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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 Q1 Mathematics 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 Q1 Mathematics 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 Q1 Mathematics 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 Q1 Mathematics 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 Q1 Mathematics 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
Modelling multiple problem-solving strategies and strategy shift in cognitive diagnosis for growth 多问题解决策略建模与成长认知诊断中的策略转换
IF 2.6 3区 心理学 Q1 Mathematics Pub Date : 2022-07-10 DOI: 10.1111/bmsp.12280
Manqian Liao, Hong Jiao

Problem-solving strategies, defined as actions people select intentionally to achieve desired objectives, are distinguished from skills that are implemented unintentionally. In education, strategy-oriented instructions that guide students to form problem-solving strategies are found to be more effective for low-achieving students than the skill-oriented instructions designed for enhancing their skill implementation ability. Although the existing longitudinal cognitive diagnosis models (CDMs) can model the change in students' dynamic skill mastery status over time, they are not designed to model the shift in students' problem-solving strategies. This study proposes a longitudinal CDM that considers both between-person multiple strategies and within-person strategy shift. The model, separating the strategy choice process from the skill implementation process, is intended to provide diagnostic information on strategy choice as well as skill mastery status. A simulation study is conducted to evaluate the parameter recovery of the proposed model and investigate the consequences of ignoring the presence of multiple strategies or strategy shift. Further, an empirical data analysis is conducted to illustrate the use of the proposed model to measure strategy shift, growth in skill implementation ability and skill mastery status.

问题解决策略被定义为人们为实现预期目标而有意选择的行动,与无意中实施的技能不同。在教育方面,指导学生形成问题解决策略的策略导向指导比旨在提高学生技能实施能力的技能导向指导更有效。虽然现有的纵向认知诊断模型(CDMs)可以模拟学生动态技能掌握状态随时间的变化,但它们并不能模拟学生问题解决策略的变化。本研究提出了一种纵向清洁发展机制,考虑了人与人之间的多重策略和人与人之间的策略转移。该模型将策略选择过程与技能实施过程分离,旨在提供关于策略选择和技能掌握状态的诊断信息。通过仿真研究来评估所提出模型的参数恢复,并研究忽略多种策略或策略转移存在的后果。此外,实证数据分析表明,该模型可用于衡量战略转移、技能实施能力增长和技能掌握状况。
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引用次数: 0
Flexible Bayesian modelling in dichotomous item response theory using mixtures of skewed item curves 基于混合倾斜项目曲线的二分类项目反应理论中的灵活贝叶斯建模
IF 2.6 3区 心理学 Q1 Mathematics Pub Date : 2022-07-05 DOI: 10.1111/bmsp.12282
Flávio B. Gonçalves, Juliane Venturelli S. L., Rosangela H. Loschi

Most item response theory (IRT) models for dichotomous responses are based on probit or logit link functions which assume a symmetric relationship between the probability of a correct response and the latent traits of individuals taking a test. This assumption restricts the use of those models to the case in which all items behave symmetrically. On the other hand, asymmetric models proposed in the literature impose that all the items in a test behave asymmetrically. This assumption is inappropriate for great majority of tests which are, in general, composed of both symmetric and asymmetric items. Furthermore, a straightforward extension of the existing models in the literature would require a prior selection of the items' symmetry/asymmetry status. This paper proposes a Bayesian IRT model that accounts for symmetric and asymmetric items in a flexible but parsimonious way. That is achieved by assigning a finite mixture prior to the skewness parameter, with one of the mixture components being a point mass at zero. This allows for analyses under both model selection and model averaging approaches. Asymmetric item curves are designed through the centred skew normal distribution, which has a particularly appealing parametrization in terms of parameter interpretation and computational efficiency. An efficient Markov chain Monte Carlo algorithm is proposed to perform Bayesian inference and its performance is investigated in some simulated examples. Finally, the proposed methodology is applied to a data set from a large-scale educational exam in Brazil.

