Pub Date : 2025-12-04DOI: 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。
{"title":"Identifiability of the polytomous local independence model with graded knowledge structures","authors":"Luca Stefanutti , Andrea Spoto","doi":"10.1016/j.jmp.2025.102956","DOIUrl":"10.1016/j.jmp.2025.102956","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"128 ","pages":"Article 102956"},"PeriodicalIF":1.5,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145665688","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}
Pub Date : 2025-12-01DOI: 10.1016/j.jmp.2025.102951
Keith A. Schneider
{"title":"Corrigendum to “An entropy model of decision uncertainty” [Journal of Mathematical Psychology 125 (2025), 102919]","authors":"Keith A. Schneider","doi":"10.1016/j.jmp.2025.102951","DOIUrl":"10.1016/j.jmp.2025.102951","url":null,"abstract":"","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"127 ","pages":"Article 102951"},"PeriodicalIF":1.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145684646","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}
Pub Date : 2025-12-01DOI: 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.
{"title":"A dynamic model of context-based retrieval","authors":"Madison D. Paron , James D. Paron , Michael J. Kahana","doi":"10.1016/j.jmp.2025.102957","DOIUrl":"10.1016/j.jmp.2025.102957","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"127 ","pages":"Article 102957"},"PeriodicalIF":1.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145618015","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}
Pub Date : 2025-11-20DOI: 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.
{"title":"On informativeness and reducibility in competence models","authors":"Huihua Shi , Bo Wang , Ning Gan , Jinjin Li","doi":"10.1016/j.jmp.2025.102955","DOIUrl":"10.1016/j.jmp.2025.102955","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"127 ","pages":"Article 102955"},"PeriodicalIF":1.5,"publicationDate":"2025-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145579063","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}
Pub Date : 2025-11-18DOI: 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 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.
{"title":"Standardized mean difference effect sizes for interval-valued data. A distance-based approach","authors":"M. Asunción Lubiano , José García-García , Antonio L. García-Izquierdo , Ana M. Castaño","doi":"10.1016/j.jmp.2025.102954","DOIUrl":"10.1016/j.jmp.2025.102954","url":null,"abstract":"<div><div>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 <span><math><mi>d</mi></math></span> 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.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"127 ","pages":"Article 102954"},"PeriodicalIF":1.5,"publicationDate":"2025-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145579064","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}
Pub Date : 2025-11-05DOI: 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.
{"title":"Modeling meta-reasoning processes using diffusion and quantum random walk models","authors":"Ritesh K. Malaiya, Richard M. Golden","doi":"10.1016/j.jmp.2025.102952","DOIUrl":"10.1016/j.jmp.2025.102952","url":null,"abstract":"<div><div>Meta-reasoning studies investigate the role of metacognitive processes in <em>monitoring</em> the success likelihood of an ongoing Reasoning task expected to require Longer Deliberation Time (RLDT), and accordingly, <em>control</em> 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 <em>I am 70% confident that the problem is solvable</em>, 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.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"127 ","pages":"Article 102952"},"PeriodicalIF":1.5,"publicationDate":"2025-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145465505","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}
Pub Date : 2025-11-02DOI: 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.
{"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}
Pub Date : 2025-09-15DOI: 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.
{"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}
Pub Date : 2025-09-12DOI: 10.1016/j.jmp.2025.102943
Eszter Gselmann , Christopher W. Doble , Yung-Fong Hsu
Iverson (2006b) proposed the law of similarity for the sensitivity functions . Compared to the former models, the generality of this one lies in that here and can also depend on the variables and . 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 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 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 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.
{"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}
Pub Date : 2025-09-03DOI: 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 , 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.
{"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}
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