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{"work":{"id":1296876,"created_at":"2012-01-26T20:09:43.355-08:00","from_world_paper_id":26277641,"updated_at":"2024-11-12T06:23:48.703-08:00","_data":{"publisher":"Springer","grobid_abstract":"In a broad class of item response theory (IRT) models for dichotomous items the unweighted total score has monotone likelihood ratio (MLR) in the latent trait 0. In this study, it is shown that for polytotnous items MLR holds for the partial credit model and a trivial generalization of this model. MLR does not necessarily hold if the slopes of the item step response functions vary over items, item steps, or both. MLR holds neither for Samejima's graded response model, nor for nonparametric versions of these three polytomous models. These results are surprising in the context of Grayson's and Huynh's results on MLR for nonparametric dichotomous IRT models, and suggest that establishing stochastic ordering properties for nonparametric polytomous IRT models will be much harder.","publication_date":"1996,1,1","publication_name":"Psychometrika","grobid_abstract_attachment_id":"7977978"},"document_type":"paper","pre_hit_view_count_baseline":0,"quality":"high","language":"en","title":"Polytomous IRT models and monotone likelihood ratio of the total score","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [1156579]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon'; 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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">In a broad class of item response theory (IRT) models for dichotomous items the unweighted total score has monotone likelihood ratio (MLR) in the latent trait 0. In this study, it is shown that for polytotnous items MLR holds for the partial credit model and a trivial generalization of this model. MLR does not necessarily hold if the slopes of the item step response functions vary over items, item steps, or both. MLR holds neither for Samejima's graded response model, nor for nonparametric versions of these three polytomous models. These results are surprising in the context of Grayson's and Huynh's results on MLR for nonparametric dichotomous IRT models, and suggest that establishing stochastic ordering properties for nonparametric polytomous IRT models will be much harder.</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":7977978,"attachmentType":"pdf","workUrl":"https://www.academia.edu/1296876/Polytomous_IRT_models_and_monotone_likelihood_ratio_of_the_total_score"}">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":7977978,"attachmentType":"pdf","workUrl":"https://www.academia.edu/1296876/Polytomous_IRT_models_and_monotone_likelihood_ratio_of_the_total_score"}"><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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Monotonicity allows items to be interpreted as measuring a trait, and it allows for a general theory of nonparametric inference for traits. This theory is based on monotone likelihood ratio and stochastic ordering properties. Thus, confirming the monotonicity assumption is essential to applications of nonparametric item response models. The results of two methods of evaluating monotonicity are presented: regressing individual item scores on the total test score and on the "rest" score, which is obtained by omitting the selected item from the total test score. It was found that the item-total regressions of some familiar dichotomous item response models with monotone IRFs exhibited nonmonotonicities that persist as the test length increased. However, item-rest regressions never exhibited nonmonotonicities under the nonparametric monotone unidimensional item response model. The implications of these results for exploratory analysis of dichotomous item response data and the application of these results to polytomous item response data are discussed. Index terms: elementary symmetric functions, essential unidimensionality, latent monotonicity, manifest monotonicity, monotone homogeneity, nonparametric item response models, strict unidimensionality.</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":"Latent and manifest monotonicity in item response models","attachmentId":7977981,"attachmentType":"pdf","work_url":"https://www.academia.edu/1296879/Latent_and_manifest_monotonicity_in_item_response_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/1296879/Latent_and_manifest_monotonicity_in_item_response_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="1" data-entity-id="1296867" 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/1296867/Stochastic_ordering_using_the_latent_trait_and_the_sum_score_in_polytomous_IRT_models">Stochastic ordering using the latent trait and the sum score in polytomous IRT 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="1156579" href="https://cmu.academia.edu/BrianJunker">Brian Junker</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Psychometrika, 1997</p><p class="ds-related-work--abstract ds2-5-body-sm">In a restricted class of item response theory (IRT) models for polytomous items the unweighted total score has monotone likelihood ratio (MLR) in the latent trait 0. MLR implies two stochastic ordering (SO) properties, denoted SOM and SOL, which are both weaker than MLR, but very useful for measurement with IRT models. Therefore, these SO properties are investigated for a broader class of IRT models for which the MLR property does not hold.