大多数项目反应理论(IRT)的二分类反应模型都是基于probit或logit链接函数,这些函数假设答对的概率与被试个体的潜在特征之间存在对称关系。这个假设限制了这些模型的使用,在这种情况下,所有项目的行为都是对称的。另一方面,文献中提出的非对称模型要求测试中的所有项目都表现得不对称。这种假设不适用于绝大多数测试,这些测试通常由对称和非对称项目组成。此外,文献中现有模型的直接扩展将需要事先选择项目的对称/不对称状态。本文提出了一个贝叶斯IRT模型,该模型以一种灵活而简洁的方式考虑了对称和非对称项目。这是通过在偏度参数之前分配一个有限混合来实现的,其中一个混合分量是零点质量。这允许在模型选择和模型平均方法下进行分析。非对称项目曲线通过中心偏态正态分布设计,在参数解释和计算效率方面具有特别吸引人的参数化。提出了一种高效的马尔可夫链蒙特卡罗算法来进行贝叶斯推理,并通过一些仿真实例对其性能进行了研究。最后,将提出的方法应用于巴西大规模教育考试的数据集。
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引用次数: 0
An explanatory mixture IRT model for careless and insufficient effort responding in self-report measures 自我报告测量中粗心和不充分努力反应的解释性混合IRT模型
IF 2.6 3区 心理学 Q1 Mathematics Pub Date : 2022-06-22 DOI: 10.1111/bmsp.12272
Esther Ulitzsch, Seyma Nur Yildirim-Erbasli, Guher Gorgun, Okan Bulut

Careless and insufficient effort responding (C/IER) on self-report measures results in responses that do not reflect the trait to be measured, thereby posing a major threat to the quality of survey data. Reliable approaches for detecting C/IER aid in increasing the validity of inferences being made from survey data. First, once detected, C/IER can be taken into account in data analysis. Second, approaches for detecting C/IER support a better understanding of its occurrence, which facilitates designing surveys that curb the prevalence of C/IER. Previous approaches for detecting C/IER are limited in that they identify C/IER at the aggregate respondent or scale level, thereby hindering investigations of item characteristics evoking C/IER. We propose an explanatory mixture item response theory model that supports identifying and modelling C/IER at the respondent-by-item level, can detect a wide array of C/IER patterns, and facilitates a deeper understanding of item characteristics associated with its occurrence. As the approach only requires raw response data, it is applicable to data from paper-and-pencil and online surveys. The model shows good parameter recovery and can well handle the simultaneous occurrence of multiple types of C/IER patterns in simulated data. The approach is illustrated on a publicly available Big Five inventory data set, where we found later item positions to be associated with higher C/IER probabilities. We gathered initial supporting validity evidence for the proposed approach by investigating agreement with multiple commonly employed indicators of C/IER.

对自我报告测量的粗心和不充分的努力反应(C/IER)导致反应不能反映要测量的特征,从而对调查数据的质量构成重大威胁。检测C/IER的可靠方法有助于提高从调查数据中得出的推论的有效性。首先,一旦检测到C/IER,就可以在数据分析中考虑到。其次,检测C/IER的方法有助于更好地了解其发生情况,这有助于设计抑制C/IER流行的调查。以前检测C/IER的方法是有限的,因为它们在总被调查者或量表水平上识别C/IER,从而阻碍了对唤起C/IER的项目特征的调查。我们提出了一个解释性的混合项目反应理论模型,该模型支持在被调查者的项目层面识别和建模C/IER,可以检测广泛的C/IER模式,并有助于更深入地理解与其发生相关的项目特征。由于该方法只需要原始回复数据,因此适用于纸笔调查和在线调查的数据。该模型具有良好的参数恢复能力,能够很好地处理模拟数据中多种类型的C/IER模式同时出现的情况。该方法在公开的五大库存数据集上进行了说明,我们发现后期的项目位置与更高的C/IER概率相关。我们通过调查与多个常用的C/IER指标的一致性,收集了初步支持有效性的证据。
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引用次数: 8
A flexible approach to modelling over-, under- and equidispersed count data in IRT: The Two-Parameter Conway–Maxwell–Poisson Model 在IRT中对过分散、欠分散和等分散计数数据建模的一种灵活方法:双参数康威-麦克斯韦-泊松模型
IF 2.6 3区 心理学 Q1 Mathematics Pub Date : 2022-06-09 DOI: 10.1111/bmsp.12273
Marie Beisemann

