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A note on the use of rank-ordered logit models for ordered response categories 关于对有序响应类别使用秩有序logit模型的说明
IF 2.6 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2022-11-03 DOI: 10.1111/bmsp.12292
Timothy R. Johnson

Models for rankings have been shown to produce more efficient estimators than comparable models for first/top choices. The discussions and applications of these models typically only consider unordered alternatives. But these models can be usefully adapted to the case where a respondent ranks a set of ordered alternatives that are ordered response categories. This paper proposes eliciting a rank order that is consistent with the ordering of the response categories, and then modelling the observed rankings using a variant of the rank ordered logit model where the distribution of rankings has been truncated to the set of admissible rankings. This results in lower standard errors in comparison to when only a single top category is selected by the respondents. And the restrictions on the set of admissible rankings reduces the number of decisions needed to be made by respondents in comparison to ranking a set of unordered alternatives. Simulation studies and application examples featuring models based on a stereotype regression model and a rating scale item response model are provided to demonstrate the utility of this approach.

排名模型已被证明比第一/第一选择的可比模型产生更有效的估计器。这些模型的讨论和应用通常只考虑无序的替代方案。但是,这些模型可以有效地适应这样的情况,即被调查者对一组有序的备选方案进行排序,这些备选方案是有序的回答类别。本文提出了一个与响应类别的排序一致的排序顺序,然后使用排序有序logit模型的一种变体对观察到的排名进行建模,其中排名的分布已被截断为可接受的排名集。与被调查者只选择一个顶级类别相比,这导致了更低的标准误差。与对一组无序选择进行排序相比,对可接受排序集的限制减少了受访者需要做出的决策数量。以刻板印象回归模型和评等量表项目反应模型为模型的模拟研究和应用实例,证明了该方法的实用性。
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引用次数: 0
Subtask analysis of process data through a predictive model 通过预测模型对过程数据进行子任务分析
IF 2.6 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2022-11-01 DOI: 10.1111/bmsp.12290
Zhi Wang, Xueying Tang, Jingchen Liu, Zhiliang Ying

Response process data collected from human–computer interactive items contain detailed information about respondents' behavioural patterns and cognitive processes. Such data are valuable sources for analysing respondents' problem-solving strategies. However, the irregular data format and the complex structure make standard statistical tools difficult to apply. This article develops a computationally efficient method for exploratory analysis of such process data. The new approach segments a lengthy individual process into a sequence of short subprocesses to achieve complexity reduction, easy clustering and meaningful interpretation. Each subprocess is considered a subtask. The segmentation is based on sequential action predictability using a parsimonious predictive model combined with the Shannon entropy. Simulation studies are conducted to assess the performance of the new method. We use a case study of PIAAC 2012 to demonstrate how exploratory analysis for process data can be carried out with the new approach.

从人机交互项目中收集的反应过程数据包含有关受访者行为模式和认知过程的详细信息。这些数据是分析受访者解决问题策略的宝贵来源。然而,不规则的数据格式和复杂的结构使标准统计工具难以应用。本文开发了一种计算高效的方法来对此类过程数据进行探索性分析。新方法将一个冗长的单个流程划分为一系列简短的子流程,以实现复杂性降低、易于聚类和有意义的解释。每个子流程都被视为一个子任务。分割是基于序列动作的可预测性,使用简约预测模型和香农熵相结合。为了评估新方法的性能,进行了仿真研究。我们使用PIAC 2012的案例研究来证明如何使用新方法对过程数据进行探索性分析。
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引用次数: 6
Two efficient selection methods for high-dimensional CD-CAT utilizing max-marginals factor from MAP query and ensemble learning approach 利用MAP查询中的最大边际因子和集成学习方法对高维CD-CAT进行高效选择
IF 2.6 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2022-10-26 DOI: 10.1111/bmsp.12288
Fen Luo, Xiaoqing Wang, Yan Cai, Dongbo Tu

