Journal of Mathematical Psychology最新文献

英文中文

The dual and the complement of a skill function 技能函数的对偶和补

IF 1.5 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2025-11-02 DOI: 10.1016/j.jmp.2025.102953

Gongxun Wang , Jinjin Li , Jun-e Feng

In knowledge structure theory, the conjunctive model is the dual of the disjunctive model. What, then, is the dual of the competence model? Regarding the competence model, prior work has established necessary and sufficient conditions for delineating knowledge spaces via the competence model and has well studied the fringe characterization of knowledge states in delineated knowledge spaces. Accordingly, what are the necessary and sufficient conditions for delineating simple closure spaces via the competence model? How can the fringe of knowledge states be characterized in delineated simple closure spaces? Furthermore, in the competence model, top space characterization is complex. How to simplify it? To address these problems, this paper proposes the dual skill function (i.e., dual competence model) and the complement skill function. The dual competence model provides a novel methodology for analyzing the competence model, enabling the transfer of results on delineated knowledge spaces to their dual closure spaces, and offering a more direct characterization of top spaces. In doing so, it effectively addresses the latter three problems. These results refine knowledge structure theory.

在知识结构理论中，合取模型是析取模型的对偶。那么，胜任力模型的双重特征是什么呢？在胜任力模型方面，前人已经建立了用胜任力模型描述知识空间的充分必要条件，并对所描述的知识空间中知识状态的边缘特征进行了较好的研究。因此，通过胜任力模型来描绘简单封闭空间的必要和充分条件是什么？如何在描述的简单封闭空间中描述知识状态的边缘？此外，在胜任力模型中，顶层空间表征比较复杂。如何简化它？针对这些问题，本文提出了双技能函数（即双胜任力模型）和互补技能函数。双能力模型为分析能力模型提供了一种新的方法，使所描述的知识空间的结果能够转移到其双封闭空间，并提供了更直接的顶层空间表征。这样，它有效地解决了后三个问题。这些结果完善了知识结构理论。

{"title":"The dual and the complement of a skill function","authors":"Gongxun Wang , Jinjin Li , Jun-e Feng","doi":"10.1016/j.jmp.2025.102953","DOIUrl":"10.1016/j.jmp.2025.102953","url":null,"abstract":"<div><div>In knowledge structure theory, the conjunctive model is the dual of the disjunctive model. What, then, is the dual of the competence model? Regarding the competence model, prior work has established necessary and sufficient conditions for delineating knowledge spaces via the competence model and has well studied the fringe characterization of knowledge states in delineated knowledge spaces. Accordingly, what are the necessary and sufficient conditions for delineating simple closure spaces via the competence model? How can the fringe of knowledge states be characterized in delineated simple closure spaces? Furthermore, in the competence model, top space characterization is complex. How to simplify it? To address these problems, this paper proposes the dual skill function (i.e., dual competence model) and the complement skill function. The dual competence model provides a novel methodology for analyzing the competence model, enabling the transfer of results on delineated knowledge spaces to their dual closure spaces, and offering a more direct characterization of top spaces. In doing so, it effectively addresses the latter three problems. These results refine knowledge structure theory.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"127 ","pages":"Article 102953"},"PeriodicalIF":1.5,"publicationDate":"2025-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145465504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Experiment-based calibration in psychology: Foundational and data-generating model 心理学中基于实验的校准：基础和数据生成模型

IF 1.5 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2025-09-15 DOI: 10.1016/j.jmp.2025.102950

