二级项目题组混合IRT模型及其稳健权重估计

在心理测量和教育测量中,二级项目和题组项目是两类常见的项目类型。由这两种项目混合构成的测试在实践中有着重要的应用。被试在答题时,由于个人的潜在能力和项目难度不匹配,常常会产生异常反应,这些异常反应会影响IRT中潜在特质估计的准确性。仿真实验证明,二级项目题组混合IRT模型的稳健估计方法在出现异常值的情况下,能够比极大似然估计对被试的潜在特质做出更加准确的估计,能够满足实际测试的需求。     

A hierarchical latent response model for inferences about examinee engagement in terms of guessing and item-level non-response

In low-stakes assessments, test performance has few or no consequences for examinees themselves, so that examinees may not be fully engaged when answering the items. Instead of engaging in solution behaviour, disengaged examinees might randomly guess or generate no response at all. When ignored, examinee disengagement poses a severe threat to the validity of results obtained from low-stakes assessments. Statistical modelling approaches in educational measurement have been proposed that account for non-response or for guessing, but do not consider both types of disengaged behaviour simultaneously. We bring together research on modelling examinee engagement and research on missing values and present a hierarchical latent response model for identifying and modelling the processes associated with examinee disengagement jointly with the processes associated with engaged responses. To that end, we employ a mixture model that identifies disengagement at the item-by-examinee level by assuming different data-generating processes underlying item responses and omissions, respectively, as well as response times associated with engaged and disengaged behaviour. By modelling examinee engagement with a latent response framework, the model allows assessing how examinee engagement relates to ability and speed as well as to identify items that are likely to evoke disengaged test-taking behaviour. An illustration of the model by means of an application to real data is presented.     

Prediction of true test scores from observed item scores and ancillary data

In many educational tests which involve constructed responses, a traditional test score is obtained by adding together item scores obtained through holistic scoring by trained human raters. For example, this practice was used until 2008 in the case of GRE^®General Analytical Writing and until 2009 in the case of TOEFL^® iBT Writing. With use of natural language processing, it is possible to obtain additional information concerning item responses from computer programs such as e‐rater^®. In addition, available information relevant to examinee performance may include scores on related tests. We suggest application of standard results from classical test theory to the available data to obtain best linear predictors of true traditional test scores. In performing such analysis, we require estimation of variances and covariances of measurement errors, a task which can be quite difficult in the case of tests with limited numbers of items and with multiple measurements per item. As a consequence, a new estimation method is suggested based on samples of examinees who have taken an assessment more than once. Such samples are typically not random samples of the general population of examinees, so that we apply statistical adjustment methods to obtain the needed estimated variances and covariances of measurement errors. To examine practical implications of the suggested methods of analysis, applications are made to GRE General Analytical Writing and TOEFL iBT Writing. Results obtained indicate that substantial improvements are possible both in terms of reliability of scoring and in terms of assessment reliability.     

四参数Logistic加权模型下被试能力稳健估计

设计项目参数、被试得分已知的测验情境,在两、三、四参数Logistic加权模型下进行能力估计,发现被试得分等级之间的能力步长存在着均匀的步长间距,被试得分能较好的反映多级记分的分数加权作用。两参数Logistic加权模型下会出现被试参数估计扰动现象,猜测现象会导致能力高估现象,失误现象会导致能力低估现象;三参数Logistic加权模型c型下能力高估现象未出现或不明显;三参数Logistic加权模型γ型下能力低估现象未出现或不明显;四参数Logistic加权模型下被试能力高估现象和低估现象都未出现或不明显,四参数Logistic加权模型是被试能力稳健性估计较好的方法。     

结合选择题与主观题信息的两阶段作弊甄别方法

为提高对高分作弊者和低抄袭比例作弊者的检验力,模拟600名考生的作答,设置3种抄袭比例（60%,80%和100%）和3种抄袭源能力（能力百分等级为60%,80%和100%）,设计两阶段作弊甄别法,第一阶段使用lz指数筛选个人拟合差的异常考生,第二阶段针对这些异常考生使用ω指数进行精确甄别。结果表明该法对高分作弊者和低抄袭比例作弊者的检验力优于仅使用答案抄袭检测法。     

