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DIF Analysis with Unknown Groups and Anchor Items. 使用未知组和锚项进行 DIF 分析。
IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-03-01 Epub Date: 2024-02-21 DOI: 10.1007/s11336-024-09948-7
Gabriel Wallin, Yunxiao Chen, Irini Moustaki

Ensuring fairness in instruments like survey questionnaires or educational tests is crucial. One way to address this is by a Differential Item Functioning (DIF) analysis, which examines if different subgroups respond differently to a particular item, controlling for their overall latent construct level. DIF analysis is typically conducted to assess measurement invariance at the item level. Traditional DIF analysis methods require knowing the comparison groups (reference and focal groups) and anchor items (a subset of DIF-free items). Such prior knowledge may not always be available, and psychometric methods have been proposed for DIF analysis when one piece of information is unknown. More specifically, when the comparison groups are unknown while anchor items are known, latent DIF analysis methods have been proposed that estimate the unknown groups by latent classes. When anchor items are unknown while comparison groups are known, methods have also been proposed, typically under a sparsity assumption - the number of DIF items is not too large. However, DIF analysis when both pieces of information are unknown has not received much attention. This paper proposes a general statistical framework under this setting. In the proposed framework, we model the unknown groups by latent classes and introduce item-specific DIF parameters to capture the DIF effects. Assuming the number of DIF items is relatively small, an L 1 -regularised estimator is proposed to simultaneously identify the latent classes and the DIF items. A computationally efficient Expectation-Maximisation (EM) algorithm is developed to solve the non-smooth optimisation problem for the regularised estimator. The performance of the proposed method is evaluated by simulation studies and an application to item response data from a real-world educational test.

确保调查问卷或教育测试等工具的公平性至关重要。解决这一问题的方法之一是进行差异项目功能(DIF)分析,即在控制其总体潜在构念水平的情况下,检查不同的子群体对特定项目的反应是否不同。DIF 分析通常用于评估项目层面的测量不变性。传统的 DIF 分析方法需要了解比较组(参照组和重点组)和锚项目(无 DIF 项目的子集)。这种先验知识并不总是可用的,因此有人提出了在未知信息的情况下进行 DIF 分析的心理测量方法。更具体地说,当比较组未知而锚项目已知时,已提出了通过潜在类别估计未知组的潜在 DIF 分析方法。当锚定项未知而对比组已知时,也有一些方法被提出,通常是在稀疏性假设下提出的--DIF 项的数量不会太多。然而,当两个信息都未知时的 DIF 分析还没有得到广泛关注。本文提出了这种情况下的一般统计框架。在所提出的框架中,我们用潜在类对未知组进行建模,并引入特定项目的 DIF 参数来捕捉 DIF 效果。假设 DIF 项目的数量相对较少,我们提出了一种[公式:见正文]正则化估计器来同时识别潜类和 DIF 项目。为解决正则化估计器的非平滑优化问题,开发了一种计算效率高的期望最大化(EM)算法。通过模拟研究和应用真实世界教育测试的项目响应数据,对所提方法的性能进行了评估。
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引用次数: 0
Book Review Computational Aspects of Psychometric Methods by Martinková & Hladká. 书评 Martinková & Hladká 著《心理测量方法的计算方面》。
IF 3 2区 心理学 Q2 Mathematics Pub Date : 2024-03-01 DOI: 10.1007/s11336-024-09954-9
Zhiqing Lin, Huilin Chen

As reported by Martinková, P., & Hladká, A. (Computational Aspects of Psychometric Methods: With R. Boca Raton, CRC Press, FL, 2023) Computational Aspects of Psychometric Methods: With R. Boca Raton, FL: CRC Press.

