Journal of Mathematical Psychology最新文献

{"title":"Two formal notions of higher-order invariance detection in humans (A proof of the invariance equivalence principle in Generalized Invariance Structure Theory and ramifications for related computations)","authors":"Ronaldo Vigo","doi":"10.1016/j.jmp.2025.102905","DOIUrl":"10.1016/j.jmp.2025.102905","url":null,"abstract":"<div><div>Invariance and symmetry principles have played a fundamental if not essential role in the theoretical development of the physical and mathematical sciences. More recently, Generalized Invariance Structure Theory (GIST; Vigo, 2013, 2015; Vigo et al., 2022) has extended this methodological trajectory with respect to the study and formal modeling of human cognition. Indeed, GIST is the first systematic and extensively tested mathematical and computational theory of concept learning and categorization behavior (i.e., human generalization) based on such principles. The theory introduces an original mathematical and computational framework, with novel, more appropriate, and more natural characterizations, constructs, and measures of invariance and symmetry with respect to cognition than existing ones in the mathematical sciences and physics. These have proven effective in predicting and explaining empirically tested behavior in the domains of perception, concept learning, categorization, similarity assessment, aesthetic judgments, and decision making, among others. GIST has its roots in a precursor theory known as Categorical Invariance Theory (CIT; Vigo, 2009). This paper gives a basic introduction to two different notions of human invariance detection proposed by GIST and its precursor CIT: namely, a notion based on a cognitive mechanism of dimensional suppression, rapid attention shifting, and partial similarity assessment referred to as <em>binding</em> (<em>s</em>-invariance) and a perturbation notion based on perturbations of the values of the dimensions on which categories of object stimuli are defined (<em>p</em>-invariance). This is followed by the first simple formal proof of the invariance equivalence principle from GIST which asserts that the two notions are equivalent under a set of strict conditions on categories. The paper ends with a brief discussion of how GIST, unlike CIT, may be used to model probabilistic process accounts of categorization, and how it naturally and directly applies to the learning of sequential categories and to multiset-based concept learning.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"125 ","pages":"Article 102905"},"PeriodicalIF":2.2,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The assessment of global optimization skills in procedural knowledge space theory","authors":"Luca Stefanutti,&nbsp;Andrea Brancaccio","doi":"10.1016/j.jmp.2025.102907","DOIUrl":"10.1016/j.jmp.2025.102907","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"125 ","pages":"Article 102907"},"PeriodicalIF":2.2,"publicationDate":"2025-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Models of human probability judgment errors","authors":"Jiaqi Huang,&nbsp;Jerome Busemeyer","doi":"10.1016/j.jmp.2025.102906","DOIUrl":"10.1016/j.jmp.2025.102906","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"125 ","pages":"Article 102906"},"PeriodicalIF":2.2,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143507981","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}

{"title":"Conjugate Bayesian analysis of the Wald model: On an exact drift-rate posterior","authors":"Constantin G. Meyer-Grant","doi":"10.1016/j.jmp.2025.102904","DOIUrl":"10.1016/j.jmp.2025.102904","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"124 ","pages":"Article 102904"},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Probabilistic models of delay discounting: “Fixed-endpoint” psychometric curves improve plausibility and performance","authors":"Isaac Kinley ,&nbsp;Joseph Oluwasola ,&nbsp;Suzanna Becker","doi":"10.1016/j.jmp.2025.102902","DOIUrl":"10.1016/j.jmp.2025.102902","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"124 ","pages":"Article 102902"},"PeriodicalIF":2.2,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143311016","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}

{"title":"Choosing is losing: How opportunity cost influences valuations and choice","authors":"Tomás Lejarraga ,&nbsp;József Sákovics","doi":"10.1016/j.jmp.2025.102901","DOIUrl":"10.1016/j.jmp.2025.102901","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"124 ","pages":"Article 102901"},"PeriodicalIF":2.2,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143167569","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}

{"title":"Analysing the bias introduced by adaptive designs to estimates of psychometric functions","authors":"Simon Bang Kristensen ,&nbsp;Katrine Bødkergaard ,&nbsp;Bo Martin Bibby","doi":"10.1016/j.jmp.2025.102899","DOIUrl":"10.1016/j.jmp.2025.102899","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"124 ","pages":"Article 102899"},"PeriodicalIF":2.2,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143167637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A class of random utility models yielding the exploded logit","authors":"Karim Kilani","doi":"10.1016/j.jmp.2025.102900","DOIUrl":"10.1016/j.jmp.2025.102900","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"124 ","pages":"Article 102900"},"PeriodicalIF":2.2,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143167636","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}

{"title":"Dimensions of knowledge structures","authors":"Jean-Paul Doignon ,&nbsp;Luca Stefanutti","doi":"10.1016/j.jmp.2024.102898","DOIUrl":"10.1016/j.jmp.2024.102898","url":null,"abstract":"<div><div>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 <em>ordinal dimension</em>, which is the dimension of the poset consisting of all states ordered by inclusion; (ii) for a knowledge space, the <em>spatial dimension</em> 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 <em>bidimension</em>, 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.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"124 ","pages":"Article 102898"},"PeriodicalIF":2.2,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143167638","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}

{"title":"Characterizing master fringes in competence-based knowledge space theory for personalized learning applications","authors":"Gongxun Wang ,&nbsp;Jinjin Li ,&nbsp;Bo Wang ,&nbsp;Chenyi Tao","doi":"10.1016/j.jmp.2024.102897","DOIUrl":"10.1016/j.jmp.2024.102897","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"124 ","pages":"Article 102897"},"PeriodicalIF":2.2,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143167568","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}