</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":"Stochastic ordering using the latent trait and the sum score in polytomous IRT models","attachmentId":7977975,"attachmentType":"pdf","work_url":"https://www.academia.edu/1296867/Stochastic_ordering_using_the_latent_trait_and_the_sum_score_in_polytomous_IRT_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/1296867/Stochastic_ordering_using_the_latent_trait_and_the_sum_score_in_polytomous_IRT_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="2" data-entity-id="126937577" 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/126937577/A_Taxonomy_of_Polytomous_Item_Response_Models">A Taxonomy of Polytomous Item Response 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="31870355" href="https://independent.academia.edu/GerhardTutz">Gerhard Tutz</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv (Cornell University), 2020</p><p class="ds-related-work--abstract ds2-5-body-sm">A common framework is provided that comprises classical ordinal item response models as the cumulative, sequential and adjacent categories models as well as nominal response models and item response tree models. The taxonomy is based on the ways binary models can be seen as building blocks of the various models. In particular one can distinguish between conditional and unconditional model components. Conditional models are by far the larger class of models containing the adjacent categories model and the whole class of hierarchically structured models. The latter is introduced as a class of models that comprises binary trees and hierarchically structured models that use ordinal models conditionally. The study of the binary models contained in latent trait models clarifies the relation between models and the interpretation of item parameters. It is also used to distinguish between ordinal and nominal models by giving a conceptualization of ordinal models. The taxonomy differs from previous taxonomies by focusing on the structured use of dichotomizations instead of the role of parameterizations.</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 Taxonomy of Polytomous Item Response Models","attachmentId":120743939,"attachmentType":"pdf","work_url":"https://www.academia.edu/126937577/A_Taxonomy_of_Polytomous_Item_Response_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/126937577/A_Taxonomy_of_Polytomous_Item_Response_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="1296868" 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/1296868/Conditional_association_essential_independence_and_monotone_unidimensional_item_response_models">Conditional association, essential independence and monotone unidimensional item response 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="1156579" href="https://cmu.academia.edu/BrianJunker">Brian Junker</a></div><p class="ds-related-work--metadata ds2-5-body-xs">The Annals of Statistics, 1993</p><p class="ds-related-work--abstract ds2-5-body-sm">We consider two recent approaches to characterizing the manifest probabilities of a strictly unidimensional latent variable representation (one satisfying local independence and response curve monotonicity with respect to a unidimensional latent variable) for binary response variables, such as those arising from the dichotomous scoring of items on standardized achievement and aptitude tests. show that conditional association is a necessary condition for strict unidimensionality; and Stout (1990) treats the class of essentially unidimensional models, in which the latent variable may be consistently estimated as the length of the response sequence grows using the proportion of positive responses. Of particular concern are strictly unidimensional representations that are minimally useful in the sense that (1) the latent variable can be consistently estimated from the responses; (2) the regression of proportion of positive responses on the latent variable is monotone; and (3) the latent variable is not constant in the population. We introduce two new conditions, a negative association condition and a natural monotonicity condition on the empirical response curves, that help link strict unidimensionality with the conditional association and essential unidimensionality approaches. These conditions are illustrated with a partial characterization of useful, strictly unidimensional representations.