Martinková, P., & Hladká, A. (Computational Aspects of Psychometric Methods:With R. Boca Raton, CRC Press, FL, 2023)《心理测量方法的计算方面》:With R. Boca Raton, FL:CRC Press.
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引用次数: 0
A Multidimensional Model to Facilitate Within Person Comparison of Attributes. 促进人内属性比较的多维模型。
IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-03-01 Epub Date: 2024-02-08 DOI: 10.1007/s11336-023-09946-1
Mark L Davison, Seungwon Chung, Nidhi Kohli, Ernest C Davenport

In psychological research and practice, a person's scores on two different traits or abilities are often compared. Such within-person comparisons require that measurements have equal units (EU) and/or equal origins: an assumption rarely validated. We describe a multidimensional SEM/IRT model from the literature and, using principles of conjoint measurement, show that its expected response variables satisfy the axioms of additive conjoint measurement for measurement on a common scale. In an application to Quality of Life data, the EU analysis is used as a pre-processing step to derive a simple structure Quality of Life model with three dimensions expressed in equal units. The results are used to address questions that can only be addressed by scores expressed in equal units. When the EU model fits the data, scores in the corresponding simple structure model will have added validity in that they can address questions that cannot otherwise be addressed. Limitations and the need for further research are discussed.

在心理学研究和实践中,经常会比较一个人在两种不同特质或能力上的得分。这种人与人之间的比较要求测量具有相等的单位(EU)和/或相等的起源:这一假设很少得到验证。我们描述了文献中的一个多维 SEM/IRT 模型,并利用联合测量的原理,证明其预期响应变量满足在一个共同量表上进行测量的加法联合测量公理。在对生活质量数据的应用中,欧盟分析被用作一个预处理步骤,以推导出一个简单结构的生活质量模型,该模型有三个维度,以等量单位表示。分析结果可用于解决只有用等量单位表示的分数才能解决的问题。当欧盟模型与数据相匹配时,相应的简单结构模型中的分数将具有更高的有效性,因为它们可以解决那些无法以其他方式解决的问题。本文讨论了局限性和进一步研究的必要性。
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引用次数: 0
Psychometric Society Meeting of the Members University of Maryland College Park, Maryland July 28, 2023. 马里兰大学学院帕克分校心理测量协会会员会议,马里兰州,2023 年 7 月 28 日。
IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-03-01 DOI: 10.1007/s11336-023-09943-4
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引用次数: 0
A Note on Improving Variational Estimation for Multidimensional Item Response Theory. 改进多维项目反应理论的变分估计。
IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-03-01 Epub Date: 2023-11-18 DOI: 10.1007/s11336-023-09939-0
Chenchen Ma, Jing Ouyang, Chun Wang, Gongjun Xu

Survey instruments and assessments are frequently used in many domains of social science. When the constructs that these assessments try to measure become multifaceted, multidimensional item response theory (MIRT) provides a unified framework and convenient statistical tool for item analysis, calibration, and scoring. However, the computational challenge of estimating MIRT models prohibits its wide use because many of the extant methods can hardly provide results in a realistic time frame when the number of dimensions, sample size, and test length are large. Instead, variational estimation methods, such as Gaussian variational expectation-maximization (GVEM) algorithm, have been recently proposed to solve the estimation challenge by providing a fast and accurate solution. However, results have shown that variational estimation methods may produce some bias on discrimination parameters during confirmatory model estimation, and this note proposes an importance-weighted version of GVEM (i.e., IW-GVEM) to correct for such bias under MIRT models. We also use the adaptive moment estimation method to update the learning rate for gradient descent automatically. Our simulations show that IW-GVEM can effectively correct bias with modest increase of computation time, compared with GVEM. The proposed method may also shed light on improving the variational estimation for other psychometrics models.

社会科学的许多领域经常使用调查工具和评估。当这些评估试图测量的结构变得多方面时,多维项目反应理论(MIRT)为项目分析、校准和评分提供了一个统一的框架和方便的统计工具。然而,估计MIRT模型的计算挑战阻碍了它的广泛使用,因为当维度数量、样本量和测试长度很大时,许多现有的方法很难在现实的时间框架内提供结果。相反,变分估计方法,如高斯变分期望最大化(GVEM)算法,最近被提出,通过提供快速和准确的解决方案来解决估计挑战。然而,结果表明,变分估计方法在验证性模型估计中可能会对判别参数产生一定的偏差,本文提出了一个重要加权版的GVEM(即IW-GVEM)来纠正MIRT模型下的这种偏差。我们还使用自适应矩估计方法来自动更新梯度下降的学习率。仿真结果表明,与GVEM相比,IW-GVEM可以在不增加计算时间的情况下有效地校正偏置。该方法对其他心理测量模型的变分估计也有一定的借鉴意义。
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引用次数: 0
Generalized Structured Component Analysis Accommodating Convex Components: A Knowledge-Based Multivariate Method with Interpretable Composite Indexes. 适应凸成分的广义结构成分分析:基于知识的多元方法与可解释的综合指数
IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-03-01 Epub Date: 2024-02-16 DOI: 10.1007/s11336-023-09944-3
Gyeongcheol Cho, Heungsun Hwang