Computerized adaptive testing for cognitive diagnosis (CD-CAT) needs to be efficient and responsive in real time to meet practical applications' requirements. For high-dimensional data, the number of categories to be recognized in a test grows exponentially as the number of attributes increases, which can easily cause system reaction time to be too long such that it adversely affects the examinees and thus seriously impacts the measurement efficiency. More importantly, the long-time CPU operations and memory usage of item selection in CD-CAT due to intensive computation are impractical and cannot wholly meet practice needs. This paper proposed two new efficient selection strategies (HIA and CEL) for high-dimensional CD-CAT to address this issue by incorporating the max-marginals from the maximum a posteriori query and integrating the ensemble learning approach into the previous efficient selection methods, respectively. The performance of the proposed selection method was compared with the conventional selection method using simulated and real item pools. The results showed that the proposed methods could significantly improve the measurement efficiency with about 1/2–1/200 of the conventional methods' computation time while retaining similar measurement accuracy. With increasing number of attributes and size of the item pool, the computation time advantage of the proposed methods becomes more significant.

计算机自适应认知诊断测试(CD-CAT)需要高效、实时响应才能满足实际应用的要求。对于高维数据,一次测试中需要识别的类别数量随着属性数量的增加呈指数增长,这很容易导致系统反应时间过长,从而对考生产生不利影响,严重影响测量效率。更重要的是,CD-CAT中由于密集的计算导致的长时间的CPU操作和内存占用是不切实际的,不能完全满足实际需要。为了解决这一问题,本文提出了两种新的高维CD-CAT高效选择策略(HIA和CEL),分别将最大后验查询的最大边际和集成学习方法集成到以前的高效选择方法中。通过模拟和真实项目池,将所提出的选择方法与传统的选择方法进行了性能比较。结果表明,该方法在保持测量精度的前提下,可以显著提高测量效率,计算时间约为传统方法的1/2-1/200。随着属性数量和项目池规模的增加,所提方法的计算时间优势越来越明显。
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引用次数: 0
A new goodness-of-fit measure for probit models: Surrogate R2 probit模型的一个新的拟合优度度量:代理R2
IF 2.6 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2022-10-17 DOI: 10.1111/bmsp.12289
Dungang Liu, Xiaorui Zhu, Brandon Greenwell, Zewei Lin

Probit models are used extensively for inferential purposes in the social sciences as discrete data are prevalent in a vast body of social studies. Among many accompanying model inference problems, a critical question remains unsettled: how to develop a goodness-of-fit measure that resembles the ordinary least square (OLS) R2 used for linear models. Such a measure has long been sought to achieve ‘comparability’ of different empirical models across multiple samples addressing similar social questions. To this end, we propose a novel R2 measure for probit models using the notion of surrogacy – simulating a continuous variable S as a surrogate of the original discrete response (Liu & Zhang, Journal of the American Statistical Association, 113, 845 and 2018). The proposed R2 is the proportion of the variance of the surrogate response explained by explanatory variables through a linear model, and we call it a surrogate R2. This paper shows both theoretically and numerically that the surrogate R2 approximates the OLS R2 based on the latent continuous variable, preserves the interpretation of explained variation, and maintains monotonicity between nested models. As no other pseudo R2, McKelvey and Zavoina's and McFadden's included, can meet all the three criteria simultaneously, our measure fills this crucial void in probit model inference.

Probit模型在社会科学中被广泛用于推理目的,因为离散数据在大量社会研究中普遍存在。在许多伴随的模型推理问题中,一个关键问题仍未解决:如何开发一个类似于用于线性模型的普通最小二乘(OLS)R2的拟合优度度量。长期以来,人们一直在寻求这样一种衡量标准,以实现解决类似社会问题的多个样本中不同实证模型的“可比性”。为此,我们使用代孕的概念为probit模型提出了一种新的R2度量——模拟连续变量S作为原始离散响应的代孕(Liu&;Zhang,Journal of the American Statistical Association,113845 and 2018)。所提出的R2是通过线性模型由解释变量解释的替代响应的方差的比例,我们称之为替代R2。本文从理论和数值上表明,代理R2基于潜在连续变量近似OLS R2,保留了对解释变化的解释,并保持了嵌套模型之间的单调性。由于没有其他伪R2,包括McKelvey和Zavoina的以及McFadden的,能够同时满足所有三个标准,我们的度量填补了probit模型推理中的这一关键空白。
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引用次数: 4
Penalization approaches in the conditional maximum likelihood and Rasch modelling context 条件最大似然和Rasch模型情境下的惩罚方法
IF 2.6 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2022-09-14 DOI: 10.1111/bmsp.12287
Can Gürer, Clemens Draxler

