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Rejoinder to Commentaries on Lyu, Bolt and Westby's "Exploring the Effects of Item Specific Factors in Sequential and IRTree Models". 对 Lyu、Bolt 和 Westby 的 "探索顺序模型和 IRTree 模型中项目特定因素的影响 "评论的反驳。
IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-09-01 Epub Date: 2023-06-16 DOI: 10.1007/s11336-023-09913-w
Weicong Lyu, Daniel M Bolt

We respond to the commentaries on Lyu, Bolt and Westby's "Exploring the effects of item specific factors in sequential and IRTree models." The commentaries raise important points that allow us to clarify our theoretical expectation for item specific factors in many educational and psychological test items. At the same time, we agree with the commentaries in acknowledging challenges associated with providing empirical evidence for their presence and reflect on strategies that might support their estimation. We maintain that the principal concern is the ambiguity item specific factors create in attempting to interpret or use the parameters beyond the first node.

我们对 Lyu、Bolt 和 Westby 的 "探索顺序模型和 IRTree 模型中项目特定因素的影响 "一文的评论做出了回应。这些评论提出了一些重要观点,使我们能够澄清我们对许多教育和心理测试项目中特定项目因素的理论预期。同时,我们也同意评注中的观点,即为项目特定因素的存在提供实证证据所面临的挑战,并反思可能支持对项目特定因素进行估计的策略。我们坚持认为,主要的问题在于,在试图解释或使用第一个节点之外的参数时,项目特定因素会造成模糊性。
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引用次数: 0
Exploring the Effects of Item-Specific Factors in Sequential and IRTree Models. 探索顺序模型和 IRTree 模型中特定项目因素的影响。
IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-09-01 Epub Date: 2023-06-16 DOI: 10.1007/s11336-023-09912-x
Weicong Lyu, Daniel M Bolt, Samuel Westby

Test items for which the item score reflects a sequential or IRTree modeling outcome are considered. For such items, we argue that item-specific factors, although not empirically measurable, will often be present across stages of the same item. In this paper, we present a conceptual model that incorporates such factors. We use the model to demonstrate how the varying conditional distributions of item-specific factors across stages become absorbed into the stage-specific item discrimination and difficulty parameters, creating ambiguity in the interpretations of item and person parameters beyond the first stage. We discuss implications in relation to various applications considered in the literature, including methodological studies of (1) repeated attempt items; (2) answer change/review, (3) on-demand item hints; (4) item skipping behavior; and (5) Likert scale items. Our own empirical applications, as well as several examples published in the literature, show patterns of violations of item parameter invariance across stages that are highly suggestive of item-specific factors. For applications using sequential or IRTree models as analytical models, or for which the resulting item score might be viewed as outcomes of such a process, we recommend (1) regular inspection of data or analytic results for empirical evidence (or theoretical expectations) of item-specific factors; and (2) sensitivity analyses to evaluate the implications of item-specific factors for the intended inferences or applications.

我们考虑了项目得分反映顺序或 IRTree 模型结果的测试项目。对于此类项目,我们认为,项目特定因素虽然无法通过经验进行测量,但往往会在同一项目的不同阶段出现。在本文中,我们提出了一个包含此类因素的概念模型。我们利用该模型证明了项目特定因素在不同阶段的不同条件分布是如何被特定阶段的项目区分度和难度参数所吸收,从而在第一阶段之后对项目和人的参数的解释中产生歧义的。我们讨论了与文献中考虑的各种应用相关的影响,包括以下方面的方法研究:(1) 重复尝试项目;(2) 答案更改/回顾;(3) 按需项目提示;(4) 项目跳过行为;以及 (5) 李克特量表项目。我们自己的实证应用以及文献中发表的几个例子都显示了各阶段违反项目参数不变量的模式,这些模式高度暗示了特定项目因素。对于使用顺序模型或 IRTree 模型作为分析模型的应用,或者对于所产生的项目得分可能被视为此类过程的结果的应用,我们建议:(1) 定期检查数据或分析结果,以寻找项目特定因素的经验证据(或理论预期);(2) 进行敏感性分析,以评估项目特定因素对预期推论或应用的影响。
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引用次数: 0
A Latent Space Diffusion Item Response Theory Model to Explore Conditional Dependence between Responses and Response Times. 用潜空间扩散项目反应理论模型探讨反应与反应时间之间的条件依赖关系。
IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-09-01 Epub Date: 2023-06-14 DOI: 10.1007/s11336-023-09920-x
Inhan Kang, Minjeong Jeon, Ivailo Partchev