Generalized structured component analysis (GSCA) is a multivariate method for examining theory-driven relationships between variables including components. GSCA can provide the deterministic component score for each individual once model parameters are estimated. As the traditional GSCA always standardizes all indicators and components, however, it could not utilize information on the indicators' scale in parameter estimation. Consequently, its component scores could just show the relative standing of each individual for a component, rather than the individual's absolute standing in terms of the original indicators' measurement scales. In the paper, we propose a new version of GSCA, named convex GSCA, which can produce a new type of unstandardized components, termed convex components, which can be intuitively interpreted in terms of the original indicators' scales. We investigate the empirical performance of the proposed method through the analyses of simulated and real data.

广义结构成分分析(GSCA)是一种多变量方法,用于研究包括成分在内的变量之间的理论驱动关系。在估算出模型参数后,GSCA 可以提供每个个体的确定性成分得分。然而,由于传统的 GSCA 总是将所有指标和成分标准化,因此在参数估计时无法利用指标的尺度信息。因此,其成分得分只能显示每个个体在某一成分中的相对地位,而不是个体在原始指标测量尺度中的绝对地位。在本文中,我们提出了一种新版本的 GSCA,称为凸 GSCA,它可以产生一种新型的非标准化分量,称为凸分量,这种分量可以直观地从原始指标量表的角度进行解释。我们通过对模拟数据和真实数据的分析,研究了所提方法的实证性能。
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引用次数: 0
A Latent Hidden Markov Model for Process Data. 过程数据的潜在隐马尔可夫模型。
IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-03-01 Epub Date: 2023-11-07 DOI: 10.1007/s11336-023-09938-1
Xueying Tang

Response process data from computer-based problem-solving items describe respondents' problem-solving processes as sequences of actions. Such data provide a valuable source for understanding respondents' problem-solving behaviors. Recently, data-driven feature extraction methods have been developed to compress the information in unstructured process data into relatively low-dimensional features. Although the extracted features can be used as covariates in regression or other models to understand respondents' response behaviors, the results are often not easy to interpret since the relationship between the extracted features, and the original response process is often not explicitly defined. In this paper, we propose a statistical model for describing response processes and how they vary across respondents. The proposed model assumes a response process follows a hidden Markov model given the respondent's latent traits. The structure of hidden Markov models resembles problem-solving processes, with the hidden states interpreted as problem-solving subtasks or stages. Incorporating the latent traits in hidden Markov models enables us to characterize the heterogeneity of response processes across respondents in a parsimonious and interpretable way. We demonstrate the performance of the proposed model through simulation experiments and case studies of PISA process data.

基于计算机的问题解决项目的反应过程数据将受访者的问题解决过程描述为一系列行动。这些数据为了解受访者解决问题的行为提供了有价值的来源。最近,已经开发了数据驱动的特征提取方法来将非结构化过程数据中的信息压缩成相对低维的特征。尽管提取的特征可以作为回归或其他模型中的协变量来理解受访者的反应行为,但由于提取的特征和原始反应过程之间的关系往往没有明确定义,因此结果通常不容易解释。在本文中,我们提出了一个统计模型来描述响应过程以及它们在受访者中的变化。所提出的模型假设响应过程遵循隐马尔可夫模型,给定被调查者的潜在特征。隐马尔可夫模型的结构类似于解决问题的过程,隐藏状态被解释为解决问题的子任务或阶段。将潜在特征纳入隐马尔可夫模型使我们能够以一种简洁和可解释的方式来表征受访者之间反应过程的异质性。我们通过模拟实验和PISA过程数据的案例研究来证明所提出的模型的性能。
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引用次数: 0
Adjusted Residuals for Evaluating Conditional Independence in IRT Models for Multistage Adaptive Testing. 用于评估多级自适应测试的IRT模型中条件独立性的调整残差。
IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-03-01 Epub Date: 2023-11-06 DOI: 10.1007/s11336-023-09935-4
Peter W van Rijn, Usama S Ali, Hyo Jeong Shin, Sean-Hwane Joo