</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":"Conditional association, essential independence and monotone unidimensional item response models","attachmentId":7977971,"attachmentType":"eps","work_url":"https://www.academia.edu/1296868/Conditional_association_essential_independence_and_monotone_unidimensional_item_response_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/1296868/Conditional_association_essential_independence_and_monotone_unidimensional_item_response_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="4" data-entity-id="57425974" 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/57425974/A_Class_of_Multidimensional_Latent_Class_IRT_Models_for_Ordinal_Polytomous_Item_Responses">A Class of Multidimensional Latent Class IRT Models for Ordinal Polytomous Item Responses</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="111983564" href="https://unifi.academia.edu/SILVIABACCI">SILVIA BACCI</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Communications in Statistics - Theory and Methods, 2014</p><p class="ds-related-work--abstract ds2-5-body-sm">We propose a class of Item Response Theory models for items with ordinal polytomous responses, which extends an existing class of multidimensional models for dichotomously-scored items measuring more than one latent trait. In the proposed approach, the random vector used to represent the latent traits is assumed to have a discrete distribution with support points corresponding to different latent classes in the population. We also allow for different parameterizations for the conditional distribution of the response variables given the latent traits-such as those adopted in the Graded Response model, in the Partial Credit model, and in the Rating Scale model-depending on both the type of link function and the constraints imposed on the item parameters. For the proposed models we outline how to perform maximum likelihood estimation via the Expectation-Maximization algorithm. Moreover, we suggest a strategy for model selection which is based on a series of steps consisting of selecting specific features, such as the number of latent dimensions, the number of latent classes, and the specific parametrization. In order to illustrate the proposed approach, we analyze data deriving from a study on anxiety and depression as perceived by oncological patients.</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 Class of Multidimensional Latent Class IRT Models for Ordinal Polytomous Item Responses","attachmentId":72336907,"attachmentType":"pdf","work_url":"https://www.academia.edu/57425974/A_Class_of_Multidimensional_Latent_Class_IRT_Models_for_Ordinal_Polytomous_Item_Responses","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/57425974/A_Class_of_Multidimensional_Latent_Class_IRT_Models_for_Ordinal_Polytomous_Item_Responses"><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="68917093" 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/68917093/The_Fisher_Information_Function_for_Ideal_Point_Item_Response_Models_for_Pick_Any_n_Data">The Fisher Information Function for Ideal Point Item Response Models for Pick Any/n Data</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="36120860" href="https://independent.academia.edu/YoshioTakane">Yoshio Takane</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2006</p><p class="ds-related-work--abstract ds2-5-body-sm">In the last two decades, researchers have developed a number of item response models for the analysis of preference data in which the regression between latent trait θ and item responses, P (θ), is single-peaked. As opposed to the monotonic functions such as the logistic function common to IRT for dominance data, these models are probabilistic analogues of Coombs' deterministic unfolding models. One potential barrier to the wider acceptance of such models is the curious fact that most ideal point item response models have bimodal item information functions. Unfortunately, mathematically rigorous explanations for this unusual behavior have not been provided by authors. More broadly, properties of the information function of ideal point IRT models are unknown. This article proves several theorems about the IIFs of ideal point models, in particular, showing that the IIF can be bimodal, unimodal, or singular depending on qualitative characteristics of P (θ), in particular the maximum value of P (θ) and P (θ). The importance of these results for test construction is also discussed and illustrated through a simple empirical example. 1.1 Ideal Point vs. Monotonic Response Patterns To understand why these data are often better characterized by a single-peaked response, consider the following statements, which are variants of Thurstone's classic capital punishment items built according to the principles outlined in Michell (1994):</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 Fisher Information Function for Ideal Point Item Response Models for Pick Any/n Data","attachmentId":79218752,"attachmentType":"pdf","work_url":"https://www.academia.edu/68917093/The_Fisher_Information_Function_for_Ideal_Point_Item_Response_Models_for_Pick_Any_n_Data","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/68917093/The_Fisher_Information_Function_for_Ideal_Point_Item_Response_Models_for_Pick_Any_n_Data"><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="1296877" 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/1296877/Nonparametric_item_response_theory_in_action_An_overview_of_the_special_issue">Nonparametric item response theory in action: An overview of the special issue</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="1156579" href="https://cmu.academia.edu/BrianJunker">Brian Junker</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Applied Psychological Measurement, 2001</p><p class="ds-related-work--abstract