Traditional measurement models assume that all item responses correlate with each other only through their underlying latent variables. This conditional independence assumption has been extended in joint models of responses and response times (RTs), implying that an item has the same item characteristics fors all respondents regardless of levels of latent ability/trait and speed. However, previous studies have shown that this assumption is violated in various types of tests and questionnaires and there are substantial interactions between respondents and items that cannot be captured by person- and item-effect parameters in psychometric models with the conditional independence assumption. To study the existence and potential cognitive sources of conditional dependence and utilize it to extract diagnostic information for respondents and items, we propose a diffusion item response theory model integrated with the latent space of variations in information processing rate of within-individual measurement processes. Respondents and items are mapped onto the latent space, and their distances represent conditional dependence and unexplained interactions. We provide three empirical applications to illustrate (1) how to use an estimated latent space to inform conditional dependence and its relation to person and item measures, (2) how to derive diagnostic feedback personalized for respondents, and (3) how to validate estimated results with an external measure. We also provide a simulation study to support that the proposed approach can accurately recover its parameters and detect conditional dependence underlying data.

传统的测量模型假定,所有项目的反应仅通过其潜在变量相互关联。这一条件独立性假设在反应和反应时间(RTs)的联合模型中得到了扩展,这意味着无论潜在能力/特质和速度水平如何,一个项目对所有被试来说都具有相同的项目特征。然而,以往的研究表明,在各种类型的测验和问卷中都违反了这一假设,而且受访者与项目之间存在着大量的交互作用,这些交互作用无法通过心理测量模型中的人和项目效应参数来捕捉,而心理测量模型中的人和项目效应参数是有条件独立假设的。为了研究条件依赖的存在和潜在认知来源,并利用它来提取被试和项目的诊断信息,我们提出了一个与个体内部测量过程信息处理率变化的潜在空间相整合的扩散项目反应理论模型。受访者和项目被映射到潜空间上,它们之间的距离代表了条件依赖性和无法解释的交互作用。我们提供了三个经验应用来说明:(1) 如何使用估计的潜在空间来说明条件依赖性及其与个人和项目测量的关系;(2) 如何为受访者提供个性化的诊断反馈;(3) 如何用外部测量来验证估计结果。我们还提供了一项模拟研究,以证明所提出的方法能够准确恢复其参数并检测潜在数据的条件依赖性。
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引用次数: 0
The Dirichlet Dual Response Model: An Item Response Model for Continuous Bounded Interval Responses. Dirichlet 双响应模型:连续有界区间反应的项目反应模型。
IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-09-01 Epub Date: 2023-07-20 DOI: 10.1007/s11336-023-09924-7
Matthias Kloft, Raphael Hartmann, Andreas Voss, Daniel W Heck

