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DINA-BAG: A Bagging Algorithm for DINA Model Parameter Estimation in Small Samples 小样本条件下DINA模型参数估计的Bagging算法
IF 2.4 3区 心理学 Q2 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2023-08-07 DOI: 10.3102/10769986231188442
D. Arthur, Hua-Hua Chang
Cognitive diagnosis models (CDMs) are the assessment tools that provide valuable formative feedback about skill mastery at both the individual and population level. Recent work has explored the performance of CDMs with small sample sizes but has focused solely on the estimates of individual profiles. The current research focuses on obtaining accurate estimates of skill mastery at the population level. We introduce a novel algorithm (bagging algorithm for deterministic inputs noisy “and” gate) that is inspired by ensemble learning methods in the machine learning literature and produces more stable and accurate estimates of the population skill mastery profile distribution for small sample sizes. Using both simulated data and real data from the Examination for the Certificate of Proficiency in English, we demonstrate that the proposed method outperforms other methods on several metrics in a wide variety of scenarios.
认知诊断模型(CDMs)是一种评估工具,可以在个人和群体水平上提供关于技能掌握的有价值的形成性反馈。最近的工作已经在小样本量的情况下探索了cdm的性能,但是只关注于个体概况的估计。目前的研究重点是在人口水平上获得对技能掌握程度的准确估计。我们引入了一种新的算法(用于确定性输入噪声和门的bagging算法),该算法受到机器学习文献中的集成学习方法的启发,并对小样本量的总体技能掌握概况分布产生更稳定和准确的估计。使用英语水平证书考试的模拟数据和真实数据,我们证明了所提出的方法在各种场景下的几个指标上优于其他方法。
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引用次数: 0
Bayesian Change-Point Analysis Approach to Detecting Aberrant Test-Taking Behavior Using Response Times 利用响应时间检测异常考生行为的贝叶斯变点分析方法
IF 2.4 3区 心理学 Q2 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2023-07-24 DOI: 10.3102/10769986231151961
Hongyue Zhu, Hong Jiao, Wei Gao, Xiangbin Meng
Change-point analysis (CPA) is a method for detecting abrupt changes in parameter(s) underlying a sequence of random variables. It has been applied to detect examinees’ aberrant test-taking behavior by identifying abrupt test performance change. Previous studies utilized maximum likelihood estimations of ability parameters, focusing on detecting one change point for each examinee. This article proposes a Bayesian CPA procedure using response times (RTs) to detect abrupt changes in examinee speed, which may be related to aberrant responding behaviors. The lognormal RT model is used to derive a procedure for detecting aberrant RT patterns. The method takes the numbers and locations of the change points as parameters in the model to detect multiple change points or multiple aberrant behaviors. Given the change points, the corresponding speed of each segment in the test can be estimated, which enables more accurate inferences about aberrant behaviors. Simulation study results indicate that the proposed procedure can effectively detect simulated aberrant behaviors and estimate change points accurately. The method is applied to data from a high-stakes computerized adaptive test, where its applicability is demonstrated.
变点分析(CPA)是一种用于检测随机变量序列下的参数突变的方法。它已被应用于通过识别考试成绩的突然变化来检测考生的异常考试行为。先前的研究使用了能力参数的最大似然估计,重点是检测每个受试者的一个变化点。本文提出了一种贝叶斯CPA程序,使用响应时间(RT)来检测考生速度的突然变化,这可能与异常反应行为有关。对数正态RT模型用于推导用于检测异常RT模式的程序。该方法以变化点的数量和位置作为模型中的参数来检测多个变化点或多个异常行为。给定变化点,可以估计测试中每个片段的相应速度,从而能够更准确地推断异常行为。仿真研究结果表明,该方法能够有效地检测模拟的异常行为,准确地估计变化点。该方法应用于高风险计算机自适应测试的数据,并证明了其适用性。
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引用次数: 0
An Improved Inferential Procedure to Evaluate Item Discriminations in a Conditional Maximum Likelihood Framework 条件最大似然框架中评价项目判别的一种改进推理方法
IF 2.4 3区 心理学 Q2 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2023-07-19 DOI: 10.3102/10769986231183335
Clemens Draxler, A. Kurz, Can Gürer, J. Nolte
A modified and improved inductive inferential approach to evaluate item discriminations in a conditional maximum likelihood and Rasch modeling framework is suggested. The new approach involves the derivation of four hypothesis tests. It implies a linear restriction of the assumed set of probability distributions in the classical approach that represents scenarios of different item discriminations in a straightforward and efficient manner. Its improvement is discussed, compared to classical procedures (tests and information criteria), and illustrated in Monte Carlo experiments as well as real data examples from educational research. The results show an improvement of power of the modified tests of up to 0.3.