让自适应测验更知人善选——基于推荐系统的选题策略

基于推荐系统中协同过滤推荐的思想, 提出两种可以利用已有答题者数据的CAT选题策略：直接基于答题者推荐(DEBR)和间接基于答题者推荐(IEBR)。通过两个模拟研究, 在不同题库和不同长度的测验中, 比较了两种推荐选题策略与两种传统选题策略(FMI和BAS)在测量精度和对题目曝光率控制上的表现, 以及影响推荐选题策略表现的因素。结果发现：两种推荐选题策略对题目曝光率的控制优于两种传统选题策略, 测量精度不亚于BAS方法, 其中DEBR侧重选题精度, IEBR对题目曝光率控制最好。已有答题者数据的特点和质量是影响推荐选题策略表现的主要因素。     

可修改答案的认知诊断计算机化自适应测验研究

允许修改答案的认知诊断计算机化自适应测验(Reviewable Cognitive Diagnostic Computerized Adaptive Testing,RCD-CAT),有利于更准确诊断被试的知识状态,题目口袋法(Item Pocket,IP)为被试提供了缓存作答并修改的机会,改进的题目口袋法(Modified IP,MIP)对IP内修改的题目重新计分。模拟研究比较了IP、MIP、stocking Ⅰ和stocking Ⅱ在RCD-CAT效果,结果发现:stocking设计的效果最优,其中stocking Ⅱ的效果略优于stocking Ⅰ,IP法和MIP法判准率要低于传统CD-CAT,stocking设计在RCD-CAT具有较好的应用前景。     

基于GRM模型的BP神经网络参数估计

目前参数估计多采用统计方法,存在耗时长、要求被试样本容量大和项目数多等缺点。本文将BP神经网络和降维法相结合,对GRM的项目参数和考生能力参数进行估计。蒙特卡洛模拟结果显示：（1）不管是人多题少还是题多人少,该网络设计下的参数估计精度都较高;（2）可以应用到多个不同等级评分的参数估计中,甚至是超过15个等级的项目参数,估计精度也较高,这是其他参数估计方法所不可比拟的;（3）运行的时长和统计估计方法相比大大缩减。     

Invariance Properties for General Diagnostic Classification Models

In item response theory (IRT), the invariance property states that item parameter estimates are independent of the examinee sample, and examinee ability estimates are independent of the test items. While this property has long been established and understood by the measurement community for IRT models, the same cannot be said for diagnostic classification models (DCMs). DCMs are a newer class of psychometric models that are designed to classify examinees according to levels of categorical latent traits. We examined the invariance property for general DCMs using the log-linear cognitive diagnosis model (LCDM) framework. We conducted a simulation study to examine the degree to which theoretical invariance of LCDM classifications and item parameter estimates can be observed under various sample and test characteristics. Results illustrated that LCDM classifications and item parameter estimates show clear invariance when adequate model data fit is present. To demonstrate the implications of this important property, we conducted additional analyses to show that using pre-calibrated tests to classify examinees provided consistent classifications across calibration samples with varying mastery profile distributions and across tests with varying difficulties.     

An application of confidence intervals and of maximum likelihood to the estimation of an examinee's ability

A mathematical definition of the theoretical relation between the examinee's actual responses to the test items and his “true ability” is selected. A maximum-likelihood solution is obtained for estimating the examinee's “true ability” from his responses to the items. The standard error of the maximum-likelihood estimate is obtained, its relation to the discriminating power of the test is pointed out, and some generalizations are drawn as to the optimum level of item difficulty. The Neyman-Pearson power function is applied to determine which of two psychological tests is the most powerful for the selection of “successful” examinees.     