The key assumption of conditional independence of item responses given latent ability in item response theory (IRT) models is addressed for multistage adaptive testing (MST) designs. Routing decisions in MST designs can cause patterns in the data that are not accounted for by the IRT model. This phenomenon relates to quasi-independence in log-linear models for incomplete contingency tables and impacts certain types of statistical inference based on assumptions on observed and missing data. We demonstrate that generalized residuals for item pair frequencies under IRT models as discussed by Haberman and Sinharay (J Am Stat Assoc 108:1435-1444, 2013. https://doi.org/10.1080/01621459.2013.835660 ) are inappropriate for MST data without adjustments. The adjustments are dependent on the MST design, and can quickly become nontrivial as the complexity of the routing increases. However, the adjusted residuals are found to have satisfactory Type I errors in a simulation and illustrated by an application to real MST data from the Programme for International Student Assessment (PISA). Implications and suggestions for statistical inference with MST designs are discussed.

在项目反应理论(IRT)模型中,针对多级自适应测试(MST)设计,提出了在给定潜在能力的情况下,项目反应条件独立性的关键假设。MST设计中的路由决策可能导致IRT模型未考虑的数据模式。这种现象与不完整列联表的对数线性模型的准独立性有关,并影响基于对观测到和缺失数据的假设的某些类型的统计推断。我们证明了Haberman和Sinharay(J Am Stat Assoc 108:1435-14442013)讨论的IRT模型下项目对频率的广义残差。https://doi.org/10.1080/01621459.2013.835660)不适用于未经调整的MST数据。调整取决于MST设计,并且随着路由的复杂性增加,调整可能很快变得不重要。然而,在模拟中发现调整后的残差具有令人满意的I型误差,并通过国际学生评估计划(PISA)对真实MST数据的应用进行了说明。讨论了MST设计对统计推断的启示和建议。
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引用次数: 0
Going Deep in Diagnostic Modeling: Deep Cognitive Diagnostic Models (DeepCDMs). 深入诊断模型:深度认知诊断模型(DeepCDMs)。
IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-03-01 Epub Date: 2023-12-11 DOI: 10.1007/s11336-023-09941-6
Yuqi Gu

Cognitive diagnostic models (CDMs) are discrete latent variable models popular in educational and psychological measurement. In this work, motivated by the advantages of deep generative modeling and by identifiability considerations, we propose a new family of DeepCDMs, to hunt for deep discrete diagnostic information. The new class of models enjoys nice properties of identifiability, parsimony, and interpretability. Mathematically, DeepCDMs are entirely identifiable, including even fully exploratory settings and allowing to uniquely identify the parameters and discrete loading structures (the " Q -matrices") at all different depths in the generative model. Statistically, DeepCDMs are parsimonious, because they can use a relatively small number of parameters to expressively model data thanks to the depth. Practically, DeepCDMs are interpretable, because the shrinking-ladder-shaped deep architecture can capture cognitive concepts and provide multi-granularity skill diagnoses from coarse to fine grained and from high level to detailed. For identifiability, we establish transparent identifiability conditions for various DeepCDMs. Our conditions impose intuitive constraints on the structures of the multiple Q -matrices and inspire a generative graph with increasingly smaller latent layers when going deeper. For estimation and computation, we focus on the confirmatory setting with known Q -matrices and develop Bayesian formulations and efficient Gibbs sampling algorithms. Simulation studies and an application to the TIMSS 2019 math assessment data demonstrate the usefulness of the proposed methodology.

