等级反应模型下项目特征曲线等值法在大型考试中的应用

在中国最大的资格考试之一的经济专业资格考试中,为保证不同年度间考试的可比性、进行题库建设和为计算机自适应考试做准备,应用项目反应理论中等级反应模型下的项目特征曲线等值法,采用铆测验等值设计,实现了4个年度考试资料的项目参数和能力参数的等值,并成功地组建了经济专业题库。在此基础上,利用等值技术对不同年份试卷的划界分数进行了比较,为经济考试的合格标准制定、确保考试的公平性提供了实证依据。     

解释性项目反应理论模型：理论与应用

解释性项目反应理论模型(Explanatory Item Response Theory Models, EIRTM)是指基于广义线性混合模型和非线性混合模型构建的项目反应理论(Item Response Theory, IRT)模型。EIRTM能在IRT模型的基础上直接加入预测变量, 从而解决各类测量问题。首先介绍EIRTM的相关概念和参数估计方法, 然后展示如何使用EIRTM处理题目位置效应、测验模式效应、题目功能差异、局部被试依赖和局部题目依赖, 接着提供实例对EIRTM的使用进行说明, 最后对EIRTM的不足之处和应用前景进行讨论。     

多维题组效应Rasch模型

首先, 本文诠释了“题组”的本质即一个存在共同刺激的项目集合。并基于此, 将题组效应划分为项目内单维题组效应和项目内多维题组效应。其次, 本文基于Rasch模型开发了二级评分和多级评分的多维题组效应Rasch模型, 以期较好地处理项目内多维题组效应。最后, 模拟研究结果显示新模型有效合理, 与Rasch题组模型、分部评分模型对比研究后表明：(1)测验存在项目内多维题组效应时, 仅把明显的捆绑式题组效应进行分离而忽略其他潜在的题组效应, 仍会导致参数的偏差估计甚或高估测验信度; (2)新模型更具普适性, 即便当被试作答数据不存在题组效应或只存在项目内单维题组效应, 采用新模型进行测验分析也能得到较好的参数估计结果。     

Increasing item complexity: A possible cause of scale shrinkage for unidimensional item response theory

When the three-parameter logistic model is applied to tests covering a broad range of difficulty, there frequently is an increase in mean item discrimination and a decrease in variance of item difficulties and traits as the tests become more difficult. To examine the hypothesis that this unexpected scale shrinkage effect occurs because the items increase in complexity as they increase in difficulty, an approximate relationship is derived between the unidimensional model used in data analysis and a multidimensional model hypothesized to be generating the item responses. Scale shrinkage is successfully predicted for several sets of simulated data.The author is grateful to Robert Mislevy for kindly providing a copy of his computer program, RESOLVE.     

测验理论的新发展:多维项目反应理论

多维项目反应理论是基于因子分析和单维项目反应理论两大背景下发展起来的一种新型测验理论。根据被试在完成一项任务时多种能力之间是如何相互作用的,多维项目反应模型可以分为补偿性模型和非补偿性模型两类。本文在系统介绍了当前普遍使用的补偿性模型的基础上,指出后续研究者应关注多维项目反应理论中多级评分和高维空间的多维模型、补偿性和非补偿性模型的融合、参数估计程序的开发和多维测验等值四个方面的研究。     

Nonparametric polytomous IRT models for invariant item ordering, with results for parametric models

It is often considered desirable to have the same ordering of the items by difficulty across different levels of the trait or ability. Such an ordering is an invariant item ordering (IIO). An IIO facilitates the interpretation of test results. For dichotomously scored items, earlier research surveyed the theory and methods of an invariant ordering in a nonparametric IRT context. Here the focus is on polytomously scored items, and both nonparametric and parametric IRT models are considered.The absence of the IIO property in twononparametric polytomous IRT models is discussed, and two nonparametric models are discussed that imply an IIO. A method is proposed that can be used to investigate whether empirical data imply an IIO. Furthermore, only twoparametric polytomous IRT models are found to imply an IIO. These are the rating scale model (Andrich, 1978) and a restricted rating scale version of the graded response model (Muraki, 1990). Well-known models, such as the partial credit model (Masters, 1982) and the graded response model (Samejima, 1969), do no imply an IIO.     

