Journal of Mathematical Psychology最新文献

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The assessment of global optimization skills in procedural knowledge space theory 程序知识空间理论中全局优化技能的评估

IF 2.2 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2025-03-02 DOI: 10.1016/j.jmp.2025.102907

Luca Stefanutti, Andrea Brancaccio

Procedural knowledge space theory aims to evaluate problem-solving skills using a formal representation of a problem space. Stefanutti et al. (2021) introduced the concept of the “shortest path space” to characterize optimal problem spaces when a task requires reaching a solution in the minimum number of moves. This paper takes that idea further. It expands the shortest-path space concept to include a wider range of optimization problems, where each move can be weighted by a real number representing its “value”. Depending on the application, the “value” could be a cost, waiting time, route length, etc. This new model, named the optimizing path space, comprises all the globally best solutions. Additionally, it sets the stage for evaluating human problem-solving skills in various areas, like cognitive and neuropsychological tests, experimental studies, and puzzles, where globally optimal solutions are required.

程序性知识空间理论旨在用问题空间的形式化表示来评估解决问题的能力。Stefanutti等人（2021）引入了“最短路径空间”的概念，当任务需要以最少的移动次数达到解决方案时，该概念描述了最优问题空间。本文进一步阐述了这一观点。它扩展了最短路径空间概念，使其包含更广泛的优化问题，其中每个移动都可以用代表其“值”的实数加权。根据应用程序的不同，“值”可以是成本、等待时间、路由长度等。这个新模型被命名为最优路径空间，它包含了所有全局最优解。此外，它还为评估人类在各个领域解决问题的能力奠定了基础，如认知和神经心理学测试、实验研究和拼图，这些领域需要全局最优解决方案。

引用次数: 0

Models of human probability judgment errors 人类概率判断错误的模型

IF 2.2 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2025-02-27 DOI: 10.1016/j.jmp.2025.102906

Jiaqi Huang, Jerome Busemeyer

One of cognitive science’s core challenges is reconciling the success of probabilistic models in explaining human cognition with the observed fallacies in human probability judgments. This tutorial delves into models that address this discrepancy, shedding light on probabilistic fallacies. It encompasses earlier accounts like heuristics and averaging models, as well as contemporary, comprehensive models like quantum probability, the Probability Plus Noise model, and the Bayesian Sampler. The tutorial concludes by introducing the most recent accounts that integrate probability judgments with choice and response time, and highlighting ongoing challenges in the field.

认知科学的核心挑战之一是协调概率模型在解释人类认知方面的成功与在人类概率判断中观察到的谬误。本教程将深入研究解决这种差异的模型，揭示概率谬论。它包含了早期的描述，如启发式和平均模型，以及当代的综合模型，如量子概率、概率加噪声模型和贝叶斯采样器。本教程最后介绍了将概率判断与选择和响应时间相结合的最新描述，并强调了该领域正在面临的挑战。

引用次数: 0

Conjugate Bayesian analysis of the Wald model: On an exact drift-rate posterior 沃尔德模型的共轭贝叶斯分析：精确漂移率后验

IF 2.2 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2025-02-17 DOI: 10.1016/j.jmp.2025.102904

Constantin G. Meyer-Grant

In cognitive psychology, simple response times are often modeled as the time required by a one-dimensional Wiener process with drift to first reach a given threshold. This stochastic process’s first-passage time follows a Wald distribution, which is a specific parameterization of the inverse-Gaussian distribution. It can be shown that the Gaussian-Gamma distribution is a conjugate prior with respect to an inverse-Gaussian likelihood, albeit under a parameterization different from that of the Wald distribution. This leads to a posterior distribution that does not directly correspond to the core parameters of the Wiener process; that is, the drift-rate and the threshold parameter. While the marginal threshold posterior under a Gaussian-Gamma prior is relatively easy to derive and turns out to be a known distribution, this is not the case for the marginal drift-rate posterior. The present work addresses this issue by providing the exact marginal posterior distributions of the drift-rate parameter under a Gaussian-Gamma prior—something that has not yet been done in the literature. Unfortunately, the probability density function of this distribution cannot be expressed in terms of elementary functions. Thus, different methods of approximation are discussed as an expedient for time-critical applications.