提出了一种改进的归纳推理方法,用于在条件最大似然和Rasch建模框架下评估项目判别。新方法涉及四个假设检验的推导。它意味着对经典方法中假设的概率分布集的线性限制,该方法以直接有效的方式表示不同项目判别的场景。与经典程序(测试和信息标准)相比,讨论了它的改进,并在蒙特卡洛实验和教育研究的真实数据示例中进行了说明。结果表明,改进试验的功率提高了0.3。
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引用次数: 0
A Multidimensional Partially Compensatory Response Time Model on Basis of the Log-Normal Distribution 基于对数正态分布的多维部分补偿响应时间模型
IF 2.4 3区 心理学 Q2 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2023-07-11 DOI: 10.3102/10769986231184153
Jochen Ranger, C. König, B. Domingue, Jörg-Tobias Kuhn, Andreas Frey
In the existing multidimensional extensions of the log-normal response time (LNRT) model, the log response times are decomposed into a linear combination of several latent traits. These models are fully compensatory as low levels on traits can be counterbalanced by high levels on other traits. We propose an alternative multidimensional extension of the LNRT model by assuming that the response times can be decomposed into two response time components. Each response time component is generated by a one-dimensional LNRT model with a different latent trait. As the response time components—but not the traits—are related additively, the model is partially compensatory. In a simulation study, we investigate the recovery of the model’s parameters. We also investigate whether the fully and the partially compensatory LNRT model can be distinguished empirically. Findings suggest that parameter recovery is good and that the two models can be distinctly identified under certain conditions. The utility of the model in practice is demonstrated with an empirical application. In the empirical application, the partially compensatory model fits better than the fully compensatory model.
在现有的对数正态响应时间(LNRT)模型的多维扩展中,将对数响应时间分解为多个潜在特征的线性组合。这些模型是完全补偿的,因为低水平的性状可以被高水平的其他性状抵消。我们通过假设响应时间可以分解为两个响应时间组件,提出了LNRT模型的另一种多维扩展。每个反应时间分量由具有不同潜在特征的一维LNRT模型生成。由于响应时间分量(而非特征)是加性相关的,因此该模型具有部分补偿性。在模拟研究中,我们研究了模型参数的恢复。我们还研究了完全代偿和部分代偿的LNRT模型是否可以区分。结果表明,参数恢复良好,在一定条件下,两种模型可以明显识别。通过实例验证了该模型在实际应用中的实用性。在实证应用中,部分补偿模型比完全补偿模型拟合效果更好。
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引用次数: 0
Alternatives to Weighted Item Fit Statistics for Establishing Measurement Invariance in Many Groups 在多组中建立测量不变性的加权项目拟合统计的替代方法
IF 2.4 3区 心理学 Q2 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2023-07-04 DOI: 10.3102/10769986231183326
Sean Joo, Montserrat Valdivia, Dubravka Svetina Valdivia, Leslie Rutkowski
Evaluating scale comparability in international large-scale assessments depends on measurement invariance (MI). The root mean square deviation (RMSD) is a standard method for establishing MI in several programs, such as the Programme for International Student Assessment and the Programme for the International Assessment of Adult Competencies. Previous research showed that the RMSD was unable to detect departures from MI when the latent trait distribution was far from item difficulty. In this study, we developed three alternative approaches to the original RMSD: equal, item information, and b-norm weighted RMSDs. Specifically, we considered the item-centered normalized weight distributions to compute the item characteristic curve difference in the RMSD procedure more efficiently. We further compared all methods’ performance via a simulation study and the item information and b-norm weighted RMSDs showed the most promising results. An empirical example is demonstrated, and implications for researchers are discussed.