Standard response formats such as rating or visual analogue scales require respondents to condense distributions of latent states or behaviors into a single value. Whereas this is suitable to measure central tendency, it neglects the variance of distributions. As a remedy, variability may be measured using interval-response formats, more specifically the dual-range slider (RS2). Given the lack of an appropriate item response model for the RS2, we develop the Dirichlet dual response model (DDRM), an extension of the beta response model (BRM; Noel & Dauvier in Appl Psychol Meas, 31:47-73, 2007). We evaluate the DDRM's performance by assessing parameter recovery in a simulation study. Results indicate overall good parameter recovery, although parameters concerning interval width (which reflect variability in behavior or states) perform worse than parameters concerning central tendency. We also test the model empirically by jointly fitting the BRM and the DDRM to single-range slider (RS1) and RS2 responses for two Extraversion scales. While the DDRM has an acceptable fit, it shows some misfit regarding the RS2 interval widths. Nonetheless, the model indicates substantial differences between respondents concerning variability in behavior. High correlations between person parameters of the BRM and DDRM suggest convergent validity between the RS1 and the RS2 interval location. Both the simulation and the empirical study demonstrate that the latent parameter space of the DDRM addresses an important issue of the RS2 response format, namely, the scale-inherent interdependence of interval location and interval width (i.e., intervals at the boundaries are necessarily smaller).

标准的回答格式(如评分或视觉类比量表)要求受访者将潜在状态或行为的分布浓缩为一个单一的值。虽然这适合测量中心倾向,但却忽略了分布的变异性。作为一种补救措施,可使用区间反应形式来测量变异性,更具体地说就是双区间滑动量表(RS2)。鉴于 RS2 缺乏合适的项目反应模型,我们开发了 Dirichlet 双反应模型(DDRM),它是贝塔反应模型(BRM;Noel & Dauvier,载于《应用心理学测量》,31:47-73,2007 年)的扩展。我们在一项模拟研究中通过评估参数恢复情况来评估 DDRM 的性能。结果表明,虽然有关区间宽度(反映行为或状态的变异性)的参数比有关中心倾向的参数表现更差,但总体上参数恢复良好。我们还通过将 BRM 和 DDRM 联合拟合到两个外向性量表的单区间滑动(RS1)和 RS2 反应中,对模型进行了经验性测试。虽然 DDRM 的拟合效果可以接受,但它在 RS2 区间宽度方面显示出一些不拟合。尽管如此,该模型还是显示出了受访者之间在行为可变性方面的巨大差异。BRM 和 DDRM 的人称参数之间的高度相关性表明,RS1 和 RS2 间隔位置之间具有趋同有效性。模拟和实证研究都表明,DDRM 的潜在参数空间解决了 RS2 回答格式的一个重要问题,即间隔位置和间隔宽度之间内在的相互依存关系(即边界处的间隔必然较小)。
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引用次数: 0
Item-Specific Factors in IRTree Models: When They Matter and When They Don't. IRTree 模型中的项目特定因素:何时重要,何时不重要?
IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-09-01 Epub Date: 2023-06-16 DOI: 10.1007/s11336-023-09916-7
Thorsten Meiser, Fabiola Reiber

Lyu et al. (Psychometrika, 2023) demonstrated that item-specific factors can cause spurious effects on the structural parameters of IRTree models for multiple nested response processes per item. Here, we discuss some boundary conditions and argue that person selection effects on item parameters are not unique to item-specific factors and that the effects presented by Lyu et al. (Psychometrika, 2023) may not generalize to the family of IRTree models as a whole. We conclude with the recommendation that IRTree model specification should be guided by theoretical considerations, rather than driven by data, in order to avoid misinterpretations of parameter differences.

Lyu等人(Psychometrika, 2023)证明,在每个项目有多个嵌套反应过程的情况下,项目特定因素会对IRTree模型的结构参数产生虚假影响。在此,我们讨论了一些边界条件,并认为对项目参数的人员选择效应并不是项目特定因素所独有的,Lyu 等人(Psychometrika,2023 年)提出的效应可能并不能推广到整个 IRTree 模型系列。最后,我们建议 IRTree 模型的规范应该以理论考虑为指导,而不是以数据为驱动,以避免对参数差异的误读。
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引用次数: 0
Rotating Factors to Simplify Their Structural Paths. 旋转因子以简化其结构路径。
IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-09-01 Epub Date: 2022-07-22 DOI: 10.1007/s11336-022-09877-3
Guangjian Zhang, Minami Hattori, Lauren A Trichtinger