在认知心理学中，简单的反应时间通常被建模为具有漂移的一维维纳过程首次达到给定阈值所需的时间。该随机过程的首次通过时间遵循Wald分布，这是反高斯分布的特定参数化。可以证明，高斯-伽马分布是相对于反高斯似然的共轭先验，尽管在参数化下与瓦尔德分布不同。这导致后验分布不直接对应于维纳过程的核心参数；即，漂移率和阈值参数。虽然在高斯-伽玛先验下的边际阈值后验相对容易推导，结果是一个已知的分布，但对于边际漂移率后验来说，情况并非如此。目前的工作通过在高斯-伽玛先验下提供漂移率参数的精确边际后验分布来解决这个问题-这在文献中尚未完成。不幸的是，这个分布的概率密度函数不能用初等函数来表示。因此，讨论了不同的近似方法，作为时间关键应用的权宜之计。

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引用次数: 0

Probabilistic models of delay discounting: “Fixed-endpoint” psychometric curves improve plausibility and performance 延迟贴现的概率模型：“固定端点”的心理测量曲线提高了可信性和绩效

IF 2.2 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2025-02-07 DOI: 10.1016/j.jmp.2025.102902

Isaac Kinley , Joseph Oluwasola , Suzanna Becker

Probabilistic models of delay discounting allow the estimation of discount functions without prescribing unrealistically sharp boundaries in decision making. However, existing probabilistic models have two implausible implications: first, that no reward is sometimes preferred over some reward (e.g., $0 now over $100 in 1 year), and second, that the same reward is sometimes preferred later rather than sooner (e.g., $100 in a year over $100 now). We introduce a class of “fixed-endpoint” models that assign these edge cases a probability of 0. We find that these outperform conventional models across a range of discount functions using nonlinear regression. We also introduce a series of generalized linear models that implicitly parameterize various discount functions, and demonstrate the same result for these.

延迟折现的概率模型允许估计折现函数，而不需要在决策中规定不切实际的尖锐边界。然而，现有的概率模型有两个令人难以置信的含义：首先，没有奖励有时比某些奖励更受欢迎（例如，现在0美元胜过一年后的100美元），其次，相同的奖励有时更受欢迎（例如，一年后的100美元胜过现在的100美元）。我们引入了一类“固定端点”模型，将这些边缘情况的概率赋值为0。我们发现这些模型在使用非线性回归的折扣函数范围内优于传统模型。我们还介绍了一系列广义线性模型，这些模型隐式参数化了各种折扣函数，并证明了这些模型的相同结果。

引用次数: 0

Choosing is losing: How opportunity cost influences valuations and choice 选择就是失败：机会成本如何影响估值和选择

IF 2.2 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2025-02-04 DOI: 10.1016/j.jmp.2025.102901

Tomás Lejarraga , József Sákovics

We propose a model of choice that accounts for opportunity costs actually suffered, as a result of renouncing the alternative not chosen. The valuation of each option is relative: The decision maker subtracts from the standard utility of any given option the psychological cost of giving up the alternative. In the presence of a default option, the final inclination of a person is the net effect of a ‘conservative’ disposition to keep the default and an ‘adventurous’ disposition toward choosing an alternative. This trait-like inclination is captured by the difference in sensitivity to giving up the default option or its alternative(s). When the options have elements in common, the conservative and adventurous dispositions operate only on their distinguishing elements. Unlike previous conceptualizations of anticipated regret, our decision maker suffers most when the foregone option is of comparable value to the chosen one. Our model can explain the empirical regularity that faced with the same choice, some people tend to favor the default option (a form of endowment effect), while others tend to favor its alternative (a form of fear of missing out). In the presence of several alternatives, the decision maker compares the default option with the best option among the alternatives.

