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Representing choice probabilities by ranking probabilities via entropy maximization 通过熵最大化排序概率来表示选择概率
IF 1.5 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-01-27 DOI: 10.1016/j.jmp.2026.102970
Karim Kilani , Hans Colonius
Falmagne’s representation problem is revisited by maximizing Shannon entropy applied to ranking probabilities, under the linear constraints imposed by choice probabilities. Unlike Falmagne’s recursive construction, our method leads directly to an explicit solution, obtained after transforming the initial system into an equivalent one via alternating sums, in the spirit of Block–Marschak polynomials. We compute this solution for the Luce model and the generalized extreme value model, and show that, as soon as there are at least four alternatives, the construction based on Shannon entropy is only one among infinitely many possible representations. Other solutions could be obtained by maximizing alternative entropy functions, further highlighting the potential role of information theory in enriching the analysis of stochastic choice.
在选择概率施加的线性约束下,通过最大化香农熵应用于排序概率来重新审视Falmagne的表示问题。与Falmagne的递归构造不同,我们的方法直接导致显式解,通过交替求和将初始系统转换为等效系统后获得,具有块-马尔沙克多项式的精神。我们计算了Luce模型和广义极值模型的解,并表明,只要存在至少四个备选方案,基于Shannon熵的构造只是无限多个可能表示中的一个。其他解决方案可以通过最大化备选熵函数来获得,进一步突出了信息理论在丰富随机选择分析方面的潜在作用。
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引用次数: 0
A hitchhiker’s guide to information theoretical measures in psychology 心理学中信息理论测量的搭便车指南
IF 1.5 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-01-06 DOI: 10.1016/j.jmp.2025.102969
Niels van Santen, Yves Rosseel, Daniele Marinazzo
In psychology, as in other sciences, information theory can be used as a tool to complement more standard regression-based methods of data analysis. It is important to see the potential of information theoretical measures as statistical tools without implying a connection to their origins in communication theory and engineering. The use of these measures may provide us with additional insights due to their sensitivity to non-linear relationships, their flexibility to the mixing of data types, and their more straightforward generalization towards investigating higher-order interactions. We briefly reintroduce information theory and compare several measures such as mutual information and co-information with correlation and regression-based methods for the investigation of variable dependence.
在心理学中,正如在其他科学中一样,信息理论可以作为一种工具来补充更标准的基于回归的数据分析方法。重要的是要看到信息理论测量作为统计工具的潜力,而不是暗示它们在通信理论和工程中的起源。由于它们对非线性关系的敏感性,对混合数据类型的灵活性,以及对调查高阶交互的更直接的泛化,这些度量的使用可以为我们提供额外的见解。本文简要地重新介绍了信息论,并将互信息和共信息等几种度量方法与基于相关和回归的变量相关性研究方法进行了比较。
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引用次数: 0
Information of absence: Capacity measures for parallel AND processing 缺席信息:并行和处理的容量度量
IF 1.5 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-22 DOI: 10.1016/j.jmp.2025.102967
Nicholas A. Altieri
Howard and colleagues (2021) reported evidence that significant resources are used to process target-absent information in detection designs. This has major implications for measuring a system’s “capacity”, particularly when using AND decision rules. Chief among these concerns are the inflated capacity measurements commonly reported in the literature. To address this, the authors suggested using a full-factorial identification decision rule instead of simple detection. Here, a new capacity measure is calculated by comparing response times in single-target trials to those obtained from double and target-absent trials. Besides fundamentally altering the design, I argue this newly proposed coefficient may deflate capacity when target-absent responses are systematically slow relative to true parallel independent predictions, or under certain violations of context-invariance. I instead propose comparing responses in the double-target AND condition to parallel independent minimum time predictions derived from single-target “no” trials. This should avoid spurious findings of super or overly limited capacity and thus provide capacity estimates more closely resembling OR detection.
