_Item_Response_Theory_to_Testing">Some Applications of Item Response Theory to Testing</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="53394044" href="https://independent.academia.edu/Pornel">Jonny Pornel</a></div><p class="ds-related-work--abstract ds2-5-body-sm">A test score that is obtained through the number-correct score is often used as estimate of an examinee&#39;s proficiency. A problem with this approach is that it does not take into account the characteristic of the item, such as the item difficulty, when estimating the proficiency. Furthermore, when test scores are used to evaluate the performance of a school, the presence of examinees who do not respond according to their true ability (e.g., guessing and copying), could yield estimates of a school performance that is lower than its actual performance. In this study, it was shown that the problem is circumvented using an approach based on the item response theory (IRT). Simulation studies were conducted to illustrate the points.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Some Applications of Item Response Theory to Testing","attachmentId":73856838,"attachmentType":"pdf","work_url":"https://www.academia.edu/60387463/Some_Applications_of_Item_Response_Theory_to_Testing","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/60387463/Some_Applications_of_Item_Response_Theory_to_Testing"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="111434139" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/111434139/Handbook_of_Item_Response_Theory_Volume_1_Models">Handbook of Item Response Theory, Volume 1, Models</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="31168484" href="https://independent.academia.edu/StanLipovetsky">Stan Lipovetsky</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Technometrics, 2021</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Handbook of Item Response Theory, Volume 1, Models","attachmentId":108976012,"attachmentType":"pdf","work_url":"https://www.academia.edu/111434139/Handbook_of_Item_Response_Theory_Volume_1_Models","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/111434139/Handbook_of_Item_Response_Theory_Volume_1_Models"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":82230053,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":82230053,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_82230053" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. You can download the paper by clicking the button above.</p></div></div></div></div><div class="ds-sidebar--container js-work-sidebar"><div class="ds-related-content--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="0" data-entity-id="111434138" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/111434138/Handbook_of_Item_Response_Theory_Applications_3_">Handbook of Item Response Theory: Applications (3)</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="31168484" href="https://independent.academia.edu/StanLipovetsky">Stan Lipovetsky</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Technometrics, 2021</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Handbook of Item Response Theory: Applications (3)","attachmentId":108976010,"attachmentType":"pdf","work_url":"https://www.academia.edu/111434138/Handbook_of_Item_Response_Theory_Applications_3_","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/111434138/Handbook_of_Item_Response_Theory_Applications_3_"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="1" data-entity-id="102194585" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/102194585/Multidimensional_Componential_Item_Response_Theory_Models_for_Polytomous_Items">Multidimensional Componential Item Response Theory Models for Polytomous Items</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="232734683" href="https://independent.academia.edu/PaulDeBoeck">Paul De Boeck</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Applied Psychological Measurement, 2001</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Multidimensional Componential Item Response Theory Models for Polytomous Items","attachmentId":102523190,"attachmentType":"pdf","work_url":"https://www.academia.edu/102194585/Multidimensional_Componential_Item_Response_Theory_Models_for_Polytomous_Items","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/102194585/Multidimensional_Componential_Item_Response_Theory_Models_for_Polytomous_Items"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="2" data-entity-id="112705942" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/112705942/Applications_of_Item_Response_Theory_Models_to_Assess_Item_Properties_and_Students_Abilities_in_Dichotomous_Responses_Items">Applications of Item Response Theory Models to Assess Item Properties and Students’ Abilities in Dichotomous Responses Items</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="62211068" href="https://independent.academia.edu/lawalbayo">bayo lawal</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Open Journal of Educational Development, 2022</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Applications of Item Response Theory Models to Assess Item Properties and Students’ Abilities in Dichotomous Responses Items","attachmentId":109852725,"attachmentType":"pdf","work_url":"https://www.academia.edu/112705942/Applications_of_Item_Response_Theory_Models_to_Assess_Item_Properties_and_Students_Abilities_in_Dichotomous_Responses_Items","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/112705942/Applications_of_Item_Response_Theory_Models_to_Assess_Item_Properties_and_Students_Abilities_in_Dichotomous_Responses_Items"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="3" data-entity-id="11520700" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/11520700/Item_Response_Theory_approaches_to_test_scoring_and_evaluating_the_score_accuracy">Item Response Theory approaches to test scoring and evaluating the score accuracy</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="519455" href="https://kent.academia.edu/AnnaBrown">Anna Brown</a></div><p class="ds-related-work--metadata ds2-5-body-xs">In Irwing, P., Booth, T. & Hughes, D. (Eds.), The Wiley Handbook of Psychometric Testing., 2015</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Item Response Theory approaches to test scoring and evaluating the score accuracy","attachmentId":37030291,"attachmentType":"pdf","work_url":"https://www.academia.edu/11520700/Item_Response_Theory_approaches_to_test_scoring_and_evaluating_the_score_accuracy","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/11520700/Item_Response_Theory_approaches_to_test_scoring_and_evaluating_the_score_accuracy"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="4" data-entity-id="30496631" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/30496631/Fundamentals_of_Item_Response_Theory">Fundamentals of Item Response Theory</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="58128520" href="https://school-site-kiev.academia.edu/%D0%A2%D0%B0%D1%82%D1%8C%D1%8F%D0%BD%D0%B0%D0%A8%D0%B5%D0%BB%D1%8F%D0%B3">Татьяна Шеляг</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fundamentals of Item Response Theory","attachmentId":50936216,"attachmentType":"pdf","work_url":"https://www.academia.edu/30496631/Fundamentals_of_Item_Response_Theory","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/30496631/Fundamentals_of_Item_Response_Theory"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="5" data-entity-id="112424190" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/112424190/A_Note_on_the_D_Scoring_Method_Adapted_for_Polytomous_Test_Items">A Note on the D-Scoring Method Adapted for Polytomous Test Items</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="99904565" href="https://independent.academia.edu/DimiterDimitrov1">Dimiter Dimitrov</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Educational and Psychological Measurement, 2018</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A Note on the D-Scoring Method Adapted for Polytomous Test Items","attachmentId":109659090,"attachmentType":"pdf","work_url":"https://www.academia.edu/112424190/A_Note_on_the_D_Scoring_Method_Adapted_for_Polytomous_Test_Items","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/112424190/A_Note_on_the_D_Scoring_Method_Adapted_for_Polytomous_Test_Items"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="6" data-entity-id="32164824" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/32164824/Handbook_of_Polytomous_Item_Response_Theory_Models_edited_by_Michael_L_Nering_and_Remo_Ostini">Handbook of Polytomous Item Response Theory Models edited by Michael L. Nering and Remo Ostini</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="62367457" href="https://independent.academia.edu/JasonSchweid">Jason Schweid</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Educational Measurement, 2011</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Handbook of Polytomous Item Response Theory Models edited by Michael L. 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href="https://independent.academia.edu/SwaminathanHariharan">Hariharan Swaminathan</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Language Testing, 1985</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Item response theory","attachmentId":91880404,"attachmentType":"pdf","work_url":"https://www.academia.edu/87754337/Item_response_theory","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/87754337/Item_response_theory"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" 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