我们提出了一个选择模型，该模型考虑了由于放弃未选择的替代方案而实际遭受的机会成本。每个选项的估值都是相对的：决策者从任何给定选项的标准效用中减去放弃该选项的心理成本。在存在默认选项的情况下，一个人的最终倾向是保留默认选项的“保守”倾向和选择替代选项的“冒险”倾向的净效应。这种特质般的倾向体现在对放弃默认选项或替代选项的敏感度差异上。当选择有共同的元素时，保守倾向和冒险倾向只在它们的不同元素上起作用。与先前预期后悔的概念不同，当放弃的选项与选择的选项具有相当的价值时，我们的决策者遭受的损失最大。我们的模型可以解释这样的经验规律：面对同样的选择，一些人倾向于默认选项（一种禀赋效应），而另一些人倾向于选择它的替代选项（一种害怕错过的形式）。在存在多个备选方案的情况下，决策者将默认方案与备选方案中的最佳方案进行比较。

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引用次数: 0

Analysing the bias introduced by adaptive designs to estimates of psychometric functions 分析自适应设计对心理测量函数估计的偏差

IF 2.2 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2025-01-29 DOI: 10.1016/j.jmp.2025.102899

Simon Bang Kristensen , Katrine Bødkergaard , Bo Martin Bibby

An adaptive design adjusts dynamically as information is accrued. In psychometrics and psychophysics, a class of studies investigates a subject’s ability to perform tasks as a function of the stimulus intensity, ie the amount or clarity of information supplied for the task. The relationship between performance and intensity is represented by a psychometric function. Such experiments routinely apply adaptive designs using both previous intensities and performance to assign stimulus intensities, the strategy being to sample intensities where information about the psychometric function is maximised. We investigate the influence of adaptation on statistical inference about the psychometric function focusing on estimation, considering parametric and non-parametric estimation under both fixed and adaptive designs and under within-subject independence as well as dependence. We study the scenarios analytically and numerically through a simulation study. We show that while asymptotic properties of estimators are preserved under adaptation, the adaptive nature of the design introduces small-sample bias, in particular in the slope parameter of the psychometric function. We supply an explanation of this phenomenon that formalises and supplements the one found in the literature. We argue that this poses a dilemma for studies applying an adaptive design in the form of a trade-off between more efficient sampling and the need to increase the number of samples to ameliorate small-sample bias.

自适应设计随着信息的积累而动态调整。在心理测量学和心理物理学中，一类研究调查了受试者执行任务的能力，将其作为刺激强度的函数，即为任务提供的信息的数量或清晰度。表现和强度之间的关系用心理测量函数表示。这类实验通常采用自适应设计，使用先前的强度和表现来分配刺激强度，策略是在有关心理测量功能的信息最大化的地方取样强度。本文以估计为中心，研究了自适应对心理测量函数统计推断的影响，考虑了固定设计和自适应设计下的参数估计和非参数估计，以及被试独立性和依赖性。我们通过模拟研究对这些场景进行了分析和数值研究。我们表明，虽然估计量的渐近性质在自适应下保持不变，但设计的自适应性质引入了小样本偏差，特别是在心理测量函数的斜率参数中。我们提供了一种对这种现象的解释，这种解释形式化并补充了文献中发现的解释。我们认为，这给应用自适应设计的研究带来了一个困境，即在更有效的抽样和需要增加样本数量以改善小样本偏差之间进行权衡。

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引用次数: 0

A class of random utility models yielding the exploded logit 产生爆炸对数的一类随机实用新型

IF 2.2 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2025-01-24 DOI: 10.1016/j.jmp.2025.102900

Karim Kilani

We reexamine a family of distributions introduced within the framework of random utility models by David Strauss. This family generates ranking probabilities of the exploded logit model and, de facto, the choice probabilities of the multinomial logit model. We explore the necessary and sufficient conditions for its validity within the copula theory. By specifying the minimal assumptions required for the support of the marginal utility distributions, we clarify and reinforce the fundamental structure of the model, proving that it relies on strict archimedean copulas. Additionally, we provide a new mathematical proof by induction on the number of alternatives confirming that these utility distributions indeed generate the exploded logit model.

