一种新的等值准则及其适用范围的探讨

受假设检验方法的启发,该文引出了一种基于项目反应理论的新等值方法——平方根等值准则。它具有一些特点：定义式中答对、答错概率同时出现而不能互相替代;极易从0—1评分模式的版本转换到多级评分版本;它可以看成是Haebara等值准则的加权形式。以等值系数估计值的误差大小为衡量标准,以Wilcoxon符号秩检验为依据,大量的Monte Carlo模拟结果显示了一种有趣的现象,即等值方法的运用范围既与项目参数估计精度有关,又与等值系数A的范围有关,但与另一个等值系数B的范围无关。当项目参数估计精度较高或中等而A取值在0.9～1.3之间,新方法往往比Stocking_Lord方法和Haebara方法的估计误差小且有显著性差异,当项目参数估计精度较低时,而A从1.0～2.0时新方法都有优越性。     

基于CTT的锚测验非等组设计中四种等值方法的比较研究

采用锚测验非等组设计的数据收集方案,对4种基于经典测量理论的等值方法进行了比较研究。研究数据取自TIMSS1999数据库,兼用等值标准误和交叉验证方法作为各等值方法比较的检验标准,利用CIPE程序对实验数据进行分析。研究结果表明,针对本研究所设置的等值情境,线性等值优于等百分位等值,其中Tucker线性方法比Levine观察分数线性方法更好一些,Braun-Holland线性方法不宜采用,频数估计等百分位方法等值误差较大,亦不足取。     

不同定义平行测验等值的群体不变性

群体不变性是等值的一个重要假设,即对不同的考生子群体等值函数一致。本研究对不同平行测验定义下线性等值的群体不变性进行了理论分析和模拟研究,模拟研究REMSD指标通过六种不同加权方式计算。结果显示,严格平行测验在信度较低时REMSD指标更大;子群体均值差异和信度差异对REMSD的影响存在明显的交互作用;REMSD指标在期望权重等权下的最大,在分数权重采用子群体比例加权最小。最后对结果进行了讨论,对REMSD权重使用及进一步研究给出了建议。     

Analytic smoothing for equipercentile equating under the common item nonequivalent populations design

A cubic spline method for smoothing equipercentile equating relationships under the common item nonequivalent populations design is described. Statistical techniques based on bootstrap estimation are presented that are designed to aid in choosing an equating method/degree of smoothing. These include: (a) asymptotic significance tests that compare no equating and linear equating to equipercentile equating; (b) a scheme for estimating total equating error and for dividing total estimated error into systematic and random components. The smoothing technique and statistical procedures are explored and illustrated using data from forms of a professional certification test.     

Using Automated Essay Scores as an Anchor When Equating Constructed Response Writing Tests

Assessments consisting of only a few extended constructed response items (essays) are not typically equated using anchor test designs as there are typically too few essay prompts in each form to allow for meaningful equating. This article explores the idea that output from an automated scoring program designed to measure writing fluency (a common objective of many writing prompts) can be used in place of a more traditional anchor. The linear-logistic equating method used in this article is a variant of the Tucker linear equating method appropriate for the limited score range typical of essays. The procedure is applied to historical data. Although the procedure only results in small improvements over identity equating (not equating prompts), it does produce a viable alternative, and a mechanism for checking that the identity equating is appropriate. This may be particularly useful for measuring rater drift or equating mixed format tests.     

Standard Errors of Kernel Equating: Accounting for Bandwidth Estimation

In standardized testing, equating is used to ensure comparability of test scores across multiple test administrations. One equipercentile observed-score equating method is kernel equating, where an essential step is to obtain continuous approximations to the discrete score distributions by applying a kernel with a smoothing bandwidth parameter. When estimating the bandwidth, additional variability is introduced which is currently not accounted for when calculating the standard errors of equating. This poses a threat to the accuracy of the standard errors of equating. In this study, the asymptotic variance of the bandwidth parameter estimator is derived and a modified method for calculating the standard error of equating that accounts for the bandwidth estimation variability is introduced for the equivalent groups design. A simulation study is used to verify the derivations and confirm the accuracy of the modified method across several sample sizes and test lengths as compared to the existing method and the Monte Carlo standard error of equating estimates. The results show that the modified standard errors of equating are accurate under the considered conditions. Furthermore, the modified and the existing methods produce similar results which suggest that the bandwidth variability impact on the standard error of equating is minimal.     

