{"title":"Efficient Corrections for Standardized Person-Fit Statistics.","authors":"Kylie Gorney, Sandip Sinharay, Carol Eckerly","doi":"10.1007/s11336-024-09960-x","DOIUrl":null,"url":null,"abstract":"<p><p>Many popular person-fit statistics belong to the class of standardized person-fit statistics, T, and are assumed to have a standard normal null distribution. However, in practice, this assumption is incorrect since T is computed using (a) an estimated ability parameter and (b) a finite number of items. Snijders (Psychometrika 66(3):331-342, 2001) developed mean and variance corrections for T to account for the use of an estimated ability parameter. Bedrick (Psychometrika 62(2):191-199, 1997) and Molenaar and Hoijtink (Psychometrika 55(1):75-106, 1990) developed skewness corrections for T to account for the use of a finite number of items. In this paper, we combine these two lines of research and propose three new corrections for T that simultaneously account for the use of an estimated ability parameter and the use of a finite number of items. The new corrections are efficient in that they only require the analysis of the original data set and do not require the simulation or analysis of any additional data sets. We conducted a detailed simulation study and found that the new corrections are able to control the Type I error rate while also maintaining reasonable levels of power. A real data example is also included.</p>","PeriodicalId":54534,"journal":{"name":"Psychometrika","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Psychometrika","FirstCategoryId":"102","ListUrlMain":"https://doi.org/10.1007/s11336-024-09960-x","RegionNum":2,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/4/1 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
Many popular person-fit statistics belong to the class of standardized person-fit statistics, T, and are assumed to have a standard normal null distribution. However, in practice, this assumption is incorrect since T is computed using (a) an estimated ability parameter and (b) a finite number of items. Snijders (Psychometrika 66(3):331-342, 2001) developed mean and variance corrections for T to account for the use of an estimated ability parameter. Bedrick (Psychometrika 62(2):191-199, 1997) and Molenaar and Hoijtink (Psychometrika 55(1):75-106, 1990) developed skewness corrections for T to account for the use of a finite number of items. In this paper, we combine these two lines of research and propose three new corrections for T that simultaneously account for the use of an estimated ability parameter and the use of a finite number of items. The new corrections are efficient in that they only require the analysis of the original data set and do not require the simulation or analysis of any additional data sets. We conducted a detailed simulation study and found that the new corrections are able to control the Type I error rate while also maintaining reasonable levels of power. A real data example is also included.
许多常用的人称拟合统计量都属于标准化人称拟合统计量 T,并假定其具有标准正态空分布。然而,在实践中,这一假设是不正确的,因为 T 是使用(a)估计的能力参数和(b)有限数量的项目计算得出的。Snijders(《心理测量学》第 66(3)期:331-342,2001 年)对 T 进行了均值和方差修正,以考虑估计能力参数的使用。Bedrick(Psychometrika 62(2):191-199,1997)和 Molenaar 与 Hoijtink(Psychometrika 55(1):75-106,1990)对 T 进行了偏度修正,以考虑有限项目数的使用。在本文中,我们将这两项研究结合起来,提出了三种新的 T 修正方法,同时考虑了估计能力参数的使用和有限项目数的使用。新的修正方法非常有效,因为它们只需要分析原始数据集,而不需要模拟或分析任何额外的数据集。我们进行了详细的模拟研究,发现新的修正方法既能控制 I 类错误率,又能保持合理的功率水平。我们还提供了一个真实数据示例。
期刊介绍:
The journal Psychometrika is devoted to the advancement of theory and methodology for behavioral data in psychology, education and the social and behavioral sciences generally. Its coverage is offered in two sections: Theory and Methods (T& M), and Application Reviews and Case Studies (ARCS). T&M articles present original research and reviews on the development of quantitative models, statistical methods, and mathematical techniques for evaluating data from psychology, the social and behavioral sciences and related fields. Application Reviews can be integrative, drawing together disparate methodologies for applications, or comparative and evaluative, discussing advantages and disadvantages of one or more methodologies in applications. Case Studies highlight methodology that deepens understanding of substantive phenomena through more informative data analysis, or more elegant data description.