ds2-5-body-sm">Although most item response theory (IRT) applications and related methodologies involve model fitting within a single parametric IRT (PIRT) family [e.g., the Rasch (1960) model or the threeparameter logistic model ( 3PLM; ], nonparametric IRT (NIRT) research has been growing in recent years. Three broad motivations for the development and continued interest in NIRT can be identified: 1. To identify a commonality among PIRT and IRT-like models, model features [e.g., local independence (LI), monotonicity of item response functions (IRFs), unidimensionality of the latent variable] should be characterized, and it should be discovered what happens when models satisfy only weakened versions of these features. Characterizing successful and unsuccessful inferences under these broad model features can be attempted in order to understand how IRT models aggregate information from data. All this can be done with NIRT. 2. Any model applied to data is likely to be incorrect. When a family of PIRT models has been shown (or is suspected) to fit poorly, a more flexible family of NIRT models often is desired. These NIRT models have been used to: (1) assess violations of LI due to nuisance traits (e.g., latent variable multidimensionality) or the testing context influencing test performance (e.g., speededness and question wording), (2) clarify questions about the sources and effects of differential item functioning, (3) provide a flexible context in which to develop methodology for establishing the most appropriate number of latent dimensions underlying a test, and (4) serve as alternatives for PIRT models in tests of fit. 3. In psychological and sociological research, when it is necessary to develop a new questionnaire or measurement instrument, there often are fewer examinees and items than are desired for fitting PIRT models in large-scale educational testing. NIRT provides tools that are easy to use in small samples. It can identify items that scale together well (follow a particular set of NIRT assumptions). NIRT also identifies several subscales with simple structure among the scales, if the items do not form a single unidimensional scale.</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":"Nonparametric item response theory in action: An overview of the special issue","attachmentId":7977980,"attachmentType":"pdf","work_url":"https://www.academia.edu/1296877/Nonparametric_item_response_theory_in_action_An_overview_of_the_special_issue","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/1296877/Nonparametric_item_response_theory_in_action_An_overview_of_the_special_issue"><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="20249286" 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/20249286/A_Nonparametric_Item_Response_Theory">A Nonparametric 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="40386512" href="https://huji.academia.edu/SYitzhaki">Shlomo Yitzhaki</a></div><p class="ds-related-work--metadata ds2-5-body-xs">SSRN Electronic Journal, 2000</p><p class="ds-related-work--abstract ds2-5-body-sm">The Item Characteristic Curve describes the relationship between the probability of correctly answering a question and ability. Ability is a latent variable. Therefore one has to impose distributional assumptions on ability in order to estimate the relationship. In this paper we overcome the need to impose an assumption on the distribution of abilities by using the properties of concentration curves and the Gini Mean Difference. As a result we are able to investigate whether the probability of correctly answering a question is monotonically related to a specific ability. The paper demonstrates the properties of the technique.</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 Nonparametric Item Response Theory","attachmentId":41233763,"attachmentType":"pdf","work_url":"https://www.academia.edu/20249286/A_Nonparametric_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/20249286/A_Nonparametric_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="8" data-entity-id="91190707" 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/91190707/A_new_family_of_asymmetric_models_for_Item_Response_Theory_a_Skew_Normal_IRT_Family">A new family of asymmetric models for Item Response Theory: a Skew-Normal IRT Family</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="246290831" href="https://independent.academia.edu/M%C3%A1rciaBranco1">Márcia Branco</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2004</p><p class="ds-related-work--abstract ds2-5-body-sm">Normal assumptions for the latent variable and symmetric item characteristics curves have been used in the last 50 years in many psychometric methods for item-response theory (IRT) models. This paper introduces a new family of asymmetric models for item response theory, namely the skew-normal item-response theory (SN-IRT) model. This family extends the ogive normal (symmetric probit-normal) model by considering: a) an accumulated skew-normal distribution for the item characteristic curve and b) skew-normal distributions are assumed as priors for latent variables for modeling individuals' ability. Four models compose the SN-IRT family: skewprobit-skew-normal, skew-probit-normal, probit-skew-normal and probit-normal models as a particular case. Hence, the SN-IRT is a more flexible model for fitting data sets with dichotomous responses. Bayesian inference methodology using two data augmentation approaches for implementing the MCMC methodology is developed. Model selection between symmetric and asymmetric models is considered by using the deviance information criterion (DIC) and the expected AIC and expected BIC and by using latent residuals. The proposed penalization (asymmetry) parameter is interpreted in the context of a particular data set related to a mathematical test. Suggestions for use the in news applications of skew probit propose in the paper are discussed.