含题组的测验等值

题组越来越多地出现在各类考试中, 采用标准的IRT模型对有题组的测验等值, 可能因忽略题组的局部相依性导致等值结果的失真。为解决此问题, 我们采用基于题组的2PTM模型及IRT特征曲线法等值, 以等值系数估计值的误差大小作为衡量标准, 以Wilcoxon符号秩检验为依据, 在几种不同情况下进行了大量的Monte Carlo模拟实验。实验结果表明, 考虑了局部相依性的题组模型2PTM绝大部分情况下都比2PLM等值的误差小且有显著性差异。另外, 用6种不同等值准则对2PTM等值并评价了不同条件下等值准则之间的优劣。     

Asymptotic standard errors of irt observed-score equating methods

A method of the IRT observed-score equating using chain equating through a third test without equating coefficients is presented with the assumption of the three-parameter logistic model. The asymptotic standard errors of the equated scores by this method are obtained using the results given by M. Liou and P.E. Cheng. The asymptotic standard errors of the IRT observed-score equating method using a synthetic examinee group with equating coefficients, which is a currently used method, are also provided. Numerical examples show that the standard errors by these observed-score equating methods are similar to those by the corresponding true score equating methods except in the range of low scores.The author is indebted to Michael J. Kolen for access to the real data used in this article and anonymous reviewers for their corrections and suggestions on this work.     

A Bayesian Nonparametric Approach to Test Equating

A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are compared through the analysis of data sets famous in the equating literature. Also, the classical percentile-rank, linear, and mean equating models are each proven to be a special case of a Bayesian model under a highly-informative choice of prior distribution.     

项目反应理论框架下的新等值方法——对数对比等值法

项目反应理论有一些以除法形式给出的多级评分模型,若采用Haebara等值法、Stocking_Lord等值法或对称相对熵等值法进行测验等值,都因其对初值有较高要求而可能导致失败。针对这一类模型,我们给出了一种新的等值方法——对数对比等值法。这种方法收敛快,对迭代初值要求低,所得结果精度较高,可以为其他等值方法提供良好的初值。研究表明,对数对比等值法还改进和推广了0-1评分的两参数Logistic模型的Logit变换等值法     

对从HSK题库中计算机自动生成试卷稳定性的试验检验

由计算机从题库中自动生成的试卷能否保持难度的相对稳定？根据IRT进行的等值误差范围有多大？为了回答这些问题,本文以共同组等值作为标准,对基于IRT之上的共同题等值误差进行了试验检验。试验中,采取一定措施保证了考生的动机水平。结果显示,IRT等值的校正方向都是正确的。在4个分测验中有3个分测验的的等值校正效果较理想,1个分测验的等值校正效果不够理想。计算机自动生成的试卷与原有人工命制的试卷在得分方面比较一致,分数相关达到0.931,获得证书的情况也是比较一致的。     

核等值：一种观察分数等值体系

核等值流程包括：预平滑、估计分数概率、连续化、等值、评估等值结果。该方法兼具线性等值与等百分位等值的优点, 各环节扩展性与包容性较强; 采用平滑与连续化处理, 可降低等值随机误差; 等值差异标准误等其所特有的概念为结果评估提供可靠的工具。连续化与带宽选择方法等因素均可影响其表现; 基于核等值的新方法为等值发展提供了新颖的视角。未来可关注核等值体系的扩充与完善、流程的更新、等值方法的结合和比较等方向。     

锚题题型与等值估计方法对等值的影响

锚测验———非等组设计是一种非常重要的等值设计方法。研究证明 :在此设计之下作为等值媒体的锚测验采用的题型不同对等值结果会有不同影响 ;采用的等值关系估计方法不同对等值结果也有不同影响 ;题型与估计方法之间还有明显的交互作用。研究认为 ,在当前的命题与评分技术水平条件下 ,锚测验以纯客观题组成为最佳 ;在锚测验题量固定的条件下 ,等值关系估计以选用频数估计法为最佳。     

Observed-score equating as a test assembly problem

A set of linear conditions on item response functions is derived that guarantees identical observed-score distributions on two test forms. The conditions can be added as constraints to a linear programming model for test assembly that assembles a new test form to have an observed-score distribution optimally equated to the distribution on an old form. For a well-designed item pool and items fitting the IRT model, use of the model results into observed-score pre-equating and prevents the necessity ofpost hoc equating by a conventional observed-score equating method. An empirical example illustrates the use of the model for an item pool from the Law School Admission Test.The authors are most indebted to Norman D. Verhelst for suggesting Proposition 4 and its proof, to the Law School Admission Council (LSAC) for making available the data set, and to Wim M. M. Tielen for his computational assistance.     