Howard及其同事(2021)报告的证据表明,在检测设计中,大量资源被用于处理目标缺失信息。这对于测量系统的“容量”具有重要意义,特别是在使用AND决策规则时。这些担忧中最主要的是文献中经常报道的膨胀能力测量。为了解决这个问题,作者建议使用全因子识别决策规则而不是简单的检测。在这里,通过比较单目标试验与双目标和无目标试验的反应时间来计算新的能力度量。除了从根本上改变设计之外,我认为,当目标缺失的响应相对于真正的并行独立预测系统缓慢时,或者在某些违反上下文不变性的情况下,这个新提出的系数可能会降低容量。相反,我建议将双目标与条件下的反应与从单目标“否”试验中得出的平行独立最小时间预测进行比较。这样可以避免出现容量过大或过度有限的虚假发现,从而提供更接近于or检测的容量估计。
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引用次数: 0
Analytical bifurcation analysis of mean-field Ising models reveals connectivity as a risk factor for psychopathology 平均场Ising模型的分析分岔分析揭示了连通性是精神病理的一个危险因素
IF 1.5 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-18 DOI: 10.1016/j.jmp.2025.102968
Han L.J. van der Maas, Lourens Waldorp
The connectivity hypothesis, central to the increasingly influential symptom network approach to psychopathology, proposes that stronger connectivity among symptoms heightens vulnerability to mental disorders. We provide an analytic derivation of this hypothesis using mean-field Ising models of depression, both in the standard 1/1 formulation and in a 0/1 variant where nodes represent symptoms as absent or present. Applying bifurcation theory, we derive the bifurcation sets and phase transition structure directly from the mean-field equations. This formal characterization elucidates how connectivity shapes system dynamics and, consistent with the network theory of mental disorders, demonstrates that increasing connectivity amplifies the risk of transitions into unhealthy states.
连通性假说是越来越有影响力的精神病理学症状网络方法的核心,它提出症状之间更强的连通性会增加对精神障碍的脆弱性。我们使用抑郁症的平均场Ising模型,在标准的- 1/1公式和0/1变体中(节点表示症状不存在或存在),对这一假设进行了分析推导。应用分岔理论,直接从平均场方程中导出了分岔集和相变结构。这一形式化描述阐明了连通性如何塑造系统动力学,并与精神障碍的网络理论相一致,证明了增加连通性会放大过渡到不健康状态的风险。
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引用次数: 0
Identifiability of the polytomous local independence model with graded knowledge structures 具有分级知识结构的多自治局部独立模型的可识别性
IF 1.5 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-04 DOI: 10.1016/j.jmp.2025.102956
Luca Stefanutti , Andrea Spoto
This article provides initial theoretical results concerning the identifiability of the polytomous local independence model (PoLIM), which is an extension of the basic local independence model (BLIM) to polytomous knowledge structures. It is well-known that the BLIM is not identifiable for graded knowledge structures. This is because there exist parameter transformations, named outcome preserving transformations, that leave unchanged the outcome of the prediction function of the model. In this article a twofold generalization is carried out. On the one side, we extend the notion of gradedness to polytomous structures, and, on the other side, we generalize the outcome preserving transformations to the case of polytomous items. These generalizations lead to the conclusion that the PoLIM is not identifiable for graded polytomous structures. This result generalizes a well-known one with the dichotomous structures. The role of equally informative items in the identifiability of the PoLIM is also investigated. The formal results are accompanied by a numerical example that applies those results to the PoLIM with a concrete polytomous structure that turns out to be graded.