认知诊断模型(CDMs)是一种离散潜变量模型,在教育和心理测量中非常流行。在这项工作中,基于深度生成模型的优势和可识别性的考虑,我们提出了一个新的 DeepCDMs 系列,以寻找深度离散诊断信息。这一类新模型具有良好的可识别性、简约性和可解释性。在数学上,DeepCDMs 是完全可识别的,甚至包括完全探索性的设置,并允许唯一识别生成模型中所有不同深度的参数和离散负载结构("[公式:见正文]-矩阵")。从统计学角度看,DeepCDMs 是简洁的,因为它们可以使用相对较少的参数来表达数据模型,这要归功于深度。实际上,DeepCDM 是可解释的,因为收缩阶梯状的深度架构可以捕捉认知概念,并提供从粗粒度到细粒度、从高层次到细节的多粒度技能诊断。在可识别性方面,我们为各种 DeepCDM 建立了透明的可识别性条件。我们的条件对多个[公式:见正文]矩阵的结构施加了直观的约束,并启发了一个生成图,当深入时,潜在层越来越小。在估计和计算方面,我们将重点放在已知[公式:见正文]-矩阵的确证设置上,并开发了贝叶斯公式和高效的吉布斯采样算法。模拟研究和对 TIMSS 2019 数学评估数据的应用证明了所提方法的实用性。
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引用次数: 0
Nodal Heterogeneity can Induce Ghost Triadic Effects in Relational Event Models. 节点异质性可诱发关系事件模型中的幽灵三联效应
IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-03-01 Epub Date: 2024-03-06 DOI: 10.1007/s11336-024-09952-x
Rūta Juozaitienė, Ernst C Wit

Temporal network data is often encoded as time-stamped interaction events between senders and receivers, such as co-authoring scientific articles or communication via email. A number of relational event frameworks have been proposed to address specific issues raised by complex temporal dependencies. These models attempt to quantify how individual behaviour, endogenous and exogenous factors, as well as interactions with other individuals modify the network dynamics over time. It is often of interest to determine whether changes in the network can be attributed to endogenous mechanisms reflecting natural relational tendencies, such as reciprocity or triadic effects. The propensity to form or receive ties can also, at least partially, be related to actor attributes. Nodal heterogeneity in the network is often modelled by including actor-specific or dyadic covariates. However, comprehensively capturing all personality traits is difficult in practice, if not impossible. A failure to account for heterogeneity may confound the substantive effect of key variables of interest. This work shows that failing to account for node level sender and receiver effects can induce ghost triadic effects. We propose a random-effect extension of the relational event model to deal with these problems. We show that it is often effective over more traditional approaches, such as in-degree and out-degree statistics. These results that the violation of the hierarchy principle due to insufficient information about nodal heterogeneity can be resolved by including random effects in the relational event model as a standard.

时态网络数据通常被编码为发送方和接收方之间有时间戳的交互事件,例如共同撰写科学文章或通过电子邮件进行通信。为了解决复杂的时间依赖性带来的具体问题,人们提出了许多关系事件框架。这些模型试图量化个人行为、内生和外生因素以及与其他个人的互动是如何随着时间的推移改变网络动态的。确定网络中的变化是否可归因于反映自然关系倾向(如互惠或三方效应)的内生机制往往是令人感兴趣的。建立或接受联系的倾向也可能(至少部分地)与参与者的属性有关。网络中的节点异质性通常是通过加入特定行为者或二元协变量来建模的。然而,在实践中要全面捕捉所有个性特征是很困难的,甚至是不可能的。不考虑异质性可能会混淆关键变量的实质性影响。这项研究表明,如果不考虑节点层面的发送者和接收者效应,就会诱发幽灵三元效应。我们提出了关系事件模型的随机效应扩展来解决这些问题。我们的研究结果表明,这种方法通常比更传统的方法(如内度和外度统计)更有效。这些结果表明,在关系事件模型中加入随机效应作为标准,可以解决由于节点异质性信息不足而导致的违反层次原则的问题。
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引用次数: 0
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Psychometrika
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