在国际大规模评估中评估量表的可比性取决于测量不变性。均方根偏差(RMSD)是几个项目中建立MI的标准方法,如国际学生评估计划和国际成人能力评估计划。先前的研究表明,当潜在特征分布远离项目难度时,RMSD无法检测出MI的偏离。在这项研究中,我们开发了三种替代原始RMSD的方法:相等、项目信息和b-范数加权RMSD。具体来说,我们考虑了以项目为中心的归一化权重分布,以更有效地计算RMSD过程中的项目特征曲线差异。我们通过模拟研究进一步比较了所有方法的性能,项目信息和b-范数加权RMSD显示出最有希望的结果。通过一个实证例子,讨论了对研究者的启示。
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引用次数: 1
Extending an Identified Four-Parameter IRT Model: The Confirmatory Set-4PNO Model 扩展已识别的四参数IRT模型:验证性集合4PNO模型
IF 2.4 3区 心理学 Q2 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2023-07-03 DOI: 10.3102/10769986231181587
Justin L. Kern
Given the frequent presence of slipping and guessing in item responses, models for the inclusion of their effects are highly important. Unfortunately, the most common model for their inclusion, the four-parameter item response theory model, potentially has severe deficiencies related to its possible unidentifiability. With this issue in mind, the dyad four-parameter normal ogive (Dyad-4PNO) model was developed. This model allows for slipping and guessing effects by including binary augmented variables—each indicated by two items whose probabilities are determined by slipping and guessing parameters—which are subsequently related to a continuous latent trait through a two-parameter model. Furthermore, the Dyad-4PNO assumes uncertainty as to which items are paired on each augmented variable. In this way, the model is inherently exploratory. In the current article, the new model, called the Set-4PNO model, is an extension of the Dyad-4PNO in two ways. First, the new model allows for more than two items per augmented variable. Second, these item sets are assumed to be fixed, that is, the model is confirmatory. This article discusses this extension and introduces a Gibbs sampling algorithm to estimate the model. A Monte Carlo simulation study shows the efficacy of the algorithm at estimating the model parameters. A real data example shows that this extension may be viable in practice, with the data fitting a more general Set-4PNO model (i.e., more than two items per augmented variable) better than the Dyad-4PNO, 2PNO, 3PNO, and 4PNO models.
考虑到项目反应中经常出现失误和猜测,纳入其影响的模型非常重要。不幸的是,最常见的包含它们的模型,四参数项目反应理论模型,由于其可能的不可识别性,可能存在严重的缺陷。考虑到这个问题,提出了二元四参数正态ogive(dyad-4PNO)模型。该模型通过包括二元增广变量(每个变量由两个项目表示,其概率由滑动和猜测参数决定)来实现滑动和猜测效应,这些变量随后通过双参数模型与连续的潜在特征相关。此外,Dyad-4PNO假设了每个增广变量上哪些项目配对的不确定性。通过这种方式,该模型本质上是探索性的。在当前的文章中,称为Set-4PNO模型的新模型在两个方面是Dyad-4PNO的扩展。首先,新模型允许每个增广变量包含两个以上的项目。其次,假设这些项目集是固定的,也就是说,模型是可验证的。本文讨论了这种扩展,并介绍了一种吉布斯采样算法来估计模型。蒙特卡罗模拟研究表明了该算法在估计模型参数方面的有效性。一个真实的数据示例表明,这种扩展在实践中可能是可行的,与Dyad-4PNO、2PNO、3PNO和4PNO模型相比,数据更适合更通用的Set-4PNO模型(即,每个增广变量超过两个项目)。
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引用次数: 0
A General Mixture Model for Cognitive Diagnosis 认知诊断的一般混合模型
IF 2.4 3区 心理学 Q2 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2023-06-14 DOI: 10.3102/10769986231176012
Joemari Olea, Kevin Carl P. Santos
Although the generalized deterministic inputs, noisy “and” gate model (G-DINA; de la Torre, 2011) is a general cognitive diagnosis model (CDM), it does not account for the heterogeneity that is rooted from the existing latent groups in the population of examinees. To address this, this study proposes the mixture G-DINA model, a CDM that incorporates the G-DINA model within the finite mixture modeling framework. An expectation–maximization algorithm is developed to estimate the mixture G-DINA model. To determine the viability of the proposed model, an extensive simulation study is conducted to examine the parameter recovery performance, model fit, and correct classification rates. Responses to a reading comprehension assessment were analyzed to further demonstrate the capability of the proposed model.
虽然广义确定性输入,噪声“和”门模型(G-DINA;de la Torre, 2011)是一种通用认知诊断模型(CDM),它没有考虑到考生群体中现有潜在群体的异质性。为了解决这个问题,本研究提出了混合G-DINA模型,这是一种将G-DINA模型纳入有限混合建模框架的清洁发展模型。提出了一种期望最大化算法来估计混合G-DINA模型。为了确定所提出模型的可行性,进行了广泛的模拟研究,以检查参数恢复性能,模型拟合和正确分类率。对阅读理解评估的反应进行了分析,以进一步证明所提出模型的能力。
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引用次数: 0
Bayesian Exploratory Factor Analysis via Gibbs Sampling 基于吉布斯抽样的贝叶斯探索因子分析
IF 2.4 3区 心理学 Q2 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2023-06-13 DOI: 10.3102/10769986231176023
Adrian Quintero, E. Lesaffre, G. Verbeke
Bayesian methods to infer model dimensionality in factor analysis generally assume a lower triangular structure for the factor loadings matrix. Consequently, the ordering of the outcomes influences the results. Therefore, we propose a method to infer model dimensionality without imposing any prior restriction on the loadings matrix. Our approach considers a relatively large number of factors and includes auxiliary multiplicative parameters, which may render null the unnecessary columns in the loadings matrix. The underlying dimensionality is then inferred based on the number of nonnull columns in the factor loadings matrix, and the model parameters are estimated with a postprocessing scheme. The advantages of the method in selecting the correct dimensionality are illustrated via simulations and using real data sets.