Applications of structural equation modeling (SEM) may encounter issues like inadmissible parameter estimates, nonconvergence, or unsatisfactory model fit. We propose a new factor rotation method that reparameterizes the factor correlation matrix in exploratory factor analysis (EFA) such that factors can be either exogenous or endogenous. The proposed method is an oblique rotation method for EFA, but it allows directional structural paths among factors. We thus referred it to as FSP (factor structural paths) rotation. In particular, we can use FSP rotation to "translate" an SEM model to incorporate theoretical expectations on both factor loadings and structural parameters. We illustrate FSP rotation with an empirical example and explore its statistical properties with simulated data. The results include that (1) EFA with FSP rotation tends to fit data better and encounters fewer Heywood cases than SEM does when there are cross-loadings and many small nonzero loadings, (2) FSP rotated parameter estimates are satisfactory for small models, and (3) FSP rotated parameter estimates are more satisfactory for large models when the structural parameter matrices are sparse.

结构方程建模(SEM)在应用中可能会遇到参数估计不准、不收敛或模型拟合不理想等问题。我们提出了一种新的因子旋转方法,该方法可以对探索性因子分析(EFA)中的因子相关矩阵进行重新参数化,从而使因子既可以是外生的,也可以是内生的。所提出的方法是 EFA 的斜向旋转方法,但它允许因子之间存在定向结构路径。因此,我们将其称为 FSP(因子结构路径)旋转法。特别是,我们可以使用 FSP 旋转来 "翻译 "一个 SEM 模型,以纳入对因子载荷和结构参数的理论预期。我们用一个经验实例来说明 FSP 旋转,并用模拟数据来探讨其统计特性。结果包括:(1) 当存在交叉负荷和许多小的非零负荷时,与 SEM 相比,使用 FSP 旋转的 EFA 往往能更好地拟合数据,遇到的 Heywood 案例也更少;(2) FSP 旋转的参数估计对小型模型是令人满意的;(3) 当结构参数矩阵稀疏时,FSP 旋转的参数估计对大型模型更令人满意。
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引用次数: 0
Fitting and Testing Log-Linear Subpopulation Models with Known Support. 利用已知支持度拟合和测试对数线性子群模型
IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-09-01 Epub Date: 2023-06-14 DOI: 10.1007/s11336-023-09922-9
David J Hessen

In this paper, the support of the joint probability distribution of categorical variables in the total population is treated as unknown. From a general total population model with unknown support, a general subpopulation model with its support equal to the set of all observed score patterns is derived. In maximum likelihood estimation of the parameters of any such subpopulation model, the evaluation of the log-likelihood function only requires the summation over a number of terms equal to at most the sample size. It is made clear that the parameters of a hypothesized total population model are consistently and asymptotically efficiently estimated by the values that maximize the log-likelihood function of the corresponding subpopulation model. Next, new likelihood ratio goodness-of-fit tests are proposed as alternatives to the Pearson chi-square goodness-of-fit test and the likelihood ratio test against the saturated model. In a simulation study, the asymptotic bias and efficiency of maximum likelihood estimators and the asymptotic performance of the goodness-of-fit tests are investigated.

