Journal of Mathematical Psychology最新文献

{"title":"Traits and tangles: An analysis of the Big Five paradigm by tangle-based clustering","authors":"Hanno von Bergen,&nbsp;Reinhard Diestel","doi":"10.1016/j.jmp.2025.102920","DOIUrl":"10.1016/j.jmp.2025.102920","url":null,"abstract":"<div><div>Using the recently developed mathematical theory of tangles, we re-assess the mathematical foundations for applications of the five factor model in personality tests by a new, mathematically rigorous, quantitative method. Our findings broadly confirm the validity of current tests, but also show that more detailed information can be extracted from existing data.</div><div>We found that the big five traits appear at different levels of scrutiny. Some already emerge at a coarse resolution of our tools at which others cannot yet be discerned, while at a resolution where these <em>can</em> be discerned, and distinguished, some of the former traits are no longer visible but have split into more refined traits or disintegrated altogether.</div><div>We also identified traits other than the five targeted in those tests. These include more general traits combining two or more of the big five, as well as more specific traits refining some of them.</div><div>All our analysis is structural and quantitative, and thus rigorous in explicitly defined mathematical terms. Since tangles, once computed, can be described concisely in terms of very few explicit statements referring only to the test questions used, our findings are also directly open to interpretation by experts in psychology.</div><div>Tangle analysis can be applied similarly to other topics in psychology. Our paper is intended to serve as a first indication of what may be possible.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"125 ","pages":"Article 102920"},"PeriodicalIF":2.2,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143823837","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":"Cognitive models of decision-making with identifiable parameters: Diffusion decision models with within-trial noise","authors":"Michael D. Nunez ,&nbsp;Anna-Lena Schubert ,&nbsp;Gidon T. Frischkorn ,&nbsp;Klaus Oberauer","doi":"10.1016/j.jmp.2025.102917","DOIUrl":"10.1016/j.jmp.2025.102917","url":null,"abstract":"<div><div>Diffusion Decision Models (DDMs) are a widely used class of models that assume an accumulation of evidence during a quick decision. These models are often used as measurement models to assess individual differences in cognitive processes such as evidence accumulation rate and response caution. An underlying assumption of these models is that there is internal noise in the evidence accumulation process. We argue that this internal noise is a relevant psychological construct that is likely to vary over participants and explain differences in cognitive ability. In some cases a change in noise is a more parsimonious explanation of joint changes in speed-accuracy tradeoffs and ability. However, fitting traditional DDMs to behavioral data cannot yield estimates of an individual’s evidence accumulation rate, caution, and internal noise at the same time. This is due to an intrinsic unidentifiability of these parameters in DDMs. We explored the practical consequences of this unidentifiability by estimating the Bayesian joint posterior distributions of parameters (and thus joint uncertainty) for simulated data. We also introduce methods of estimating these parameters. Fundamentally, these parameters can be identified in two ways: (1) We can assume that one of the three parameters is fixed to a constant. We show that fixing one parameter, as is typical in fitting DDMs, results in parameter estimates that are ratios of true cognitive parameters including the parameter that is fixed. By fixing another parameter instead of noise, different ratios are estimated, which may be useful for measuring individual differences. (2) Alternatively, we could use additional observed variables that we can reasonably assume to be related to model parameters. Electroencephalographic (EEG) data or single-unit activity from animals can yield candidate measures. We show parameter recovery for models with true (simulated) connections to such additional covariates, as well as some recovery in misspecified models. We evaluate this approach with both single-trial and participant-level additional observed variables. Our findings reveal that with the integration of additional data, it becomes possible to discern individual differences across all parameters, enhancing the utility of DDMs without relying on strong assumptions. However, there are some important caveats with these new modeling approaches, and we provide recommendations for their use. This research paves the way to use the deeper theoretical understanding of sequential sampling models and the new modeling methods to measure individual differences in internal noise during decision-making.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"125 ","pages":"Article 102917"},"PeriodicalIF":2.2,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143799868","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":"2025-03-01","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":"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":"2025-03-01","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":"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":"2025-03-01","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":"2025-03-01","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}

{"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":"2025-03-01","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":"2025-03-01","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":"2025-03-01","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":"On using the fixed-point property of binary mixtures to discriminate among models of recognition memory","authors":"F. Gregory Ashby","doi":"10.1016/j.jmp.2024.102889","DOIUrl":"10.1016/j.jmp.2024.102889","url":null,"abstract":"<div><div>A variety of different recognition-memory models make different psychological assumptions, but similar predictions about ROC curves in old–new recognition-memory experiments. Some models assume that recognition responses are produced by a unitary process and other models assume they are a binary mixture of two qualitatively different types of responses. This note shows that despite their similar ROC predictions, the binary-mixture models make some striking predictions that the unitary models do not make. Specifically, in any experiment that includes conditions in which the mixture probability varies but the component distributions do not, the binary-mixture models predict that all response time probability density functions must intersect at the same time point (if they intersect at all). Similarly, they also all predict that if the ROC curves intersect, they must also all intersect at the same point.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"123 ","pages":"Article 102889"},"PeriodicalIF":2.2,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652220","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}