RETEST EFFECTS ON IDENTICAL AND PARALLEL FORMS IN CERTIFICATION AND LICENSURE TESTING

Examinees who take credentialing tests and other types of high-stakes assessments are usually provided an opportunity to repeat the test if they are unsuccessful on initial attempts. To prevent examinees from obtaining unfair score increases by memorizing the content of specific test items, testing agencies usually assign an alternate form to repeat examinees. Given that the use of multiple forms presents both practical and psychometric challenges, it is important to determine if unwarranted score gains occur. Most research indicates that repeat examinees realize score gains when taking the same form twice; however, the research is far from conclusive, particularly within the context of credentialing. For the present investigations, two samples of repeat examinees were randomly assigned to receive either the same test form or a different, but parallel, form on the second occasion. Study 1 found score gains of about 0.79 SD units for 71 examinees who repeated a certification examination in computed tomography. Study 2 found gains of 0.48 SD units for 765 examinees who repeated a radiography certification examination. In both studies score gains for examinees receiving the parallel test were nearly indistinguishable from score gains for those who received the same test. Factors are identified that may influence the generalizability of these findings to other assessment contexts.     

多级计分测验中基于残差统计量的被试拟合研究

本文提出一种多级计分项目下的个人拟合统计量R, 考察它在检测6种常见的异常作答模式(作弊、猜测、随机、粗心、创新作答、混合异常)下的表现, 并与标准化对数似然统计量l_zp进行比较。结果表明：(1) 在异常作答覆盖率较低并且异常作答类型为作弊和猜测时, R的检测率显著高于l_zp; (2) 随着测验长度和被试异常程度的增加, 两种统计量的检测率都会上升; (3) 在一些条件下, R与l_zp检测效果接近。实证数据分析进一步展示了R统计量的使用方法和过程, 结果也表明R统计量具有较好的应用前景。     

Optimum examinee samples for item parameter estimation in item response theory: A multi-objective programming approach

This paper proposes a multi-objective programming method for determining samples of examinees needed for estimating the parameters of a group of items. In the numerical experiments, optimum samples are compared to uniformly and normally distributed samples. The results show that the samples usually recommended in the literature are well suited for estimating the difficulty parameters. Furthermore, they are also adequate for estimating the discrimination parameters in the three-parameter model, butnot for the guessing parameters.     

普通话测试的录音评分可行性、信度及经济效率

该研究采用心理测量中的概化(generalizability theory)理论,通过两个研究,分析国家语言文字工作委员会的普通话测试中采用录音评分的可行性,并探讨了其信度、经济效率及心理测量等特性。研究共有25名被试及8名评分员。结果表明录音评分和现场评分测试的结果是一致的,最少能区分90％的能力差异。此外,研究亦指出现行测试的评分者人数及题数已经算足够,但仍可依考生能力特性等,作一些调整以提高测试效率。     

Detecting Social Desirability Bias Using Factor Mixture Models

Based on the conceptualization that social desirable bias (SDB) is a discrete event resulting from an interaction between a scale's items, the testing situation, and the respondent's latent trait on a social desirability factor, we present a method that makes use of factor mixture models to identify which examinees are most likely to provide biased responses, which items elicit the most socially desirable responses, and which external variables predict SDB. Problems associated with the common use of correlation coefficients based on scales' total scores to diagnose SDB and partial correlations to correct for SDB are discussed. The method is demonstrated with an analysis of SDB in the Attitude toward Interprofessional Service-Learning scale with a sample of students from health-related fields.     

Investigating the relationship between item exposure and test overlap: Item sharing and item pooling

To date, exposure control procedures that are designed to control item exposure and test overlap simultaneously are based on the assumption of item sharing between pairs of examinees. However, examinees may obtain test information from more than one examinee in practice. This larger scope of information sharing needs to be taken into account in refining exposure control procedures. To control item exposure and test overlap among a group of examinees larger than two, the relationship between the two indices needs to be identified first. The purpose of this paper is to analytically derive the relationships between item exposure rate and each of the two forms of test overlap, item sharing and item pooling, for fixed‐length computerized adaptive tests. Item sharing is defined as the number of common items shared by all examinees in a group, while item pooling is the number of overlapping items that an examinee has with a group of examinees. The accuracy of the derived relationships was verified using numerical examples. The relationships derived will lay the foundation for future development of procedures to simultaneously control item exposure and item sharing or item pooling among a group of examinees larger than two.     