本文将总人口中分类变量联合概率分布的支持度视为未知数。从支持度未知的一般总体模型中,可以推导出支持度等于所有观测得分模式集合的一般子总体模型。在对任何此类子群体模型的参数进行最大似然估计时,只需对对数似然函数进行求和,求和项的数量最多等于样本量。这就清楚地表明,假设的总体模型参数可以通过使相应子总体模型的对数似然函数最大化的值得到一致且渐近有效的估计。接下来,我们提出了新的似然比拟合优度检验,以替代皮尔逊卡方拟合优度检验和针对饱和模型的似然比检验。在模拟研究中,研究了最大似然估计器的渐近偏差和效率以及拟合优度检验的渐近性能。
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引用次数: 0
Book Review. 书评。
IF 3 2区 心理学 Q2 Mathematics Pub Date : 2023-07-06 DOI: 10.1007/s11336-023-09923-8
Youn Seon Lim
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引用次数: 0
Book Review 书评
IF 3 2区 心理学 Q2 Mathematics Pub Date : 2023-07-01 DOI: 10.1007/s11336-023-09927-4
Ji Seung Yang, Yang Liu, Sungyeun Kim
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引用次数: 0
A Test to Distinguish Monotone Homogeneity from Monotone Multifactor Models. 区分单调同质性与单调多因素模型的测试。
IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-06-01 Epub Date: 2023-03-18 DOI: 10.1007/s11336-023-09905-w
Jules L Ellis, Klaas Sijtsma

The goodness-of-fit of the unidimensional monotone latent variable model can be assessed using the empirical conditions of nonnegative correlations (Mokken in A theory and procedure of scale-analysis, Mouton, The Hague, 1971), manifest monotonicity (Junker in Ann Stat 21:1359-1378, 1993), multivariate total positivity of order 2 (Bartolucci and Forcina in Ann Stat 28:1206-1218, 2000), and nonnegative partial correlations (Ellis in Psychometrika 79:303-316, 2014). We show that multidimensional monotone factor models with independent factors also imply these empirical conditions; therefore, the conditions are insensitive to multidimensionality. Conditional association (Rosenbaum in Psychometrika 49(3):425-435, 1984) can detect multidimensionality, but tests of it (De Gooijer and Yuan in Comput Stat Data Anal 55:34-44, 2011) are usually not feasible for realistic numbers of items. The only existing feasible test procedures that can reveal multidimensionality are Rosenbaum's (Psychometrika 49(3):425-435, 1984) Case 2 and Case 5, which test the covariance of two items or two subtests conditionally on the unweighted sum of the other items. We improve this procedure by conditioning on a weighted sum of the other items. The weights are estimated in a training sample from a linear regression analysis. Simulations show that the Type I error rate is under control and that, for large samples, the power is higher if one dimension is more important than the other or if there is a third dimension. In small samples and with two equally important dimensions, using the unweighted sum yields greater power.

单维单调潜变量模型的拟合优度可以用以下经验条件来评估:非负相关性(Mokken,载于《量表分析的理论和程序》,Mouton,海牙,1971 年)、显单调性(Junker,载于《统计年鉴》21:1359-1378,1993 年)、阶 2 的多变量总正向性(Bartolucci 和 Forcina,载于《统计年鉴》28:1206-1218,2000 年)和非负偏相关性(Bartolucci 和 Forcina,载于《统计年鉴》28:1206-1218,2000 年):1359-1378,1993)、阶 2 的多变量总正向性(Bartolucci 和 Forcina 在 Ann Stat 28:1206-1218, 2000)以及非负偏相关(Ellis 在 Psychometrika 79:303-316, 2014)。我们证明,具有独立因子的多维单调因子模型也意味着这些经验条件;因此,这些条件对多维性并不敏感。条件关联(Rosenbaum,发表于《Psychometrika》49(3):425-435,1984 年)可以检测多维性,但对其进行测试(De Gooijer 和 Yuan,发表于《Comput Stat Data Anal》55:34-44,2011 年)通常对现实的项目数不可行。现有可行的能揭示多维性的测试程序只有罗森鲍姆(Psychometrika 49(3):425-435,1984 年)的案例 2 和案例 5,它们测试两个项目或两个子测试的协方差,条件是其他项目的非加权和。我们改进了这一程序,以其他项目的加权和为条件。权重是在训练样本中通过线性回归分析估算出来的。模拟结果表明,I 类错误率在可控范围内,而且在大样本中,如果一个维度比另一个维度更重要,或者存在第三个维度,则权重会更高。对于小样本和两个同样重要的维度,使用非加权和会产生更大的功率。
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引用次数: 0
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Psychometrika
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