Recent detection methods for Differential Item Functioning (DIF) include approaches like Rasch Trees, DIFlasso, GPCMlasso and Item Focussed Trees, all of which - in contrast to well established methods - can handle metric covariates inducing DIF. A new estimation method shall address their downsides by mainly aiming at combining three central virtues: the use of conditional likelihood for estimation, the incorporation of linear influence of metric covariates on item difficulty and the possibility to detect different DIF types: certain items showing DIF, certain covariates inducing DIF, or certain covariates inducing DIF in certain items. Each of the approaches mentioned lacks in two of these aspects. We introduce a method for DIF detection, which firstly utilizes the conditional likelihood for estimation combined with group Lasso-penalization for item or variable selection and L1-penalization for interaction selection, secondly incorporates linear effects instead of approximation through step functions, and thirdly provides the possibility to investigate any of the three DIF types. The method is described theoretically, challenges in implementation are discussed. A dataset is analysed for all DIF types and shows comparable results between methods. Simulation studies per DIF type reveal competitive performance of cmlDIFlasso, particularly when selecting interactions in case of large sample sizes and numbers of parameters. Coupled with low computation times, cmlDIFlasso seems a worthwhile option for applied DIF detection.

差分项功能(DIF)的最新检测方法包括Rasch树、DIFlasso、GPCMlasso和Item Focussed树等方法,与已有的方法相比,所有这些方法都可以处理引起DIF的度量协变量。一种新的估计方法应该解决它们的缺点,主要针对结合三个核心优点:使用条件似然进行估计,纳入度量协变量对项目难度的线性影响,以及检测不同DIF类型的可能性:某些项目显示DIF,某些协变量诱发DIF,或某些项目中某些协变量诱发DIF。所提到的每一种方法都缺少这两个方面。本文提出了一种DIF检测方法,该方法首先利用条件似然法进行估计,结合项目或变量选择的群体laso惩罚和交互选择的l1惩罚,其次采用线性效应代替步长函数逼近,第三种方法提供了研究三种DIF类型中的任何一种的可能性。对该方法进行了理论描述,并讨论了实现中存在的问题。对所有DIF类型的数据集进行分析,并显示方法之间的可比结果。每种DIF类型的仿真研究揭示了cmlDIFlasso具有竞争力的性能,特别是在选择大样本量和参数数量的相互作用时。加上较低的计算时间,cmlDIFlasso似乎是应用DIF检测的值得选择。
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引用次数: 2
Ordinal state-trait regression for intensive longitudinal data 密集纵向数据的有序状态-特征回归
IF 2.6 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2022-09-08 DOI: 10.1111/bmsp.12285
Prince P. Osei, Philip T. Reiss

In many psychological studies, in particular those conducted by experience sampling, mental states are measured repeatedly for each participant. Such a design allows for regression models that separate between- from within-person, or trait-like from state-like, components of association between two variables. But these models are typically designed for continuous variables, whereas mental state variables are most often measured on an ordinal scale. In this paper we develop a model for disaggregating between- from within-person effects of one ordinal variable on another. As in standard ordinal regression, our model posits a continuous latent response whose value determines the observed response. We allow the latent response to depend nonlinearly on the trait and state variables, but impose a novel penalty that shrinks the fit towards a linear model on the latent scale. A simulation study shows that this penalization approach is effective at finding a middle ground between an overly restrictive linear model and an overfitted nonlinear model. The proposed method is illustrated with an application to data from the experience sampling study of Baumeister et al. (2020, Personality and Social Psychology Bulletin, 46, 1631).