Dominik R. Bach

Experiment-based calibration is a novel method for measurement validation, which – unlike classical validity metrics – does not require stable between-person variance. In this approach, the latent variable to be measured is manipulated by an experiment, and its predicted scores – termed standard scores – are compared against the measured scores. Previous work has shown that under plausible boundary conditions, the correlation between standard and measured scores – termed retrodictive validity – is informative about measurement accuracy, i.e. combined trueness and precision. Here, I expand these findings in several directions. First, I formalise the approach in a probability-theoretic framework with the concept of a standardised calibration space. Second, I relate this framework to classical validity theory and show that the boundary conditions in fact apply to any form of criterion validity, including classical convergent validity. Thus, I state precise and empirically quantifiable boundary conditions under which criterion validity metrics are informative on validity. Third, I relate these boundary conditions to confounding variables, i.e. correlated latent variables. I show that in the limit, calibration will converge on the latent variable that is most closely related to the standard. Finally, I provide a framework for modelling the data-generating process with Markov kernels, and identify sufficient conditions under which the data generation model results in a calibration space. In sum, this article provides a formal probability-theoretic framework for experiment-based calibration and facilitates modelling and empirical assessment of the data generating processes.

基于实验的校准是测量验证的一种新方法，它与经典的效度度量不同，不需要稳定的人间方差。在这种方法中，要测量的潜在变量被实验操纵，其预测分数-称为标准分数-与测量分数进行比较。以前的工作表明，在合理的边界条件下，标准分数和测量分数之间的相关性——称为追溯效度——对测量精度，即真实度和精度的结合提供了信息。在这里，我将从几个方面扩展这些发现。首先，我用标准化校准空间的概念在概率论框架中形式化了该方法。其次，我将这个框架与经典有效性理论联系起来，并表明边界条件实际上适用于任何形式的标准有效性，包括经典收敛有效性。因此，我陈述了精确的和经验上可量化的边界条件，在这些条件下，标准有效性度量是关于有效性的信息。第三，我将这些边界条件与混淆变量，即相关潜在变量联系起来。我表明，在极限情况下，校准将收敛于与标准最密切相关的潜在变量。最后，我提供了一个用马尔可夫核对数据生成过程建模的框架，并确定了数据生成模型在校准空间中产生的充分条件。总之，本文为基于实验的校准提供了一个正式的概率论框架，并促进了数据生成过程的建模和经验评估。

{"title":"Experiment-based calibration in psychology: Foundational and data-generating model","authors":"Dominik R. Bach","doi":"10.1016/j.jmp.2025.102950","DOIUrl":"10.1016/j.jmp.2025.102950","url":null,"abstract":"<div><div>Experiment-based calibration is a novel method for measurement validation, which – unlike classical validity metrics – does not require stable between-person variance. In this approach, the latent variable to be measured is manipulated by an experiment, and its predicted scores – termed standard scores – are compared against the measured scores. Previous work has shown that under plausible boundary conditions, the correlation between standard and measured scores – termed retrodictive validity – is informative about measurement accuracy, i.e. combined trueness and precision. Here, I expand these findings in several directions. First, I formalise the approach in a probability-theoretic framework with the concept of a standardised calibration space. Second, I relate this framework to classical validity theory and show that the boundary conditions in fact apply to any form of criterion validity, including classical convergent validity. Thus, I state precise and empirically quantifiable boundary conditions under which criterion validity metrics are informative on validity. Third, I relate these boundary conditions to confounding variables, i.e. correlated latent variables. I show that in the limit, calibration will converge on the latent variable that is most closely related to the standard. Finally, I provide a framework for modelling the data-generating process with Markov kernels, and identify sufficient conditions under which the data generation model results in a calibration space. In sum, this article provides a formal probability-theoretic framework for experiment-based calibration and facilitates modelling and empirical assessment of the data generating processes.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"127 ","pages":"Article 102950"},"PeriodicalIF":1.5,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145059932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Iverson’s law of similarity 关于艾弗森的相似定律

IF 1.5 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2025-09-12 DOI: 10.1016/j.jmp.2025.102943

Eszter Gselmann , Christopher W. Doble , Yung-Fong Hsu

Iverson (2006b) proposed the law of similarity

ξ_{s} (λ x) = γ (λ, s) ξ_{η (λ, s)} (x)

for the sensitivity functions

ξ_{s} (s \in S)

. Compared to the former models, the generality of this one lies in that here

γ

and

η

can also depend on the variables

λ

and

s

. In the literature, this model (or its special cases) is usually considered together with a given psychophysical representation (e.g. Fechnerian, subtractive, or affine). Our goal, however, is to study at first Iverson’s law of similarity on its own. We show that if certain mild assumptions are fulfilled, then

ξ

can be written in a rather simple form containing only one-variable functions. The obtained form proves to be very useful when we assume some kind of representation.