本文给出了关于多局部独立模型(polytomous local independence model, PoLIM)可辨识性的初步理论结果,该模型是基本局部独立模型(BLIM)在多局部知识结构上的扩展。众所周知,对于分级的知识结构,blm是不可识别的。这是因为存在参数转换,称为结果保留转换,使模型的预测函数的结果保持不变。在本文中进行了双重推广。一方面,我们将等级的概念扩展到多同构结构,另一方面,我们将结果保留变换推广到多同构项目的情况。这些归纳得出的结论是,PoLIM不能被分级多层结构识别。这个结果推广了一个众所周知的二分类结构。同样翔实的项目在PoLIM的可识别性的作用也进行了调查。正式的结果伴随着一个数值例子,将这些结果应用于具有具体的多聚体结构的PoLIM,结果是分级的。
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引用次数: 0
Corrigendum to “An entropy model of decision uncertainty” [Journal of Mathematical Psychology 125 (2025), 102919] “决策不确定性的熵模型”的更正[数学心理学杂志125 (2025),102919]
IF 1.5 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-01 DOI: 10.1016/j.jmp.2025.102951
Keith A. Schneider
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引用次数: 0
A dynamic model of context-based retrieval 基于上下文检索的动态模型
IF 1.5 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-01 DOI: 10.1016/j.jmp.2025.102957
Madison D. Paron , James D. Paron , Michael J. Kahana
We propose a comprehensive model of how experiences are encoded and retrieved from memory. At the core of the model is a dynamic retrieval process incorporating two essential mechanisms: iterative retrieval, whereby information is sequentially sampled from memory to access the full history of experiences; and competitive retrieval, whereby the most prominent features in memory inhibit the recollection of other features. Together with context-based encoding, the model quantitatively explains well-known facts about response order and inter-response times in recall experiments. We show that our retrieval process maps closely to existing decision frameworks, such as drift–diffusion models, suggesting that the memory system plays a fundamental role in a wide-ranging set of decision-making settings.
我们提出了一个关于经验如何被编码和从记忆中检索的综合模型。该模型的核心是一个包含两个基本机制的动态检索过程:迭代检索,即信息按顺序从记忆中采样以访问完整的经验历史;以及竞争性检索,即记忆中最突出的特征会抑制对其他特征的回忆。与基于上下文的编码一起,该模型定量地解释了回忆实验中关于反应顺序和反应间时间的众所周知的事实。研究表明,我们的检索过程与现有的决策框架(如漂移-扩散模型)密切相关,这表明记忆系统在广泛的决策设置中起着基本作用。
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引用次数: 0
On informativeness and reducibility in competence models 论胜任力模型的信息性和可约性
IF 1.5 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-11-20 DOI: 10.1016/j.jmp.2025.102955
Huihua Shi , Bo Wang , Ning Gan , Jinjin Li
Informativeness refers to the extent to which competence states can be inferred from knowledge states by using the equivalence relation induced by problem functions. This concept is closely tied to the minimal or maximal elements within the equivalence classes of skills. This paper primarily explores, within the framework of conjunctive competence models, the relationship between informativeness and floors, which are defined as the greatest lower bounds within these equivalence classes. To represent informativeness, an order embedding between two ordered sets is constructed. Additionally, the study extends its analysis to disjunctive competence models and general competence models. Building on this foundation, we investigate the properties of reducible conjunctive and disjunctive competence models, presenting a method for deriving a unique irreducible domain restriction.
信息性是指利用问题函数推导出的等价关系从知识状态中推断出能力状态的程度。这个概念与技能等价类中的最小或最大元素密切相关。本文主要探讨了在连接能力模型的框架内,信息量与地板之间的关系,地板被定义为这些等价类中的最大下界。为了表示信息,构造了两个有序集之间的有序嵌入。此外,本研究还将分析范围扩展到析取胜任力模型和一般胜任力模型。在此基础上,我们研究了可约合和析取能力模型的性质,给出了一种推导唯一不可约域约束的方法。
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引用次数: 0
Standardized mean difference effect sizes for interval-valued data. A distance-based approach 区间值数据的标准化平均差异效应大小。基于距离的方法
IF 1.5 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-11-18 DOI: 10.1016/j.jmp.2025.102954
M. Asunción Lubiano , José García-García , Antonio L. García-Izquierdo , Ana M. Castaño
There is a large literature in psychological and behavioral sciences describing mean difference effect size indices for real-valued data. These indices are essential for integrating results from different studies, diverse types of data, or various rating scales. The emergence of new types and sources of data motivates the need to adapt the existing effect size measures or to develop new ones in order to facilitate the comparison of the observed experimental outcomes. To this purpose, some indices of the Cohen d family are to be extended throughout this article in order to deal with interval-valued data by following a distance-based approach and its utility will be illustrated by means of a real-life example where interval-valued responses were collected in a questionnaire.
