项目间多维测验作答时间数据分析：潜在特质速度间效应建模

随着计算机测验使用的普及化,被试在心理与教育测验上的作答反应时的获取也越发便利。为了充分利用项目反应时信息,单维与多维的反应时模型相继被提出。然后,在项目间多维反应时数据中,潜在特质速度之间可能存在共同关系（比如,层阶关系）,此时现有的反应时模型并不能适用。基于此,本研究提出了高阶对数正态反应时模型与双因子对数正态反应时模型。在模拟研究中,高阶对数正态反应时模型与双因子对数正态反应时模型的各参数都能被准确估计。在瑞文标准推理测验的三组测验项目的反应时数据中,双因子对数正态反应时模型表现出更为优秀的拟合效果,同时基于多个统计量说明了局部与全局潜在特质速度同时存在的必要性。因此,在项目间多维测验反应时数据分析中,非常有必要考虑多维潜在特质速度之间的共同效应。     

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。     

多维项目反应理论补偿性模型参数估计:基于广义回归神经网络集合

运用广义回归神经网络(GRNN)方法对小样本多维项目反应理论(MIRT)补偿性模型的项目参数进行估计,尝试解决传统参数估计方法样本数量要求较大的问题。MIRT双参数Logistic补偿模型被设置为二级计分的二维模型。首先,模拟二维能力参数、项目参数值与考生作答矩阵。其次,把通过主成分分析得到的前两个因子在每个题目上的载荷作为区分度的初始值以及题目通过率作为难度的初始值,这两个指标的初始值作为神经网络的输入。集成100个神经网络,其输出值的均值作为MIRT的项目参数估计值。最后,设置2×2种(能力相关水平:0.3和0.7; 两种估计方法:GRNN和MCMC方法)实验处理,对GRNN和MCMC估计方法的返真性进行比较。结果表明,小样本的情况下,基于GRNN集成方法的参数估计结果优于MCMC方法。     

多水平IRT的发展与应用述评

阶层线性模型是处理阶层结构数据的高级统计方法, 项目反应理论是精确测量被试能力的现代测量理论。多水平项目反应理论将阶层线性模型和项目反应理论相结合, 将项目反应模型嵌套在阶层线性模型内, 实现了项目参数和不同水平能力参数的估计, 对回归系数和误差项变异的估计也更加精确。作者概述了多水平项目反应理论的发展历程, 并从项目功能差异、测验等值、学校效能研究等方面评述了多水平项目反应理论在心理与教育测量中的应用, 总结了多水平项目反应理论的价值, 同时展望了今后的研究趋势。     

多维项目反应理论等级反应模型

基于因子分析和单维项目反应理论的多维项目反应理论是测量理论的新发展方向之一。但是, 多维项目反应理论仍处于不成熟的发展阶段, 多数研究也只是以二级评分为主。本文首先介绍了逻辑斯蒂形式的多维等级反应模型, 并以二维等级反应模型为例, 分析了模型的数学函数图像及其性质。然后, 推导出了多维等级反应模型的项目信息函数, 并结合实例进行了讨论。进一步地, 本文阐述了使用联合极大似然估计和马尔科夫链蒙特卡洛方法估计多维等级反应模型参数的思想。最后, 指出了一些有待研究的问题。     

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。     

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.     

项目反应理论新进展：基于3PLM和GRM的混合模型

IRT中的计量模型较多,不同计量模型适合不同特点的数据资料,实际工作者应根据实际情况选择适当的IRT模型来分析数据。我国是个考试、测评大国,测评的题型丰富多样,在实际应用IRT时,一个模型往往很难反应所有数据资料本身的特点,这时可考虑应用多个IRT模型（即“混合模型”）来分析,以达到对数据的最佳拟合。本文对混合模型的思想方法及原理、参数估计的实现、以及模型性能进行了研究,发现：（1）本文自主开发的混合模型参数估计程序Mix_Tu具有较高的返真性,且与国际知名测量软件Parscale相当。（2）在“项目异常”情况下,Mix_Tu程序对参数b和c的估计受数据异常程度的影响要大于Parscale程序,而对参数a的估计受数据异常程度的影响要小于Parscale程序,而在参数theta上两个程序相当。（3）在“被试异常”情况下,Mix_Tu程序对所有参数的估计受数据异常程度的影响均要小于Parscale程序,Mix_Tu程序表现的更为稳健。     

概率性输入,噪音“与”门(PINA)模型

当前认知诊断测验的主要目的是对被试进行合理分类,进而采用类别变量去描述被试对某技能或知识(即认知属性)的掌握情况,但该粗糙的分类方法不能精细地区分不同被试之间的差异。对此,采用掌握概率这一连续变量去描述被试对某认知属性的掌握情况是一种值得尝试的做法。本文首先基于高阶潜在特质(简称"潜质")模型给出了认知属性掌握概率的量化定义,之后与多成分潜质模型相结合提出了概率性输入,噪音"与"门(PINA)模型;其次,采用MCMC算法实现了对PINA的参数估计,结果表明参数估计程序对各参数的估计返真性均较好;最后,以ECPE数据为例来说明PINA在实际测验分析中具有可行性。     

IRT中最小化χ2/EM参数估计方法

对IRT的双参数Logistic模型（2PLM）中未知参数估计问题,给出了一个新的估计方法――最小化χ2/EM估计。新方法在充分考虑项目反应理论(IRT)与经典测量理论(CTT)之间的差异的前提下,从统计计算的角度改进了Berkson的最小化χ2估计,取消了Berkson实施最小化χ2估计时需要已知能力参数的不合实际的前提,扩大了应用范围。实验结果表明新方法能力参数的估计结果与BILOG相比,精确度要高,且当样本容量超过2000时,项目参数的估计结果也优于BILOG。实验还表明新方法稳健性好     

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。     

A rasch model for partial credit scoring

A unidimensional latent trait model for responses scored in two or more ordered categories is developed. This “Partial Credit” model is a member of the family of latent trait models which share the property of parameter separability and so permit “specifically objective” comparisons of persons and items. The model can be viewed as an extension of Andrich's Rating Scale model to situations in which ordered response alternatives are free to vary in number and structure from item to item. The difference between the parameters in this model and the “category boundaries” in Samejima's Graded Response model is demonstrated. An unconditional maximum likelihood procedure for estimating the model parameters is developed. Preparation of this paper was supported by grants from the Spencer Foundation and the National Institute for Justice. I would like to thank Professor Benjamin D. Wright of the University of Chicago for his very kind help with the various drafts of this paper.     