在许多心理学研究中,特别是那些通过经验抽样进行的研究,反复测量每个参与者的心理状态。这样的设计允许回归模型将两个变量之间的关联成分从人与人之间,或特征与状态之间分离开来。但这些模型通常是为连续变量设计的,而心理状态变量通常是在有序尺度上测量的。在本文中,我们建立了一个模型来分解一个序数变量对另一个序数变量的人与人之间的影响。与标准有序回归一样,我们的模型假设一个连续的潜在响应,其值决定了观察到的响应。我们允许潜在反应非线性地依赖于特征和状态变量,但施加了一个新的惩罚,在潜在尺度上缩小了对线性模型的拟合。仿真研究表明,这种惩罚方法可以有效地在过度限制的线性模型和过度拟合的非线性模型之间找到一个中间地带。Baumeister等人(2020,Personality and Social Psychology Bulletin, 46, 1631)的经验抽样研究数据说明了该方法的应用。
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引用次数: 0
Compromised item detection: A Bayesian change-point perspective 折衷项目检测:贝叶斯变更点视角
IF 2.6 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2022-09-07 DOI: 10.1111/bmsp.12286
Yang Du, Susu Zhang, Hua-Hua Chang

Psychometric methods for accurate and timely detection of item compromise have been a long-standing topic. While Bayesian methods can incorporate prior knowledge or expert inputs as additional information for item compromise detection, they have not been employed in item compromise detection itself. The current study proposes a two-phase Bayesian change-point framework for both stationary and real-time detection of changes in each item's compromise status. In Phase I, a stationary Bayesian change-point model for compromise detection is fitted to the observed responses over a specified time-frame. The model produces parameter estimates for the change-point of each item from uncompromised to compromised, as well as structural parameters accounting for the post-change response distribution. Using the post-change model identified in Phase I, the Shiryaev procedure for sequential testing is employed in Phase II for real-time monitoring of item compromise. The proposed methods are evaluated in terms of parameter recovery, detection accuracy, and detection efficiency under various simulation conditions and in a real data example. The proposed method also showed superior detection accuracy and efficiency compared to the cumulative sum procedure.

准确和及时地检测项目妥协的心理测量方法一直是一个长期存在的话题。虽然贝叶斯方法可以将先验知识或专家输入作为附加信息用于物品折衷检测,但它们尚未被用于物品折衷检测本身。目前的研究提出了一个两阶段的贝叶斯变化点框架,用于固定和实时检测每个项目妥协状态的变化。在第一阶段,一个平稳的贝叶斯变化点模型的妥协检测拟合观察响应在一个特定的时间框架。该模型产生了每个项目从未受损到受损的变化点的参数估计,以及反映变化后响应分布的结构参数。采用第一阶段确定的后变化模型,第二阶段采用顺序测试的Shiryaev程序对项目妥协进行实时监测。在不同的仿真条件和实际数据实例下,从参数恢复、检测精度和检测效率三个方面对所提方法进行了评价。与累积求和法相比,该方法具有更高的检测精度和效率。
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引用次数: 1
The biasing effects of selection and attrition on estimating the mean 选择和损耗对估计平均值的偏置效应
IF 2.6 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2022-08-07 DOI: 10.1111/bmsp.12284
Seunghoo Lee, Jorge Mendoza

Organizational and validation researchers often work with data that has been subjected to selection on the predictor and attrition on the criterion. These researchers often use the data observed under these conditions to estimate either the predictor or criterion's restricted population means. We show that the restricted means due to direct or indirect selection are a function of the population means plus the selection ratios. Thus, any difference between selected mean groups reflects the population difference plus the selection ratio difference. When there is also attrition on the criterion, the estimation of group differences becomes even more complicated. The effect of selection and attrition induces measurement bias when estimating the restricted population mean of either the predictor or criterion. A sample mean observed under selection and attrition does not estimate either the population mean or the restricted population mean. We propose several procedures under normality that yield unbiased estimates of the mean. The procedures focus on correcting the effects of selection and attrition. Each procedure was evaluated with a Monte Carlo simulation to ascertain its strengths and weaknesses. Given appropriate sample size and conditions, we show that these procedures yield unbiased estimators of the restricted and unrestricted population means for both predictor and criterion. We also show how our findings have implications for replicating selected group differences.