Motivated by Hsu and Iverson (2016), we then study the above model assuming that the mapping

η

is multiplicatively translational. First, we show how these mappings can be characterized. Later we turn to the examination of Falmagne’s power law. According to our results, the corresponding function

ξ

can have a Fechnerian representation, and also it can have a subtractive representation. We close the paper with the study of the shift invariance property.

Iverson （2006b）提出了灵敏度函数ξs（s∈s）的相似律ξs(λx)=γ(λ,s)ξη(λ,s)(x)。与之前的模型相比，这个模型的通用性在于，这里的γ和η也可以取决于变量λ和s。在文献中，这个模型（或它的特殊情况）通常与给定的心理物理表示（例如，费契纳式，减法式或仿射式）一起考虑。然而，我们的目标是首先研究艾弗森的相似性定律本身。我们证明，如果满足某些温和的假设，则ξ可以写成只包含单变量函数的相当简单的形式。当我们假设某种表示时，所得到的形式证明是非常有用的。在Hsu和Iverson（2016）的激励下，我们假设映射η是乘平移的，然后研究上述模型。首先，我们将展示如何对这些映射进行表征。稍后我们将讨论法尔曼幂定律。根据我们的结果，相应的函数ξ可以有一个法式表示，也可以有一个减法式表示。最后，我们研究了平移不变性。

{"title":"On Iverson’s law of similarity","authors":"Eszter Gselmann , Christopher W. Doble , Yung-Fong Hsu","doi":"10.1016/j.jmp.2025.102943","DOIUrl":"10.1016/j.jmp.2025.102943","url":null,"abstract":"<div><div><span><span>Iverson (2006b)</span></span> proposed the law of similarity <span><span><span><math><mrow><msub><mrow><mi>ξ</mi></mrow><mrow><mi>s</mi></mrow></msub><mrow><mo>(</mo><mi>λ</mi><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mi>γ</mi><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><mi>s</mi><mo>)</mo></mrow><msub><mrow><mi>ξ</mi></mrow><mrow><mi>η</mi><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><mi>s</mi><mo>)</mo></mrow></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span></span></span>for the sensitivity functions <span><math><mrow><msub><mrow><mi>ξ</mi></mrow><mrow><mi>s</mi></mrow></msub><mspace></mspace><mrow><mo>(</mo><mi>s</mi><mo>∈</mo><mi>S</mi><mo>)</mo></mrow></mrow></math></span>. Compared to the former models, the generality of this one lies in that here <span><math><mi>γ</mi></math></span> and <span><math><mi>η</mi></math></span> can also depend on the variables <span><math><mi>λ</mi></math></span> and <span><math><mi>s</mi></math></span>. In the literature, this model (or its special cases) is usually considered together with a given psychophysical representation (e.g. Fechnerian, subtractive, or affine). Our goal, however, is to study at first Iverson’s law of similarity on its own. We show that if certain mild assumptions are fulfilled, then <span><math><mi>ξ</mi></math></span> can be written in a rather simple form containing only one-variable functions. The obtained form proves to be very useful when we assume some kind of representation.</div><div>Motivated by <span><span>Hsu and Iverson (2016)</span></span>, we then study the above model assuming that the mapping <span><math><mi>η</mi></math></span> is multiplicatively translational. First, we show how these mappings can be characterized. Later we turn to the examination of Falmagne’s power law. According to our results, the corresponding function <span><math><mi>ξ</mi></math></span> can have a Fechnerian representation, and also it can have a subtractive representation. We close the paper with the study of the shift invariance property.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"127 ","pages":"Article 102943"},"PeriodicalIF":1.5,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Causal analysis of absolute and relative risk reductions 绝对和相对风险降低的原因分析

