贝叶斯题组随机效应模型的必要性及影响因素

题组模型可以解决传统IRT模型由于题目间局部独立性假设违背时所导致的参数估计偏差。为探讨题组随机效应模型的适用范围, 采用Monte Carlo模拟研究, 分别使用2-PL贝叶斯题组随机效应模型(BTRM)和2-PL贝叶斯模型(BM)对数据进行拟合, 考虑了题组效应、题组长度、题目数量和局部独立题目比例的影响。结果显示：(1) BTRM不受题组效应和题组长度影响, BM对参数估计的误差随题组效应和题组长度增加而增加。(2) BTRM具有一定的普遍性, 且当题组效应大, 题组长, 题目数量大时使用该模型能减少估计误差, 但是当题目数量较小时, 两个模型得到的能力估计误差都较大。(3)当局部独立题目的比例较大时, 两种模型得到的参数估计差异不大。     

高中英语阅读测验中题组模型的选择与应用

本研究通过高中英语阅读测验实测数据,对比分析双参数逻辑斯蒂克模型 (2PL-IRT)和加入不同数量题组的双参数逻辑斯蒂克模型 (2PL-TRT), 探究题组数量对参数估计及模型拟合的影响。结果表明：(1) 2PL-IRT模型对能力介于-1.50到0.50的被试,能力参数估计偏差较大;(2)将题组效应大于0.50的题组作为局部独立题目纳入模型,会导致部分题目区分度参数的低估和大部分题目难度参数的高估;(3)题组效应越大,将其当作局部独立题目纳入模型估计项目参数的偏差越大。     

当前考试理论研究的进展

近二十年以来,考试理论(Testing Theories)的研究取得了长足进展,这种进展表现在两个方面一方面,在上个世纪六十年代由Lord提出的项目反应理论(Item Response Theory,IRT)得到了很大的扩展,出现了多维度项目反应理论(multi-dimensional IRT)、非参数项目反应理论(Nonparametric IRT)以及认知诊断理论(Cognitively Diagnostic Theory)等;另一方面,项目反应理论在考试实践中得到了广泛的应用,使考试实践产生了革命性的变化,出现了计算机自适应考试(Computerized Adaptive Testing,CAT).     

中文版无手机恐惧量表的修订

该研究以国外学者Caglar Yildirim和Ana-Paula Correia于2015年编制的Nomophobia量表为基础,修订出了适用于国内的中文版无手机恐惧量表。研究首先使用探索性结构方程模型对量表结构进行初探; 其次使用项目反应模型进行项目分析并根据其分析结果对项目进行修改和筛选,最终形成正式版量表; 最后对正式版量表其进行信效度检验,并再次对量表题目进行项目分析。最终量表共16道题目,包括害怕无法获得信息、害怕失去便利、害怕失去联系和害怕失去网络连接4个维度; 总量表的Cronbach α系数为0.931,四维度的α系数分别为:0.789,0.816,0.887和0.896。CFA验证性结果显示量表结构较好(χ2/df=3.91,RMSEA=0.067,TLI=0.941,CFI=0.952,SRMR=0.04); 使用手机成瘾倾向量表作为校标的结果显示二者之间相关为0.626,效度良好。最终量表项目区分度在[1.734,4.806]之间,四维度区分度均值为2.1765,2.72,3.2925和3.883,项目难度参数在[-1.830,4.806]之间。综上结果显示该研究编制的无手机恐惧量表各项指标均达到了心理测量学要求,可供后续研究使用     

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。     

Mix-DINA——基于混合分布的多策略认知诊断模型

个体在完成多种类型认知任务时普遍使用了多种策略,且不同策略解题难度存在差异。但常见的测量模型忽视了这一事实,研究基于混合分布项目反应模型开发了Mix-DINA模型。其主要优点是:(1)可同时报告被试的知识状态与策略使用倾向;(2)不同策略对应题目参数自由估计,使之更符合主流心理学观点。研究通过模拟数据验证了自编Mix-DINA模型估计程序分析各类多策略作答时的有效性,结果显示Mix-DINA模型在分析单策略作答时也具有一定的稳健性。最后讨论了研究的局限,对多策略认知诊断的进一步研究给出了建议。     

在GLMM框架下统一GT与IRT

本文首次提出使用广义线性混合模型(Generalized Linear Mixed Model, GLMM)对概化理论(GT)和项目反应理论(IRT)进行统合,即在一次统计中就能同时获得GT和IRT所需要的估计结果。模拟研究结果显示：相比于传统的GT方差分量估计方法——期望均值平方(Expected Mean Squares, EMS),GLMM可以获得更准确的方差分量、G系数和Φ系数,而且GLMM获得的题目难度参数估计精度优于传统Rasch模型。实证研究展示GLMM在实际心理测量数据分析中的应用。     