IRT与MIRT在测验垂直等值中的应用

测验垂直等值是指将测试同一心理特质的不同水平的测验转换到同一个分数量尺上的过程。IRT与MIRT是实现垂直等值的主要方法。IRT无需假设被试的能力分布, 参数估计不依赖于样本, 是构建垂直量表的有效方法, 但测验不满足单维假设时其应用受到限制。MIRT结合IRT和因素分析的特点对IRT进行了拓展, 可更有效估计多维测验的项目参数和被试能力参数, 在垂直等值中有重要应用。已有研究主要探讨IRT和MIRT在垂直等值应用中的适用性、标定方法和参数估计方法, 比较研究两种方法的特性。未来研究应纳入更多变量条件进行比较研究, 拓展方法的应用。     

Equipercentile equating via data-imputation techniques

In the design of common-item equating, two groups of examinees are administered separate test forms, and each test form contains a common subset of items. We consider test equating under this situation as an incomplete data problem—that is, examinees have observed scores on one test form and missing scores on the other. Through the use of statistical data-imputation techniques, the missing scores can be replaced by reasonable estimates, and consequently the forms may be directly equated as if both forms were administered to both groups. In this paper we discuss different data-imputation techniques that are useful for equipercentile equating; we also use empirical data to evaluate the accuracy of these techniques as compared with chained equipercentile equating.A paper presented at the European Meeting of the Psychometric Society, Barcelona, Spain, July, 1993.     

概率分布等值法及其应用

在项目反应理论框架下,根据已有文献提出了开发新的测验等值准则的方法,即许多准则都可以看成是通过对锚题上作答反应概率分布进行变换而导出。据此揭示了两个著名的等值准则——Haebara方法和Stocking-Lord方法之间的联系,并且导出了一个新的等值准则——余弦等值准则。为了讨论余弦准则的行为表现,开展了一系列Monte-Carlo模拟研究。模拟结果表明,余弦准则在多级评分模型GPCM上表现比Haebara方法和Stocking--Lord方法都好,而对GRM和2PLM,其表现不如Haebara,但可以和Stocking-Lord方法相提并论。这一发现提醒我们等值准则的选用是否恰当,不仅与等值系数所落的范围有关,而且还与项目反应函数（IRF）有更密切的关系     

大学英语四、六级考试分数等值研究

对现有的大学英语四、六级考试分数等值模式中存在的若干问题进行了深入的分析,并提出了新的解决方案——一个基于铆题设计和两参数IRT模型的解决方案。主要包括：（1）用两参数逻辑斯蒂模型替代原来的Rasch模型,以改进题目模型的适合性;（2）用共同题目的等值设计取代原来的共同被试等值设计,解决共同被试等值设计中,等值考生的动机水平难以控制的难题;（3）建立专用的等值用题库,并且一次性完成其中铆题的预测和参数标定工作,以解决原来等值模式中存在的误差累积问题。同时,由于铆题的保密工作难度较小,因此,等值专用题库对保证等值结果的可靠性也具有重大意义;（4）本文还对新的分数等值方案进行了真实的考试数据等值计算实验,并得到了一个令人满意的分数等值结果。     

A test-theoretic approach to observed-score equating

Observed-score equating using the marginal distributions of two tests is not necessarily the universally best approach it has been claimed to be. On the other hand, equating using the conditional distributions given the ability level of the examinee is theoretically ideal. Possible ways of dealing with the requirement of known ability are discussed, including such methods as conditional observed-score equating at point estimates or posterior expected conditional equating. The methods are generalized to the problem of observed-score equating with a multivariate ability structure underlying the scores. This article is based on the author's Presidential Address given on July 7, 2000 at the 65th Annual Meeting of the Psychometric Society held at the University of British Columbia, Vancouver, Canada. The author is most indebted to Wim M.M. Tielen for his computational assistance and Cees A.W. Glas for his comments on a draft of this paper.     

一种新的等值方法：核等值法

该文介绍了一种新的等值方法一核等值法。首先介绍了核等值法的研究过程、它的主要特点以及五个步骤（前平滑处理、估计分数概率、连续化、等值、计算等值标准误）。之后,介绍了核等值法与其他传统的观察分等值方法的差异,最后是对核等值法的评价。