我们重新审视了David Strauss在随机实用模型框架内引入的一系列分布。这个族生成爆炸logit模型的排序概率，事实上，生成多项logit模型的选择概率。探讨了它在联结理论中成立的充分必要条件。通过指定支持边际效用分布所需的最小假设，我们澄清并加强了模型的基本结构，证明它依赖于严格的阿基米德copula。此外，我们提供了一个新的数学证明，通过对备选数的归纳法，确认这些效用分布确实产生了爆炸logit模型。

引用次数: 0

Dimensions of knowledge structures 知识结构的维度

IF 2.2 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2025-01-10 DOI: 10.1016/j.jmp.2024.102898

Jean-Paul Doignon , Luca Stefanutti

A knowledge structure is inherently one-dimensional when its collection of states forms a chain. But how to define the dimension of a knowledge structure in general? We investigate four options: (i) the ordinal dimension, which is the dimension of the poset consisting of all states ordered by inclusion; (ii) for a knowledge space, the spatial dimension which is the least number of one-dimensional knowledge spaces which generate the space (a notion extending from learning spaces to knowledge spaces the dual of the convex dimension of an antimatroid); (iii) the bidimension, which is the bidimension of the membership relation from items to states, in either the intersection or the union version of the bidimension. Our results establish or disprove inequalities among the four dimension parameters for knowledge structures, for knowledge spaces, for terse knowledge structures, for terse knowledge spaces, and finally for learning spaces. We finally list some problems for future research.

当一个知识结构的状态集合形成一条链时，它本质上是一维的。但是一般来说，如何定义知识结构的维度呢？我们研究了四种选项：(i)有序维度，它是由包含有序的所有状态组成的偏序集的维度；（ii）对于知识空间，指产生该空间的一维知识空间数量最少的空间维度（从学习空间扩展到知识空间的概念，即反矩阵的凸维的对偶）；（iii）二维，这是从项目到状态的隶属关系的二维，在二维的交集或联合版本中。我们的结果建立或反驳了知识结构、知识空间、简洁知识结构、简洁知识空间和学习空间的四维参数之间的不等式。最后提出了一些有待进一步研究的问题。

引用次数: 0

Characterizing master fringes in competence-based knowledge space theory for personalized learning applications 基于能力的知识空间理论在个性化学习中的应用

IF 2.2 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2024-12-28 DOI: 10.1016/j.jmp.2024.102897

Gongxun Wang , Jinjin Li , Bo Wang , Chenyi Tao

This paper proposes a general method to directly compute the outer (inner) master fringe of the knowledge state based on the top or bottom of the equivalence class of competence state, and a general method for personalized learning guidance (reinforcement learning recommendation) based on competences and the master fringe. Two characterization theorems are mainly given: one characterizes the top (bottom) of competence states using skill functions; the other characterizes the outer (inner) master fringe of knowledge states using problem functions. As applications of two characterization theorems, the first is to provide a new method to directly obtain the corresponding competence state’s top or bottom from the knowledge state. The second application is to integrate skills into the competence-based master fringe, which takes into account the influence of students’ latent competences, resulting in more precise values.

本文提出了一种基于能力状态等价类的顶或底直接计算知识状态的外（内）主条纹的通用方法，以及一种基于能力和主条纹的个性化学习指导（强化学习推荐）的通用方法。主要给出了两个表征定理：一个是利用技能函数表征能力状态的上（下）层；另一种是利用问题函数表征知识状态的外（内）主边缘。作为两个表征定理的应用，一是提供了一种从知识状态中直接获得相应能力状态的顶或底的新方法。二是将技能融入到以能力为基础的master fringe中，考虑到学生潜在能力的影响，得到更精确的数值。

引用次数: 0

Remarks on learning spaces 关于学习空间的评论

IF 2.2 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2024-11-20 DOI: 10.1016/j.jmp.2024.102890

Xun Ge

This paper discusses learning spaces in the sense of Eppstein et al. (2008) to show that: (1) a learning space need not to have a base; (2) an essentially finite learning space need not to be well-graded; (3) the positive content family of a closed rooted medium need not to be a knowledge structure, and so it need not to be a learning space. These results disprove three assertions in Eppstein et al. (2008).

本文在 Eppstein 等人（2008 年）的意义上讨论了学习空间，以说明(1) 学习空间不一定要有基底；(2) 本质上有限的学习空间不一定要有良好的分级；(3) 封闭有根媒介的正向内容族不一定是知识结构，因此也不一定是学习空间。这些结果推翻了 Eppstein 等人（2008）的三个论断。

引用次数: 0

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Journal of Mathematical Psychology

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