</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 new family of asymmetric models for Item Response Theory: a Skew-Normal IRT Family","attachmentId":94547833,"attachmentType":"pdf","work_url":"https://www.academia.edu/91190707/A_new_family_of_asymmetric_models_for_Item_Response_Theory_a_Skew_Normal_IRT_Family","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/91190707/A_new_family_of_asymmetric_models_for_Item_Response_Theory_a_Skew_Normal_IRT_Family"><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="102194607" 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/102194607/The_Heteroscedastic_Graded_Response_Model_with_a_Skewed_Latent_Trait_Testing_Statistical_and_Substantive_Hypotheses_Related_to_Skewed_Item_Category_Functions">The Heteroscedastic Graded Response Model with a Skewed Latent Trait: Testing Statistical and Substantive Hypotheses Related to Skewed Item Category Functions</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="232734683" href="https://independent.academia.edu/PaulDeBoeck">Paul De Boeck</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Psychometrika, 2012</p><p class="ds-related-work--abstract ds2-5-body-sm">The Graded Response Model (GRM; Samejima, Estimation of ability using a response pattern of graded scores, Psychometric Monograph No. 17, Richmond, VA: The Psychometric Society, 1969) can be derived by assuming a linear regression of a continuous variable, Z, on the trait, θ, to underlie the ordinal item scores (Takane & de Leeuw in Psychometrika, 52:393-408, 1987). Traditionally, a normal distribution is specified for Z implying homoscedastic error variances and a normally distributed θ. In this paper, we present the Heteroscedastic GRM with Skewed Latent Trait, which extends the traditional GRM by incorporation of heteroscedastic error variances and a skew-normal latent trait. An appealing property of the extended GRM is that it includes the traditional GRM as a special case. This enables specific tests on the normality assumption of Z. We show how violations of normality in Z can lead to asymmetrical category response functions. The ability to test this normality assumption is beneficial from both a statistical and substantive perspective. In a simulation study, we show the viability of the model and investigate the specificity of the effects. We apply the model to a dataset on affect and a dataset on alexithymia.</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 Heteroscedastic Graded Response Model with a Skewed Latent Trait: Testing Statistical and Substantive Hypotheses Related to Skewed Item Category Functions","attachmentId":102523215,"attachmentType":"pdf","work_url":"https://www.academia.edu/102194607/The_Heteroscedastic_Graded_Response_Model_with_a_Skewed_Latent_Trait_Testing_Statistical_and_Substantive_Hypotheses_Related_to_Skewed_Item_Category_Functions","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/102194607/The_Heteroscedastic_Graded_Response_Model_with_a_Skewed_Latent_Trait_Testing_Statistical_and_Substantive_Hypotheses_Related_to_Skewed_Item_Category_Functions"><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":7977978,"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":7977978,"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_7977978" 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="16260011" 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/16260011/MultiLCIRT_An_R_package_for_multidimensional_latent_class_item_response_models">MultiLCIRT: An R package for multidimensional latent class item response models</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="35352968" href="https://vegajournal.academia.edu/SilviaBacci">Silvia Bacci</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Computational Statistics and Data Analysis, 2014</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":"MultiLCIRT: An R package for multidimensional latent class item response models","attachmentId":42601783,"attachmentType":"pdf","work_url":"https://www.academia.edu/16260011/MultiLCIRT_An_R_package_for_multidimensional_latent_class_item_response_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-related-work-grid-card-view-pdf" href="https://www.academia.edu/16260011/MultiLCIRT_An_R_package_for_multidimensional_latent_class_item_response_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-related-work-sidebar-card" data-collection-position="1" 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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