IF 1.5 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2025-09-03 DOI: 10.1016/j.jmp.2025.102942

Björn Meder , Charley M. Wu , Felix G. Rebitschek

Any medical innovation must first prove its benefits with reliable evidence from clinical trials. Evidence is commonly expressed using two metrics, summarizing treatment benefits based on either absolute risk reductions (ARRs) or relative risk reductions (RRRs). Both metrics are derived from the same data, but they implement conceptually distinct ideas. Here, we analyze these risk reductions measures from a causal modeling perspective. First, we show that ARR is equivalent to

Δ P

, while RRR is equivalent to causal power, thus clarifying the implicit causal assumptions. Second, we show how this formal equivalence establishes a relationship with causal Bayes nets theory, offering a basis for incorporating risk reduction metrics into a computational modeling framework. Leveraging these analyses, we demonstrate that under dynamically varying baseline risks, ARRs and RRRs lead to strongly diverging predictions. Specifically, the inherent assumption of a linear parameterization of the underlying causal graph can lead to incorrect conclusions when generalizing treatment benefits (e.g, predicting the effect of a vaccine in new populations with different baseline risks). Our analyses highlight the shared principles underlying risk reduction metrics and measures of causal strength, emphasizing the potential for explicating causal structure and inference in medical research.

任何医学创新都必须首先用临床试验的可靠证据证明其益处。证据通常使用两个指标来表达，根据绝对风险降低（ARRs）或相对风险降低（RRRs）来总结治疗益处。这两种指标都来自相同的数据，但它们执行的概念却截然不同。在这里，我们从因果模型的角度分析这些风险降低措施。首先，我们证明ARR等价于ΔP，而RRR等价于因果力，从而澄清了隐含的因果假设。其次，我们展示了这种形式等价如何与因果贝叶斯网络理论建立关系，为将风险降低指标纳入计算建模框架提供了基础。利用这些分析，我们证明了在动态变化的基线风险下，arr和rrr导致了强烈的预测差异。具体而言，在概括治疗益处（例如，预测疫苗在具有不同基线风险的新人群中的效果）时，潜在因果图的线性参数化的固有假设可能导致不正确的结论。我们的分析强调了风险降低指标和因果强度测量的共同原则，强调了在医学研究中解释因果结构和推断的潜力。

{"title":"Causal analysis of absolute and relative risk reductions","authors":"Björn Meder , Charley M. Wu , Felix G. Rebitschek","doi":"10.1016/j.jmp.2025.102942","DOIUrl":"10.1016/j.jmp.2025.102942","url":null,"abstract":"<div><div>Any medical innovation must first prove its benefits with reliable evidence from clinical trials. Evidence is commonly expressed using two metrics, summarizing treatment benefits based on either absolute risk reductions (ARRs) or relative risk reductions (RRRs). Both metrics are derived from the same data, but they implement conceptually distinct ideas. Here, we analyze these risk reductions measures from a causal modeling perspective. First, we show that ARR is equivalent to <span><math><mrow><mi>Δ</mi><mi>P</mi></mrow></math></span>, while RRR is equivalent to causal power, thus clarifying the implicit causal assumptions. Second, we show how this formal equivalence establishes a relationship with causal Bayes nets theory, offering a basis for incorporating risk reduction metrics into a computational modeling framework. Leveraging these analyses, we demonstrate that under dynamically varying baseline risks, ARRs and RRRs lead to strongly diverging predictions. Specifically, the inherent assumption of a linear parameterization of the underlying causal graph can lead to incorrect conclusions when generalizing treatment benefits (e.g, predicting the effect of a vaccine in new populations with different baseline risks). Our analyses highlight the shared principles underlying risk reduction metrics and measures of causal strength, emphasizing the potential for explicating causal structure and inference in medical research.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"127 ","pages":"Article 102942"},"PeriodicalIF":1.5,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144989436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Characterization of countable and continuous Richter–Peleg multi-utility representations 可数连续Richter-Peleg多效用表示的表征

IF 1.5 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2025-08-01 DOI: 10.1016/j.jmp.2025.102940