在心理学和行为科学中有大量文献描述了实值数据的平均差异效应大小指数。这些指数对于整合来自不同研究、不同类型数据或不同评级量表的结果至关重要。新的数据类型和来源的出现促使需要调整现有的效应大小度量或开发新的效应大小度量,以便于对观察到的实验结果进行比较。为此目的,本文将扩展Cohen d族的一些指数,以便通过遵循基于距离的方法来处理区间值数据,并通过在问卷中收集区间值回答的现实生活示例来说明其效用。
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引用次数: 0
Modeling meta-reasoning processes using diffusion and quantum random walk models 使用扩散和量子随机游走模型建模元推理过程
IF 1.5 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-11-05 DOI: 10.1016/j.jmp.2025.102952
Ritesh K. Malaiya, Richard M. Golden
Meta-reasoning studies investigate the role of metacognitive processes in monitoring the success likelihood of an ongoing Reasoning task expected to require Longer Deliberation Time (RLDT), and accordingly, control further cognitive resource allocation to maximize success likelihood. A Meta-reasoning study may require participants to report their intermediate confidence judgment repeatedly within RLDT, e.g., a response that I am 70% confident that the problem is solvable, requested every 15 s. Based on existing Meta-reasoning studies, the current study first identified a set of observable Meta-reasoning phenomena on how intermediate confidence judgment evolves within RLDT and its impact on response choice and response time. Then, based on identified Meta-reasoning phenomena, certain computational features, serving as guidelines, were proposed to facilitate the construction and evaluation of random walk models describing these phenomena. The Markov Random-Walk formulation of the Drift-Diffusion Model (MR-DDM) and the Quantum Random-Walk Model (QRM) have been widely utilized to model response choice, response time, and intermediate and final confidence judgments in decision-making studies. Hence, the proposed computational features were utilized to evaluate the effectiveness of existing MR-DDM and QRM in describing meta-reasoning processes. Also, potential extensions of MR-DDM and QRM were identified for further empirical investigations. The current study also briefly reviewed an existing Item Response Theory (IRT) based extension of a continuous state continuous time Drift-Diffusion Model, named Q-Diffusion, that has been utilized to model RLDT without explicitly constraining the model to describe Meta-reasoning phenomena. Utilizing insights from Q-Diffusion and proposed computational features, the current study identified potential extensions of the MR-DDM for further empirical investigations.
元推理研究探讨了元认知过程在监测需要较长审议时间(RLDT)的正在进行的推理任务的成功可能性方面的作用,并相应地控制进一步的认知资源分配以最大化成功可能性。元推理研究可能要求参与者在RLDT内重复报告他们的中间信心判断,例如,每隔15秒要求我回答我有70%的信心这个问题是可以解决的。在现有元推理研究的基础上,本研究首先发现了一组可观察到的元推理现象,揭示了中间置信度判断在RLDT中的演变及其对反应选择和反应时间的影响。然后,在识别元推理现象的基础上,提出了一定的计算特征作为指导,以促进描述这些现象的随机游走模型的构建和评估。漂移扩散模型(MR-DDM)和量子随机漫步模型(QRM)的马尔可夫随机漫步公式已被广泛应用于决策研究中的响应选择、响应时间以及中间和最终置信度判断。因此,利用所提出的计算特征来评估现有MR-DDM和QRM在描述元推理过程中的有效性。此外,本文还对MR-DDM和QRM的潜在扩展进行了进一步的实证研究。本研究还简要回顾了现有的基于项目反应理论(IRT)的连续状态连续时间漂移扩散模型(Q-Diffusion)的扩展,该模型已被用于模拟RLDT,但没有明确约束模型描述元推理现象。利用Q-Diffusion的见解和提出的计算特征,本研究确定了MR-DDM的潜在扩展,以进行进一步的实证研究。
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引用次数: 0
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Journal of Mathematical Psychology
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