{"title":"Item-Fit Statistic Based on Posterior Probabilities of Membership in Ability Groups.","authors":"Bartosz Kondratek","doi":"10.1177/01466216221108061","DOIUrl":null,"url":null,"abstract":"<p><p>A novel approach to item-fit analysis based on an asymptotic test is proposed. The new test statistic, <math> <mrow><msubsup><mi>χ</mi> <mi>w</mi> <mn>2</mn></msubsup> </mrow> </math> , compares pseudo-observed and expected item mean scores over a set of ability bins. The item mean scores are computed as weighted means with weights based on test-takers' <i>a posteriori</i> density of ability within the bin. This article explores the properties of <math> <mrow><msubsup><mi>χ</mi> <mi>w</mi> <mn>2</mn></msubsup> </mrow> </math> in case of dichotomously scored items for unidimensional IRT models. Monte Carlo experiments were conducted to analyze the performance of <math> <mrow><msubsup><mi>χ</mi> <mi>w</mi> <mn>2</mn></msubsup> </mrow> </math> . Type I error of <math> <mrow><msubsup><mi>χ</mi> <mi>w</mi> <mn>2</mn></msubsup> <mo> </mo></mrow> </math> was acceptably close to the nominal level and it had greater power than Orlando and Thissen's <math><mrow><mi>S</mi> <mo>-</mo> <msup><mi>x</mi> <mn>2</mn></msup> </mrow> </math> . Under some conditions, power of <math> <mrow><msubsup><mi>χ</mi> <mi>w</mi> <mn>2</mn></msubsup> </mrow> </math> also exceeded the one reported for the computationally more demanding Stone's <math> <mrow><msup><mi>χ</mi> <mrow><mn>2</mn> <mo>∗</mo></mrow> </msup> </mrow> </math> .</p>","PeriodicalId":48300,"journal":{"name":"Applied Psychological Measurement","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9382089/pdf/10.1177_01466216221108061.pdf","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Psychological Measurement","FirstCategoryId":"102","ListUrlMain":"https://doi.org/10.1177/01466216221108061","RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PSYCHOLOGY, MATHEMATICAL","Score":null,"Total":0}
引用次数: 3
Abstract
A novel approach to item-fit analysis based on an asymptotic test is proposed. The new test statistic, , compares pseudo-observed and expected item mean scores over a set of ability bins. The item mean scores are computed as weighted means with weights based on test-takers' a posteriori density of ability within the bin. This article explores the properties of in case of dichotomously scored items for unidimensional IRT models. Monte Carlo experiments were conducted to analyze the performance of . Type I error of was acceptably close to the nominal level and it had greater power than Orlando and Thissen's . Under some conditions, power of also exceeded the one reported for the computationally more demanding Stone's .
提出了一种基于渐近检验的项目拟合分析新方法。新的检验统计量χ w 2比较了一组能力箱上的伪观察和预期项目平均得分。项目平均得分以加权平均数计算,权重基于考生在bin中的后验能力密度。本文探讨了单维IRT模型中二分类得分项目的χ w 2的性质。通过蒙特卡罗实验对χ w2的性能进行了分析。χ w 2的I型误差可接受地接近名义水平,其功率大于Orlando和Thissen的S - x2。在某些条件下,χ w 2的幂也超过了计算要求更高的Stone的χ 2 *所报告的幂。
期刊介绍:
Applied Psychological Measurement publishes empirical research on the application of techniques of psychological measurement to substantive problems in all areas of psychology and related disciplines.