Gianni Bosi , Esteban Induráin , Ana Munárriz , Yeray R. Rincón

This paper contributes to the theoretical literature on decision models where agents may encounter challenges in comparing alternatives. We introduce a characterization of countable Richter–Peleg multi-utility representations, both semicontinuous (upper and lower) and continuous, within preorders that may not be total. The proposed theorems provide a comprehensive mathematical framework, complementing previous results of Alcantud et al. and Bosi on countable multi-utility representations. Our characterizations establish necessary and sufficient conditions through topological properties and constructive methods via indicator functions. Furthermore, we introduce a topological framework aligned with the property of strong local non-satiation and provide a novel theorem containing sufficient conditions for the existence of countable upper semi-continuous multi-utility representations of a preorder. The results demonstrate that preference representations can be achieved using countably many functions rather than uncountable families, with implications for computational tractability and the identification of maximal elements in optimization contexts.

本文对决策模型的理论文献做出了贡献，其中代理在比较备选方案时可能遇到挑战。我们引入了可计数Richter-Peleg多效用表示的特征，包括半连续（上和下）和连续，在可能不是总数的预订中。提出的定理提供了一个全面的数学框架，补充了Alcantud等人和Bosi之前关于可数多效用表示的结果。我们的刻画通过拓扑性质和构造方法通过指示函数建立了充分必要条件。此外，我们引入了一个具有强局部不满足性质的拓扑框架，并给出了一个新的定理，该定理包含了一个预序的可计数上半连续多效用表示存在的充分条件。结果表明，偏好表示可以使用可数的多个函数而不是不可数的族来实现，这对优化环境中的计算可追溯性和最大元素的识别具有重要意义。

{"title":"Characterization of countable and continuous Richter–Peleg multi-utility representations","authors":"Gianni Bosi , Esteban Induráin , Ana Munárriz , Yeray R. Rincón","doi":"10.1016/j.jmp.2025.102940","DOIUrl":"10.1016/j.jmp.2025.102940","url":null,"abstract":"<div><div>This paper contributes to the theoretical literature on decision models where agents may encounter challenges in comparing alternatives. We introduce a characterization of countable Richter–Peleg multi-utility representations, both semicontinuous (upper and lower) and continuous, within preorders that may not be total. The proposed theorems provide a comprehensive mathematical framework, complementing previous results of Alcantud et al. and Bosi on countable multi-utility representations. Our characterizations establish necessary and sufficient conditions through topological properties and constructive methods via indicator functions. Furthermore, we introduce a topological framework aligned with the property of strong local non-satiation and provide a novel theorem containing sufficient conditions for the existence of countable upper semi-continuous multi-utility representations of a preorder. The results demonstrate that preference representations can be achieved using countably many functions rather than uncountable families, with implications for computational tractability and the identification of maximal elements in optimization contexts.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"126 ","pages":"Article 102940"},"PeriodicalIF":1.5,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An alternative attribute map for polytomous assessment structures 用于多单元评估结构的可选属性映射

IF 1.5 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2025-08-01 DOI: 10.1016/j.jmp.2025.102941

Bo Wang , Jinjin Li , Bochi Xu , Wen Sun , Yingru Lin

The present paper introduces an attribute map that offers an alternative approach to modeling polytomous item–response relationships. This new attribute map is based on the principle that each available attribute can independently enable an item to reach a specific observable response level. The paper rigorously defines this attribute map and establishes the corresponding item–response function. Using these two maps, a coherent attribute structure is constructed, leading to a competence-based polytomous assessment structure. Finally, a straightforward mathematical example is provided to illustrate the validity and practical applicability of this theoretical framework.