贝叶斯方法在因子分析中推断模型维数时,通常假设因子载荷矩阵为下三角结构。因此,结果的顺序会影响结果。因此,我们提出了一种无需对加载矩阵施加任何预先限制即可推断模型维数的方法。我们的方法考虑了相对较多的因素,并包括辅助的乘法参数,这可能会使加载矩阵中不必要的列变为空。然后根据因子加载矩阵中非空列的数量推断底层维度,并使用后处理方案估计模型参数。通过仿真和实际数据集说明了该方法在选择正确维数方面的优势。
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引用次数: 0
Bayesian Estimation of Attribute Hierarchy for Cognitive Diagnosis Models 认知诊断模型属性层次的贝叶斯估计
IF 2.4 3区 心理学 Q2 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2023-06-13 DOI: 10.3102/10769986231174918
Yinghan Chen, Shiyu Wang
Attribute hierarchy, the underlying prerequisite relationship among attributes, plays an important role in applying cognitive diagnosis models (CDM) for designing efficient cognitive diagnostic assessments. However, there are limited statistical tools to directly estimate attribute hierarchy from response data. In this study, we proposed a Bayesian formulation for attribute hierarchy within CDM framework and developed an efficient Metropolis within Gibbs algorithm to estimate the underlying hierarchy along with the specified CDM parameters. Our proposed estimation method is flexible and can be adapted to a general class of CDMs. We demonstrated our proposed method via a simulation study, and the results from which show that the proposed method can fully recover or estimate at least a subgraph of the underlying structure across various conditions under a specified CDM model. The real data application indicates the potential of learning attribute structure from data using our algorithm and validating the existing attribute hierarchy specified by content experts.
属性层次是属性之间潜在的前提关系,在应用认知诊断模型设计高效的认知诊断评估中起着重要作用。然而,从响应数据中直接估计属性层次的统计工具有限。在本研究中,我们提出了CDM框架中属性层次的贝叶斯公式,并开发了一种高效的Metropolis within Gibbs算法来估计底层层次以及指定的CDM参数。我们提出的估计方法是灵活的,可以适用于一般类型的cdm。我们通过模拟研究证明了我们提出的方法,结果表明,在特定的CDM模型下,所提出的方法可以在各种条件下完全恢复或估计至少一个底层结构的子图。实际数据应用表明,使用我们的算法从数据中学习属性结构并验证由内容专家指定的现有属性层次结构的潜力。
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引用次数: 1
Deep Learning Imputation for Asymmetric and Incomplete Likert-Type Items 非对称和不完全Likert型项目的深度学习推断
IF 2.4 3区 心理学 Q2 EDUCATION & EDUCATIONAL RESEARCH Pub Date : 2023-06-13 DOI: 10.3102/10769986231176014
Zachary K. Collier, Minji Kong, Olushola Soyoye, Kamal Chawla, Ann M. Aviles, Y. Payne
Asymmetric Likert-type items in research studies can present several challenges in data analysis, particularly concerning missing data. These items are often characterized by a skewed scaling, where either there is no neutral response option or an unequal number of possible positive and negative responses. The use of conventional techniques, such as discriminant analysis or logistic regression imputation, for handling missing data in asymmetric items may result in significant bias. It is also recommended to exercise caution when employing alternative strategies, such as listwise deletion or mean imputation, because these methods rely on assumptions that are often unrealistic in surveys and rating scales. This article explores the potential of implementing a deep learning-based imputation method. Additionally, we provide access to deep learning-based imputation to a broader group of researchers without requiring advanced machine learning training. We apply the methodology to the Wilmington Street Participatory Action Research Health Project.
研究中的不对称Likert类型项目可能会在数据分析中带来一些挑战,尤其是在缺失数据方面。这些项目的特点往往是比例倾斜,要么没有中立的回应选项,要么可能的积极和消极回应数量不等。使用判别分析或逻辑回归插补等传统技术来处理不对称项目中的缺失数据可能会导致显著的偏差。还建议在使用替代策略时谨慎行事,如列表删除或平均值插补,因为这些方法依赖于在调查和评级量表中往往不切实际的假设。本文探讨了实现基于深度学习的插补方法的潜力。此外,我们为更广泛的研究人员群体提供了基于深度学习的插补,而不需要高级机器学习训练。我们将该方法应用于威尔明顿街参与行动研究健康项目。
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引用次数: 0
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Journal of Educational and Behavioral Statistics
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