心理科学领域内的客观测量——Rasch模型之特点及发展趋势

Rasch模型是在国外学术界受到广泛关注和深入研究的一个潜在特质模型。该模型为解决心理科学领域内测量的客观性问题提供了一个可行性很高的解决方案。而国内关于Rasch模型的理论探讨和应用研究却并不多见。不同于一般项目反应理论, Rasch模型要求所收集的数据必须符合模型的先验要求, 而不是使用不同的参数去适应数据的特点。Rasch模型的主要特点(包括个体与题目共用标尺、线性数据、参数分离)确保了客观测量的实现。未来关于Rasch模型的研究方向包括多维度Rasch模型、测验的等值与链接、计算机自适应性考试, 大型应用测量系统(比如Lexile系统)等等。     

经典测验理论和项目反应理论对题目分析的对比研究

项目反应理论(Item Resporse Theory IRT)被一些人认为是当代心理测量三大发展方向之一。在某些方面,它比经典测验理论(Classical TestTheory CTT)更为合理。本文利用1986年上海市师范类高等院校招生考试的理科数学试卷中选择题的实际考试资料,先用CTT计算有关题目指数,再用IRT对题目绘制题目特征曲线ICC(Item Charicteriotic Curve)并按Logstic模型对题目参数作出了估计,从而对题目分析结果作了对比研究。最后,本文对IRT与CTT在我国的运用、提出了若干看法。     

项目反应理论的形成与基本理论假设

项目反应理论(Item Response Theory)是近二十多年来在西欧和北美各国教育与心理测量领域得以迅速发展和广泛应用的一种新的教育和测量理论。在美国,有人称其为教育与心理测量领域的“爱因斯坦相对论”,喻其带来了教育与心理测量理论的革命。     

Log-Multiplicative Association Models as Item Response Models

Log-multiplicative association (LMA) models, which are special cases of log-linear models, have interpretations in terms of latent continuous variables. Two theoretical derivations of LMA models based on item response theory (IRT) arguments are presented. First, we show that Anderson and colleagues (Anderson &; Vermunt, 2000; Anderson &; Böckenholt, 2000; Anderson, 2002), who derived LMA models from statistical graphical models, made the equivalent assumptions as Holland (1990) when deriving models for the manifest probabilities of response patterns based on an IRT approach. We also present a second derivation of LMA models where item response functions are specified as functions of rest-scores. These various connections provide insights into the behavior of LMA models as item response models and point out philosophical issues with the use of LMA models as item response models. We show that even for short tests, LMA and standard IRT models yield very similar to nearly identical results when data arise from standard IRT models. Log-multiplicative association models can be used as item response models and do not require numerical integration for estimation.     

A nonlinear mixed model framework for item response theory

Mixed models take the dependency between observations based on the same cluster into account by introducing 1 or more random effects. Common item response theory (IRT) models introduce latent person variables to model the dependence between responses of the same participant. Assuming a distribution for the latent variables, these IRT models are formally equivalent with nonlinear mixed models. It is shown how a variety of IRT models can be formulated as particular instances of nonlinear mixed models. The unifying framework offers the advantage that relations between different IRT models become explicit and that it is rather straightforward to see how existing IRT models can be adapted and extended. The approach is illustrated with a self-report study on anger.     

Robust Measurement via A Fused Latent and Graphical Item Response Theory Model

Item response theory (IRT) plays an important role in psychological and educational measurement. Unlike the classical testing theory, IRT models aggregate the item level information, yielding more accurate measurements. Most IRT models assume local independence, an assumption not likely to be satisfied in practice, especially when the number of items is large. Results in the literature and simulation studies in this paper reveal that misspecifying the local independence assumption may result in inaccurate measurements and differential item functioning. To provide more robust measurements, we propose an integrated approach by adding a graphical component to a multidimensional IRT model that can offset the effect of unknown local dependence. The new model contains a confirmatory latent variable component, which measures the targeted latent traits, and a graphical component, which captures the local dependence. An efficient proximal algorithm is proposed for the parameter estimation and structure learning of the local dependence. This approach can substantially improve the measurement, given no prior information on the local dependence structure. The model can be applied to measure both a unidimensional latent trait and multidimensional latent traits.     