本文介绍了一种属性映射，它提供了一种建模多自治项目响应关系的替代方法。这个新的属性映射基于这样一个原则，即每个可用属性都可以独立地使一个项目达到特定的可观察响应级别。本文严格定义了该属性映射，并建立了相应的项响应函数。使用这两个映射，构建了一个连贯的属性结构，从而形成了一个基于能力的多同构评估结构。最后，给出了一个简单的数学例子来说明该理论框架的有效性和实际适用性。

引用次数: 0

Random utility without regularity 无规律性的随机效用

IF 2.2 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2025-07-27 DOI: 10.1016/j.jmp.2025.102938

Johannes Müller-Trede , Michel Regenwetter

Classical random utility models imply a consistency property called regularity. Decision makers who satisfy regularity are at least as likely to choose an option

x

from a set

X

of available options as from any larger set

Y

that contains

X

. In light of ample empirical evidence for context-dependent choice that violates regularity, some researchers have questioned the descriptive validity of all random utility models. In this article, we show that not all random utility models imply regularity. We propose a general framework for random utility models that accommodate context dependence and may violate regularity. Mathematically, like the classical models, context-dependent random utility models form convex polytopes. They yield behavioral predictions for those choice sets from which choices are made, by specifying combinations of preference rankings across two or more contexts. We discuss how context-dependent models can be less or more parsimonious than the classical models. Random utility models with or without regularity can be tested with contemporary methods of order-constrained inference.

经典的随机实用模型暗示了一种称为规律性的一致性。满足规律性的决策者从一组可选选项x中选择选项x的可能性至少与从包含x的更大集合Y中选择选项x的可能性一样大。鉴于违反规律性的情境依赖选择的大量经验证据，一些研究人员质疑所有随机实用模型的描述性有效性。在本文中，我们表明并非所有的随机实用新型都意味着规律性。我们为随机实用新型提出了一个通用框架，以适应上下文依赖性和可能违反规律性。在数学上，与经典模型一样，上下文相关的随机实用新型形成凸多面体。它们通过在两个或多个上下文中指定偏好排名的组合，对做出选择的那些选择集产生行为预测。我们讨论了上下文相关模型如何比经典模型更少或更简洁。具有或不具有规律性的随机实用新型可以用现代的顺序约束推理方法进行测试。

{"title":"Random utility without regularity","authors":"Johannes Müller-Trede , Michel Regenwetter","doi":"10.1016/j.jmp.2025.102938","DOIUrl":"10.1016/j.jmp.2025.102938","url":null,"abstract":"<div><div>Classical random utility models imply a consistency property called <em>regularity</em>. Decision makers who satisfy regularity are at least as likely to choose an option <span><math><mi>x</mi></math></span> from a set <span><math><mi>X</mi></math></span> of available options as from any larger set <span><math><mi>Y</mi></math></span> that contains <span><math><mi>X</mi></math></span>. In light of ample empirical evidence for context-dependent choice that violates regularity, some researchers have questioned the descriptive validity of all random utility models. In this article, we show that not all random utility models imply regularity. We propose a general framework for random utility models that accommodate context dependence and may violate regularity. Mathematically, like the classical models, context-dependent random utility models form convex polytopes. They yield behavioral predictions for those choice sets from which choices are made, by specifying combinations of preference rankings across two or more contexts. We discuss how context-dependent models can be less or more parsimonious than the classical models. Random utility models with or without regularity can be tested with contemporary methods of order-constrained inference.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"126 ","pages":"Article 102938"},"PeriodicalIF":2.2,"publicationDate":"2025-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The stochastic 2-binary choice problem 随机二叉选择问题

IF 2.2 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2025-07-19 DOI: 10.1016/j.jmp.2025.102939

Paola Manzini , Marco Mariotti , Henrik Petri

The classic (to date unsolved) stochastic binary choice problem asks under what conditions a given stochastic choice function defined on pairs of alternatives derives from a random ranking. We propose a solution to the problem for the case in which at most two rankings are assigned positive probability. This case is psychologically motivated and interesting for applications. It is structurally different from the general case in that the choice functions that are derived from a random ranking do not necessarily form a convex polytope, hence they are not even in principle described by a set of linear inequalities.