组织和验证研究人员经常使用的数据已经受到选择的预测和损耗的标准。这些研究人员经常使用在这些条件下观察到的数据来估计预测器或标准的限制种群均值。我们证明了由于直接或间接选择而产生的有限均值是总体均值加上选择比率的函数。因此,所选平均组之间的任何差异反映了总体差异加上选择比率差异。当标准也存在损耗时,对群体差异的估计就变得更加复杂了。在估计预测器或标准的限制种群均值时,选择和损耗的影响会引起测量偏差。在选择和损耗下观察到的样本均值既不能估计总体均值,也不能估计受限总体均值。我们提出了几种在正态性下产生无偏均值估计的方法。程序的重点是纠正选择和流失的影响。每个程序都用蒙特卡罗模拟进行评估,以确定其优点和缺点。给定适当的样本量和条件,我们表明,这些程序产生无偏估计的限制和不受限制的人口意味着对预测器和标准。我们还展示了我们的发现如何对复制选定的群体差异产生影响。
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引用次数: 0
CD-polytomous knowledge spaces and corresponding polytomous surmise systems cd -多分知识空间和相应的多分猜测系统
IF 2.6 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2022-07-29 DOI: 10.1111/bmsp.12283
Bo Wang, Jinjin Li, Wen Sun

Heller (2021) generalized quasi-ordinal knowledge spaces to polytomous items. Inspired by this paper, we propose CD-polytomous knowledge space and its polytomous surmise system. A Galois connection is established between the collection K of all polytomous knowledge structures and the collection F1 of particular polytomous attribute functions. The closed elements of the Galois connection are CD-polytomous knowledge spaces in K and polytomous surmise functions in F1, respectively. With the help of these, this paper provides a characterization of the polytomous knowledge structure corresponding to the polytomous surmise function that is weakly factorial. Based on the finite sets of items and response values, these results generalize the previous approaches for polytomous knowledge spaces.

Heller(2021)将拟序知识空间推广到多同构项目。受本文启发,我们提出了cd -多同构知识空间及其多同构猜测系统。在所有多同构知识结构的集合K和特定多同构属性函数的集合f1之间建立了伽罗瓦连接。伽罗瓦连接的封闭元素分别是K中的cd -多同构知识空间和f1中的多同构猜测函数。在此基础上,本文给出了对应于弱阶乘的多析猜测函数的多析知识结构的表征。基于项目和响应值的有限集合,这些结果推广了先前的多聚知识空间方法。
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引用次数: 7
Item selection methods with exposure and time control for computerized classification test 计算机分类测验中具有曝光和时间控制的选题方法
IF 2.6 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2022-07-15 DOI: 10.1111/bmsp.12281
Yingshi Huang, He Ren, Ping Chen

Computerized classification testing (CCT) commonly chooses items maximizing information at the cut score, which yields the most information for decision-making. However, a corollary problem is that all examinees will be given the same set of items, resulting in high test overlap rate and unbalanced item bank usage, which threatens test security. Moreover, another pivotal issue for CCT is time control. Since both the extremely long response time (RT) and large RT variability across examinees intensify time-induced anxiety, it is crucial to reduce the number of examinees exceeding the time limitation and the differences between examinees' test-taking times. To satisfy these practical needs, this paper proposes the novel idea of stage adaptiveness to tailor the item selection process to the decision-making requirement in each step and generate fresh insight into the existing response time selection method. Results indicate that a balanced item usage as well as short and stable test times across examinees can be achieved via the new methods.

计算机分类测试(CCT)通常选择在分值上信息最大化的项目,这为决策提供了最多的信息。然而,随之而来的一个问题是,所有考生都将被分配相同的考题,导致考试重叠率高,题库使用不平衡,威胁到考试的安全性。此外,CCT的另一个关键问题是时间控制。由于超长的反应时间和较大的反应时间变异性会加剧考生的时间焦虑,因此减少超长的考生数量和考生之间的应试时间差异至关重要。为了满足这些实际需求,本文提出了阶段适应性的新思想,将项目选择过程定制为每个步骤的决策需求,并对现有的响应时间选择方法产生新的见解。结果表明,通过新方法,考生可以实现平衡的项目使用以及短而稳定的考试时间。
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引用次数: 0
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British Journal of Mathematical & Statistical Psychology
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