A taxonomy of item response models

A number of models for categorical item response data have been proposed in recent years. The models appear to be quite different. However, they may usefully be organized as members of only three distinct classes, within which the models are distinguished only by assumptions and constraints on their parameters. “Difference models” are appropriate for ordered responses, “divide-by-total” models may be used for either ordered or nominal responses, and “left-side added” models are used for multiple-choice responses with guessing. The details of the taxonomy and the models are described in this paper. The present study was supported in part by two postdoctoral fellowships awarded to Lynne Steinberg: an Educational Testing Service Postdoctoral Fellowship at ETS, Princeton, NJ and an NIMH Individual National Research Service Award at Stanford University, Stanford, CA. Helpful comments by the editor and three anonymous reviewers are gratefully acknowledged.     

An item response model with internal restrictions on item difficulty

An IRT model based on the Rasch model is proposed for composite tasks, that is, tasks that are decomposed into subtasks of different kinds. There is one subtask for each component that is discerned in the composite tasks. A component is a generic kind of subtask of which the subtasks resulting from the decomposition are specific instantiations with respect to the particular composite tasks under study. The proposed model constrains the difficulties of the composite tasks to be linear combinations of the difficulties of the corresponding subtask items, which are estimated together with the weights used in the linear combinations, one weight for each kind of subtask. Although the model does not belong to the exponential family, its parameters can be estimated using conditional maximum likelihood estimation. The approach is demonstrated with an application to spelling tasks. We thank Eric Maris for his helpful comments.     

题目位置效应的概念及检测

题目位置效应(Item Position Effect, IPE)是指在剔除随机误差的影响之后, 同一道题目在不同测验间因题目位置的变化而导致题目参数的变化。IPE的存在会严重威胁依赖于项目反应理论参数不变性特征的相关应用, 比如测验等值和计算机化自适应测验。目前关于这一领域的研究主要集中于对IPE的检测, 而对所检测到的效应进行进一步的解释, 则是今后的研究重点。另外, 在不同的研究情境下深入探讨IPE, 对于基础研究领域和实践领域都具有重要意义。     

Exact and best confidence intervals for the ability parameter of the Rasch model

A commonly used method to evaluate the accuracy of a measurement is to provide a confidence interval that contains the parameter of interest with a given high probability. Smallest exact confidence intervals for the ability parameter of the Rasch model are derived and compared to the traditional, asymptotically valid intervals based on the Fisher information. Tables of the exact confidence intervals, termed Clopper-Pearson intervals, can be routinely drawn up by applying a computer program designed by and obtainable from the author. These tables are particularly useful for tests of only moderate lengths where the asymptotic method does not provide valid confidence intervals.     

An extension of the rating scale model with an application to the measurement of change

The polytomous unidimensional Rasch model with equidistant scoring, also known as the rating scale model, is extended in such a way that the item parameters are linearly decomposed into certain basic parameters. The extended model is denoted as the linear rating scale model (LRSM). A conditional maximum likelihood estimation procedure and a likelihood-ratio test of hypotheses within the framework of the LRSM are presented. Since the LRSM is a generalization of both the dichotomous Rasch model and the rating scale model, the present algorithm is suited for conditional maximum likelihood estimation in these submodels as well. The practicality of the conditional method is demonstrated by means of a dichotomous Rasch example with 100 items, of a rating scale example with 30 items and 5 categories, and in the light of an empirical application to the measurement of treatment effects in a clinical study.Work supported in part by the Fonds zur Förderung der Wissenschaftlichen Forschung under Grant No. P6414.