Refining the two‐parameter testlet response model by introducing testlet discrimination parameters

For testlet response data, traditional item response theory (IRT) models are often not appropriate due to local dependence presented among items within a common testlet. Several testlet‐based IRT models have been developed to model examinees' responses. In this paper, a new two‐parameter normal ogive testlet response theory (2PNOTRT) model for dichotomous items is proposed by introducing testlet discrimination parameters. A Bayesian model parameter estimation approach via a data augmentation scheme is developed. Simulations are conducted to evaluate the performance of the proposed 2PNOTRT model. The results indicated that the estimation of item parameters is satisfactory overall from the viewpoint of convergence. Finally, the proposed 2PNOTRT model is applied to a set of real testlet data.     

混合IRT潜在模型及其应用轨迹

项目反应理论是测量被试潜在特质的现代测量理论, 潜在类别分析是基于模型的潜在特质分类技术。混合项目反应理论将项目反应理论与潜在类别分析相结合, 能够同时对被试分类并量化其潜在特质。在阐述混合项目反应理论概念、原理的基础上, 介绍了MRM、mNRM和mPCM等几种常见混合模型及其参数估计方法, 并从心理与行为特征分类、项目功能差异检测、测验效度评价等方面评述了其在心理测验中的应用发展轨迹。     

Specifying Ability Growth Models Using a Multidimensional Item Response Model for Repeated Measures Categorical Ordinal Item Response Data

When categorical ordinal item response data are collected over multiple timepoints from a repeated measures design, an item response theory (IRT) modeling approach whose unit of analysis is an item response is suitable. This study proposes a few longitudinal IRT models and illustrates how a popular compensatory multidimensional IRT model can be utilized to formulate such longitudinal IRT models, which permits an investigation of ability growth at both individual and population levels. The equivalence of an existing multidimensional IRT model and those longitudinal IRT models is also elaborated so that one can make use of an existing multidimensional IRT model to implement the longitudinal IRT models.     

On a Generalization of Local Independence in Item Response Theory Based on Knowledge Space Theory

Psychometrika - Knowledge space theory (KST) structures are introduced within item response theory (IRT) as a possible way to model local dependence between items. The aim of this paper is...     

Polytomous IRT models and monotone likelihood ratio of the total score

In a broad class of item response theory (IRT) models for dichotomous items the unweighted total score has monotone likelihood ratio (MLR) in the latent trait. In this study, it is shown that for polytomous items MLR holds for the partial credit model and a trivial generalization of this model. MLR does not necessarily hold if the slopes of the item step response functions vary over items, item steps, or both. MLR holds neither for Samejima's graded response model, nor for nonparametric versions of these three polytomous models. These results are surprising in the context of Grayson's and Huynh's results on MLR for nonparametric dichotomous IRT models, and suggest that establishing stochastic ordering properties for nonparametric polytomous IRT models will be much harder.Hemker's research was supported by the Netherlands Research Council, Grant 575-67-034. Junker's research was supported in part by the National Institutes of Health, Grant CA54852, and by the National Science Foundation, Grant DMS-94.04438.     

Minimax d-optimal designs for item response theory models

Various different item response theory (IRT) models can be used in educational and psychological measurement to analyze test data. One of the major drawbacks of these models is that efficient parameter estimation can only be achieved with very large data sets. Therefore, it is often worthwhile to search for designs of the test data that in some way will optimize the parameter estimates. The results from the statistical theory on optimal design can be applied for efficient estimation of the parameters.A major problem in finding an optimal design for IRT models is that the designs are only optimal for a given set of parameters, that is, they are locally optimal. Locally optimal designs can be constructed with a sequential design procedure. In this paper minimax designs are proposed for IRT models to overcome the problem of local optimality. Minimax designs are compared to sequentially constructed designs for the two parameter logistic model and the results show that minimax design can be nearly as efficient as sequentially constructed designs.     

题组反应理论及其在中学英语考试中的应用研究

题组作为众多测验中的一种常见题型,由于项目间存在一定程度的依赖性而违背了局部独立性假设,若用项目反应模型进行参数估计将会出现较大的偏差.题组反应理论将被试与题组的交互作用纳入到模型中,解决了项目间相依性的问题.笔者对题组反应理论的发展、基本原理及其相关研究进行了综述,并将其应用在中学英语考试中.与项目反应理论相对比,结果发现：（1）题组反应模型与项目反应模型在各参数估计值的相关系数较强,尤其是能力参数和难度参数;（2）在置信区间宽度的比较上,题组反应模型在各个参数上均窄于项目反应模型,即题组反应模型的估计精度优于项目反应模型.