[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-592260-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-592260-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","a-new-approach-to-test-score-equating-using-item-response-theory-with-fixed-c-parameters","A New Approach to Test Score Equating Using Item Response Theory with Fixed C-Parameters","","A linear transformation can link item response theory (IRT) parameter estimates across calibration runs without changing response probabilities, enabling score equating between tests. This study evaluates a new procedure that fixes C-parameters for anchor items when applying IRT equating. Because C-parameters are unaffected by linear transformations, the method can improve practicality and avoid difficulties in estimating accurate anchor C-parameters. Findings support recommending fixed C-parameters for anchor-item equating using the Stocking and Lord framework.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/a-new-approach-to-test-score-equating-using-item-response-theory-with-fixed-c-parameters/592260/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/a-new-approach-to-test-score-equating-using-item-response-theory-with-fixed-c-parameters/592260.png","ImageObject",300,407,{"name":42,"@type":43},"Grenda","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-27","2026-10-15",true,{"@type":52,"interactionType":53,"userInteractionCount":33},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"Why can a linear equation convert IRT parameter estimates onto another score scale?","Question",{"text":62,"@type":63},"Under the IRT model, parameter estimates from different calibration runs are linearly related. A linear transformation expresses the transformed parameters on the old score scale without changing the probability of a correct response.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"What is the purpose of fixing C-parameters for anchor items in IRT equating?",{"text":67,"@type":63},"The study proposes fixing C-parameters for anchor items so that the equating process avoids challenges in obtaining accurate C-parameters. This is justified because C-parameters are not affected by linear transformations.",{"name":69,"@type":60,"acceptedAnswer":70},"Which equating framework does the paper focus on when proposing the fixed-C approach?",{"text":71,"@type":63},"The paper focuses on a new approach to test score equating with the Stocking and Lord (SL) characteristic curve method, while noting the rationale can extend to other equating methods.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},592260,1792211485,{"code":4,"msg":81,"data":82},"success",[83,87,91,95,100,105,110,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":92,"show_sort_weight":93,"slug":94},"Exam",70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":112,"slug":113},8,30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":111,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":33,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":139,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":145,"preview_page_count":4},7971474921005,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Asia Pacific Education Review Copyright 2008 by Education Research Institute  \n2008, Vol. 9, No.3, 248-261.  \nA New Approach to Test Score Equating Using Item Response  \nTheory with Fixed C-Parameters  \nGuemin Lee Anne R. Fitzpatrick  \nYonsei University Educational Testing Services  \nKorea USA  \nBecause parameter estimates from different calibration runs under the IRT model are linearly related, a linear equation can convert IRT parameter estimates onto another scale metric without changing the probability of a correct response (Kolen & Brennan, 1995, 2004) . This study was designed to explore a new approach to finding alinear equation by fixing C-parameters for anchor items in IRT equating. A rationale for fixing C-parameters for anchor items in IRT equating can be established from the fact that the C-parameters are not affected by any linear transformation. This new approach can avoid the difficulty in getting accurate C-parameters for anchor items embedded in the application of the IRT model. Based upon our findings in this study, we would recommend using the new approach to fix C-parameters for anchor items in IRT equating.  \nKey words: Equating, Item Response Theory, Stocking and Lord Method  \nIntroduction  \nWhen a new test is administered as part of a high stakes testing program, the test must usually be linked to a previously established score scale. To do this, it is common to administer and calibrate a set of anchor items with the new test. The anchor items have parameter estimates on the previously established score scale. The new parameter estimates for these anchor items are used to link the new test to the old scale to establish score equivalents between old  \nGuemin Lee, Department of Education, Yonsei University, Korea; Anne R. Fitzpatrick, Educational Testing Services, USA.  \nThis work was supported by a Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) (KRF-2005-003-B00229) .  \nCorrespondence concerning this article should be addressed to Guemin Lee, Department of Education, Yonsei University, 134 Shinchon-Dong, Seodaemoon-Ku, Seoul, Korea. E-mail: guemin @[yonsei.ac.kr](yonsei.ac.kr)  \nand new forms. This process is usually called IRT equating.  \nWhen the IRT model holds, the parameter estimates from different calibration runs are linearly related. A linear equation can convert IRT parameter estimates onto anther scale metric without changing the probability of a correct response in IRT models. The equating constants, m1 (slope) and m2 (intercept), are used to transform the new parameter estimates so that they are expressed on the old score scale using the following equations,  \n⎧B* = m1B + m2  \n⎨⎪A* = A / m1  \n⎪⎩C* = C (1)  \nwhere A, B, and C are the item parameters in the 3PL model, and the * mark represents transformed parameters. Because C-parameters are on the probability metric, those remain the same before and after transformation.  \nThere are several ways of determining equating  \nconstants, m1 and m2 . Probably the most straightforward way would be to substitute the means and standard deviations of the item parameter estimates in equation 1. Marco (1977) described the mean/sigma method, in which the means and standard deviations of the b-parameter estimates from the common items are used to find m1 and m2 . Loyd and Hoover (1980) developed the mean/mean method. In this method, the mean of the a-parameter estimates is used to find the m1 constant and the mean of the b-parameter estimates is used to find the m2 constant. However, the mean/sigma and mean/mean methods have been criticized in that the equating constants could be overly influenced by the differences of item parameter estimates (Kolen & Brenna, 1994) .  \nCharacteristic curve methods were proposed to consider all of the item parameter estimates simultaneously in finding m1 and m2 equating constants. Haebara (1980) developed a function to express the difference between item characteristic ","cbCaimHMf7ZTTYx9","https://ap.wps.com/l/cbCaimHMf7ZTTYx9","pdf",997633,14,"English","# Introduction\n## IRT equating and linear transformations\n## Equating constants m1 and m2\n## Existing approaches and characteristic-curve methods\n## Stocking and Lord method and new fixed-C approach","[{\"question\":\"Why can a linear equation convert IRT parameter estimates onto another score scale?\",\"answer\":\"Under the IRT model, parameter estimates from different calibration runs are linearly related. A linear transformation expresses the transformed parameters on the old score scale without changing the probability of a correct response.\"},{\"question\":\"What is the purpose of fixing C-parameters for anchor items in IRT equating?\",\"answer\":\"The study proposes fixing C-parameters for anchor items so that the equating process avoids challenges in obtaining accurate C-parameters. This is justified because C-parameters are not affected by linear transformations.\"},{\"question\":\"Which equating framework does the paper focus on when proposing the fixed-C approach?\",\"answer\":\"The paper focuses on a new approach to test score equating with the Stocking and Lord (SL) characteristic curve method, while noting the rationale can extend to other equating methods.\"}]","A New Approach to Test Score Equating Using Item Response Theory with Fixed C-Parameters | PDF",1792074183,35]