可修改答案的计算机化自适应测验的方法

与传统的纸笔测验(Paper And Pencil Based Test, P&P)相比计算机化自适应测验(Computerized Adaptive Testing, CAT)根据被试的作答反应自适应地选择题目, 它不仅缩短了测验长度, 还极大地提高了测验的准确性。然而, 目前绝大多数CAT不允许被试修改答案, 研究者主要担心修改答案会降低CAT的有效性。允许修改答案符合被试一贯的测验习惯, 修改之后的分数更能反映被试真实的水平, 从而能够进一步促进CAT在实际中的应用。现有的研究主要从三个方面提出了可修改答案CAT的控制方法：一是测验设计; 二是改进选题策略; 三是建构模型。未来的研究应进一步探讨这些方法之间的比较与结合, 以及对可修改答案认知诊断CAT (Cognitive Diagnostic CAT, CD-CAT)的研究。     

认知诊断CAT中具有非统计约束选题方法的比较

项目曝光控制和内容约束关系到测验安全、测验的信度和效度, 是计算机化自适应测验(Computerized Adaptive Testing, CAT)中两类重要的非统计约束条件。本文在认知诊断CAT中针对内容约束和项目曝光控制要求, 运用5种方法选择测验项目。它们分别是：(1) Monte Carlo方法与项目合格方法相结合, 记为MC-IE; (2) Monte Carlo方法与最大优先指标方法相结合, 记为MC-MPI; (3) Monte Carlo方法与限制阈值方法相结合, 记为MC-RT; (4) Monte Carlo方法与限制进度指标方法相结合, 记为MC-RPG以及(5) Monte Carlo方法与最大后验概率方法相结合, 记为MC-PP。然后通过在线性、收敛、发散、无结构和独立五种属性结构下构建题库并运用重参化融融统和模型模拟被试反应比较它们的选题表现。研究发现, (1) 相同选题方法在不同属性结构下项目曝光率的分布类似, 测量精度按线性、收敛、发散、无结构和独立结构的顺序依次降低; (2) 相同属性结构下, 不同方法的测量精度高低依次为MC-PP、MC-IE、MC-RT、MC-MPI和MC-RPG方法; 项目曝光均匀性优劣依次为MC-RPG、MC-MPI、MC-RT、MC-IE和MC-PP方法。统一量纲值表明, MC-RPG方法的综合表现最好, MC-MPI方法的表现次之。     

The linear transformation model with frailties for the analysis of item response times

The item response times (RTs) collected from computerized testing represent an underutilized source of information about items and examinees. In addition to knowing the examinees’ responses to each item, we can investigate the amount of time examinees spend on each item. In this paper, we propose a semi‐parametric model for RTs, the linear transformation model with a latent speed covariate, which combines the flexibility of non‐parametric modelling and the brevity as well as interpretability of parametric modelling. In this new model, the RTs, after some non‐parametric monotone transformation, become a linear model with latent speed as covariate plus an error term. The distribution of the error term implicitly defines the relationship between the RT and examinees’ latent speeds; whereas the non‐parametric transformation is able to describe various shapes of RT distributions. The linear transformation model represents a rich family of models that includes the Cox proportional hazards model, the Box–Cox normal model, and many other models as special cases. This new model is embedded in a hierarchical framework so that both RTs and responses are modelled simultaneously. A two‐stage estimation method is proposed. In the first stage, the Markov chain Monte Carlo method is employed to estimate the parametric part of the model. In the second stage, an estimating equation method with a recursive algorithm is adopted to estimate the non‐parametric transformation. Applicability of the new model is demonstrated with a simulation study and a real data application. Finally, methods to evaluate the model fit are suggested.