经典的（到目前为止尚未解决的）随机二元选择问题是，在什么条件下，定义在选择对上的给定随机选择函数来自随机排序。对于最多两个排名被赋正概率的情况，我们提出了一个解决方案。这种情况是心理动机和有趣的应用程序。它在结构上不同于一般情况，因为由随机排序得到的选择函数不一定形成凸多面体，因此它们在原则上甚至不能用一组线性不等式来描述。

引用次数: 0

Expected exponential discounting in inter-temporal decision making 跨期决策中的预期指数折现

IF 2.2 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2025-05-30 DOI: 10.1016/j.jmp.2025.102927

Tom H. Rosenström , Alasdair I. Houston

We present a novel interpretation of delay discounting – a theoretical mechanism by which decision-makers discount the current value of reward if it is obtained at a future time rather than immediately. The theory proposes that decision-makers rationally account for the natural phenomenon of compounded interests (use exponential discounting) but need to take an average or expected value over some uncertainty distribution for the compound interest rate. Hence, the name Expected Exponential Discounting (EED) theory of inter-temporal choice. We show that EED provides a mechanism that unifies multiple empirically discovered descriptive discounting functions and fits to key qualitative findings about delay discounting in humans under non-sequential contexts, such as for hypothetical questions about delayed rewards. The general, falsifiable and comparatively minimal EED theory provides a good sanity check for more complex accounts of delay discounting, but also supports the derivation of new empirical predictions and reference points.

我们提出了延迟折现的一种新解释——一种理论机制，通过这种机制，如果奖励是在未来而不是立即获得的，决策者就会对当前价值进行折现。该理论提出，决策者理性地考虑复利的自然现象（使用指数贴现），但需要对复利的某些不确定性分布取平均值或期望值。因此，期望指数贴现（EED）的跨期选择理论得名。我们表明，EED提供了一种机制，统一了多个经验发现的描述性折扣函数，并适合于非顺序环境下人类延迟折扣的关键定性发现，例如关于延迟奖励的假设问题。一般的，可证伪的和相对最小的EED理论为更复杂的延迟折扣帐户提供了良好的完整性检查，但也支持新的经验预测和参考点的推导。

引用次数: 0

Honey, I shrunk the irrelevant effects! Simple and flexible approximate Bayesian regularization 亲爱的，我缩小了无关的效果！简单灵活的近似贝叶斯正则化

IF 2.2 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology

Pub Date : 2025-05-29 DOI: 10.1016/j.jmp.2025.102925

Diana Karimova , Sara van Erp , Roger Th.A.J. Leenders , Joris Mulder

In the social and behavioral sciences and related fields, statistical models are becoming increasingly complex with more parameters to explain intricate dependency structures among larger sets of variables. Regularization techniques, like penalized regression, help identify key parameters by shrinking negligible effects to zero, resulting in parsimonious solutions with strong predictive performance. This paper introduces a simple and flexible approximate Bayesian regularization (ABR) procedure, combining a Gaussian approximation of the likelihood with a Bayesian shrinkage prior to obtain a regularized posterior. Parsimonious (interpretable) solutions are obtained by taking the posterior modes. Parameter uncertainty is quantified using the full posterior. Implemented in the R package shrinkem, the method is evaluated in synthetic and empirical applications. Its flexibility is demonstrated across various models, including linear regression, relational event models, mediation analysis, factor analysis, and Gaussian graphical models.

在社会和行为科学及相关领域，统计模型正变得越来越复杂，有更多的参数来解释更大的变量集之间复杂的依赖结构。正则化技术，如惩罚回归，通过将可忽略的影响缩小到零来帮助识别关键参数，从而产生具有强大预测性能的简洁解决方案。本文介绍了一种简单灵活的近似贝叶斯正则化（ABR）方法，将似然的高斯近似与贝叶斯收缩相结合来获得正则化后验。采用后验模态得到简约（可解释）解。参数的不确定性是用全后验量化的。在R封装收缩中实现，该方法在综合和经验应用中进行了评估。它的灵活性在各种模型中得到展示，包括线性回归、关系事件模型、中介分析、因素分析和高斯图形模型。

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Journal of Mathematical Psychology

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