Several psychometric tests and self-reports generate count data (e.g., divergent thinking tasks). The most prominent count data item response theory model, the Rasch Poisson Counts Model (RPCM), is limited in applicability by two restrictive assumptions: equal item discriminations and equidispersion (conditional mean equal to conditional variance). Violations of these assumptions lead to impaired reliability and standard error estimates. Previous work generalized the RPCM but maintained some limitations. The two-parameter Poisson counts model allows for varying discriminations but retains the equidispersion assumption. The Conway–Maxwell–Poisson Counts Model allows for modelling over- and underdispersion (conditional mean less than and greater than conditional variance, respectively) but still assumes constant discriminations. The present work introduces the Two-Parameter Conway–Maxwell–Poisson (2PCMP) model which generalizes these three models to allow for varying discriminations and dispersions within one model, helping to better accommodate data from count data tests and self-reports. A marginal maximum likelihood method based on the EM algorithm is derived. An implementation of the 2PCMP model in R and C++ is provided. Two simulation studies examine the model's statistical properties and compare the 2PCMP model to established models. Data from divergent thinking tasks are reanalysed with the 2PCMP model to illustrate the model's flexibility and ability to test assumptions of special cases.

一些心理测试和自我报告产生计数数据(例如,发散性思维任务)。最著名的计数数据项响应理论模型,即Rasch Poisson计数模型(RPCM),其适用性受到两个限制性假设的限制:相等的项目判别和等分散(条件均值等于条件方差)。违反这些假设会导致可靠性和标准误差估计受损。以前的工作推广了RPCM,但仍然存在一些局限性。双参数泊松计数模型允许不同的区别,但保留等色散假设。康威-麦克斯韦-泊松计数模型允许建模过分散和欠分散(条件均值分别小于和大于条件方差),但仍然假设恒定的区别。目前的工作引入了双参数康威-麦克斯韦-泊松(2PCMP)模型,该模型将这三个模型进行了推广,以允许在一个模型内进行不同的区分和分散,有助于更好地适应计数数据测试和自我报告的数据。提出了一种基于EM算法的边际极大似然方法。在R和c++中提供了2PCMP模型的实现。两项模拟研究检验了模型的统计特性,并将2PCMP模型与已建立的模型进行了比较。用2PCMP模型重新分析发散性思维任务的数据,以说明该模型的灵活性和检验特殊情况假设的能力。
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引用次数: 4
Score-based measurement invariance checks for Bayesian maximum-a-posteriori estimates in item response theory 项目反应理论中贝叶斯最大后验估计的基于分数的测量不变性检验
IF 2.6 3区 心理学 Q1 Mathematics Pub Date : 2022-06-06 DOI: 10.1111/bmsp.12275
Rudolf Debelak, Samuel Pawel, Carolin Strobl, Edgar C. Merkle

A family of score-based tests has been proposed in recent years for assessing the invariance of model parameters in several models of item response theory (IRT). These tests were originally developed in a maximum likelihood framework. This study discusses analogous tests for Bayesian maximum-a-posteriori estimates and multiple-group IRT models. We propose two families of statistical tests, which are based on an approximation using a pooled variance method, or on a simulation approach based on asymptotic results. The resulting tests were evaluated by a simulation study, which investigated their sensitivity against differential item functioning with respect to a categorical or continuous person covariate in the two- and three-parametric logistic models. Whereas the method based on pooled variance was found to be useful in practice with maximum likelihood as well as maximum-a-posteriori estimates, the simulation-based approach was found to require large sample sizes to lead to satisfactory results.

近年来,人们提出了一系列基于分数的测试来评估项目反应理论(IRT)中几个模型参数的不变性。这些测试最初是在最大似然框架中开发的。本研究讨论了贝叶斯最大后验估计和多组IRT模型的类似检验。我们提出了两类统计检验,它们基于使用混合方差方法的近似,或基于基于渐近结果的模拟方法。由此产生的测试通过模拟研究进行评估,该研究调查了它们对两参数和三参数逻辑模型中分类或连续人协变量的差异项目功能的敏感性。尽管基于混合方差的方法被发现在实践中对最大似然和最大后验估计是有用的,但基于模拟的方法被发现需要大样本量才能产生令人满意的结果。
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引用次数: 0
期刊
British Journal of Mathematical & Statistical Psychology
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