Robustness of Parameter Estimation to Assumptions of Normality in the Multidimensional Graded Response Model

A central assumption that is implicit in estimating item parameters in item response theory (IRT) models is the normality of the latent trait distribution, whereas a similar assumption made in categorical confirmatory factor analysis (CCFA) models is the multivariate normality of the latent response variables. Violation of the normality assumption can lead to biased parameter estimates. Although previous studies have focused primarily on unidimensional IRT models, this study extended the literature by considering a multidimensional IRT model for polytomous responses, namely the multidimensional graded response model. Moreover, this study is one of few studies that specifically compared the performance of full-information maximum likelihood (FIML) estimation versus robust weighted least squares (WLS) estimation when the normality assumption is violated. The research also manipulated the number of nonnormal latent trait dimensions. Results showed that FIML consistently outperformed WLS when there were one or multiple skewed latent trait distributions. More interestingly, the bias of the discrimination parameters was non-ignorable only when the corresponding factor was skewed. Having other skewed factors did not further exacerbate the bias, whereas biases of boundary parameters increased as more nonnormal factors were added. The item parameter standard errors recovered well with both estimation algorithms regardless of the number of nonnormal dimensions.     

An autoregressive growth model for longitudinal item analysis

A first-order autoregressive growth model is proposed for longitudinal binary item analysis where responses to the same items are conditionally dependent across time given the latent traits. Specifically, the item response probability for a given item at a given time depends on the latent trait as well as the response to the same item at the previous time, or the lagged response. An initial conditions problem arises because there is no lagged response at the initial time period. We handle this problem by adapting solutions proposed for dynamic models in panel data econometrics. Asymptotic and finite sample power for the autoregressive parameters are investigated. The consequences of ignoring local dependence and the initial conditions problem are also examined for data simulated from a first-order autoregressive growth model. The proposed methods are applied to longitudinal data on Korean students’ self-esteem.     

Continuous and discrete latent structure models for item response data

Relations are examined between latent trait and latent class models for item response data. Conditions are given for the two-latent class and two-parameter normal ogive models to agree, and relations between their item parameters are presented. Generalizationss are then made to continuous models with more than one latent trait and discrete models with more than two latent classes, and methods are presented for relating latent class models to factor models for dichotomized variables. Results are illustrated using data from the Law School Admission Test, previously analyzed by several authors.     

Latent variable models for analyzing children's processing ability

In this paper, we develop a latent processing ability model to analyze the speed of processing ability data. Our approach can not only effectively evaluate the effects of covariates on the latent processing ability, but also estimate the latent trait of each child by calculating its posterior mean. In addition, we derive the correlations structure of latent traits among different age groups. Simulations are conducted to evaluate the performance of our proposed model. The results indicated that the estimation of model parameters is satisfactory overall. The method is evaluated using real data from children aged 4–7 years in Changchun, China.     

Multicomponent latent trait models for ability tests

A major research direction for ability measurement has been to identify the information-processes that are involved in solving test items through mathematical modeling of item difficulty. However, this research has had limited impact on ability measurement, since person parameters are not included in the process models. The current paper presents some multicomponent latent trait models for reproducing test performance from both item and person parameters on processing components. Components are identified from item subtasks, in which performance is a logistic function (i.e., Rasch model) of person and item parameters, and then are combined according to a mathematical model of processing on the composite item.The author would like to thank David Thissen for his invaluable insights concerning this model and an anonymous reviewer for his suggestion about the sample space for the model.This research was partially supported by National Institute of Education grant number NIE-6-7-0156 to Susan E. Whitely, principal investigator. However the opinions expressed herein do not necessarily reflect the position or policy of the National Institute of Education, and no official endorsement by the National Institute of Education should be referred. Part of this paper was presented at the annual meeting of thePsychometric Society, Monterey, California: June, 1979.     

Latent variable selection in multidimensional item response theory models using the expectation model selection algorithm

The aim of latent variable selection in multidimensional item response theory (MIRT) models is to identify latent traits probed by test items of a multidimensional test. In this paper the expectation model selection (EMS) algorithm proposed by Jiang et al. (2015) is applied to minimize the Bayesian information criterion (BIC) for latent variable selection in MIRT models with a known number of latent traits. Under mild assumptions, we prove the numerical convergence of the EMS algorithm for model selection by minimizing the BIC of observed data in the presence of missing data. For the identification of MIRT models, we assume that the variances of all latent traits are unity and each latent trait has an item that is only related to it. Under this identifiability assumption, the convergence of the EMS algorithm for latent variable selection in the multidimensional two-parameter logistic (M2PL) models can be verified. We give an efficient implementation of the EMS for the M2PL models. Simulation studies show that the EMS outperforms the EM-based L₁ regularization in terms of correctly selected latent variables and computation time. The EMS algorithm is applied to a real data set related to the Eysenck Personality Questionnaire.