Pub Date : 2024-11-12DOI: 10.1016/j.jmp.2024.102889
F. Gregory Ashby
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.
{"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":"2024-11-12","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}
Pub Date : 2024-10-31DOI: 10.1016/j.jmp.2024.102888
Andrea Brancaccio, Luca Stefanutti
In procedural knowledge space theory (PKST), a “problem space” is a formal representation of the knowledge that is needed for solving all of the problems of a certain type. The competence state of a real problem solver is a subset of the problem space which satisfies a specific condition, named the “sub-path assumption”. There could exist specific “symmetries” in a problem space that make certain parts of it “equivalent” up to those symmetries. Whenever an equivalence relation is introduced for elements in a problem space, the question almost naturally arises whether the collection of the induced equivalence classes forms, itself, a problem space. This is the main question addressed in the present article, which is restated as the problem of defining a homomorphism of one problem space into another problem space. Two types of homomorphisms are examined, which are named the “strong” and the “weak homomorphism”. The former corresponds to the usual notion of “operation preserving mapping”. The latter preserves operations in only one direction. Two algorithms are developed for testing the existence of homomorphisms between problem spaces. The notions and algorithms are illustrated in a series of three examples in which quite well-known neuro-psychological and cognitive tests are employed.
{"title":"Homomorphisms between problem spaces","authors":"Andrea Brancaccio, Luca Stefanutti","doi":"10.1016/j.jmp.2024.102888","DOIUrl":"10.1016/j.jmp.2024.102888","url":null,"abstract":"<div><div>In procedural knowledge space theory (PKST), a “problem space” is a formal representation of the knowledge that is needed for solving all of the problems of a certain type. The competence state of a real problem solver is a subset of the problem space which satisfies a specific condition, named the “sub-path assumption”. There could exist specific “symmetries” in a problem space that make certain parts of it “equivalent” up to those symmetries. Whenever an equivalence relation is introduced for elements in a problem space, the question almost naturally arises whether the collection of the induced equivalence classes forms, itself, a problem space. This is the main question addressed in the present article, which is restated as the problem of defining a homomorphism of one problem space into another problem space. Two types of homomorphisms are examined, which are named the “strong” and the “weak homomorphism”. The former corresponds to the usual notion of “operation preserving mapping”. The latter preserves operations in only one direction. Two algorithms are developed for testing the existence of homomorphisms between problem spaces. The notions and algorithms are illustrated in a series of three examples in which quite well-known neuro-psychological and cognitive tests are employed.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"123 ","pages":"Article 102888"},"PeriodicalIF":2.2,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554922","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}
Pub Date : 2024-10-28DOI: 10.1016/j.jmp.2024.102887
Natham Aguirre
The Inhibited Elements Model (Brandon et al., 2000; Wagner and Brandon, 2000) has been proposed as an elemental model that may reproduce the configural model proposed by Pearce (1987, 1994), and although its mathematical formalization has been recently improved by Thorwart and Lachnit (2020), whether it actually reproduces Pearce’s model has remained an open question. In this work I further develop the mathematical formalization of the Inhibited Elements Model by casting it within the formalism proposed by Ghirlanda (2015, 2018). In doing so I will derive the conditions under which the Inhibited Elements Model reproduces Pearce’s model, showing that when all stimuli are assumed of the same “salience” these models coincide only when the application is restricted to compounds that either contain each other or have no common elements. Finally, the mathematical formalization developed here will be applied to the analytic comparison of the Inhibited Elements Model, Rescorla and Wagner’s model (Rescorla and Wagner, 1972; Wagner and Rescorla, 1972), and Pearce’s model in the context of several learning phenomena.
抑制要素模型（Brandon et al., 2000; Wagner and Brandon, 2000）作为一种要素模型被提出来，它可以再现皮尔斯（1987, 1994）提出的构型模型，尽管最近索瓦特和拉赫尼特（2020）对其数学形式化进行了改进，但它是否真的再现了皮尔斯的模型仍是一个未决问题。在这项工作中，我将进一步发展抑制要素模型的数学形式化，将其纳入吉兰达（2015，2018）提出的形式主义中。在此过程中，我将推导出抑制元素模型重现 Pearce 模型的条件，表明当所有刺激都被假定具有相同的 "显著性 "时，只有当应用仅限于相互包含或没有共同元素的化合物时，这些模型才会重合。最后，我们将把在此基础上发展起来的数学形式化方法用于分析比较 "抑制元素模型"、雷斯科拉和瓦格纳的模型（雷斯科拉和瓦格纳，1972；瓦格纳和雷斯科拉，1972）以及皮尔斯模型在若干学习现象中的应用。
{"title":"On the mathematical formalization of the Inhibited Elements Model","authors":"Natham Aguirre","doi":"10.1016/j.jmp.2024.102887","DOIUrl":"10.1016/j.jmp.2024.102887","url":null,"abstract":"<div><div>The Inhibited Elements Model (Brandon et al., 2000; Wagner and Brandon, 2000) has been proposed as an elemental model that may reproduce the configural model proposed by Pearce (1987, 1994), and although its mathematical formalization has been recently improved by Thorwart and Lachnit (2020), whether it actually reproduces Pearce’s model has remained an open question. In this work I further develop the mathematical formalization of the Inhibited Elements Model by casting it within the formalism proposed by Ghirlanda (2015, 2018). In doing so I will derive the conditions under which the Inhibited Elements Model reproduces Pearce’s model, showing that when all stimuli are assumed of the same “salience” these models coincide only when the application is restricted to compounds that either contain each other or have no common elements. Finally, the mathematical formalization developed here will be applied to the analytic comparison of the Inhibited Elements Model, Rescorla and Wagner’s model (Rescorla and Wagner, 1972; Wagner and Rescorla, 1972), and Pearce’s model in the context of several learning phenomena.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"123 ","pages":"Article 102887"},"PeriodicalIF":2.2,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142533979","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 : 2024-10-10DOI: 10.1016/j.jmp.2024.102885
Vladislav Myrov , Elena Gorina , Kristina Vodorezova , Maria Dvoeglazova , Ekaterina Koshmanova , Elena S. Gorbunova , Tadamasa Sawada
Within an Ames room, the perceived size of objects, such as people, changes dynamically when the objects move about within the room. The shape of the Ames room is not actually rectangular but it is perceived to be rectangular. Unfortunately, the geometrical properties of the Ames room have often been misunderstood, and rooms that have different shapes are also referred to as “Ames rooms” in many articles. In this study, the geometrical properties of the original Ames rooms constructed by Adelbert Ames, Jr. were analyzed and the generalization of the Ames room was discussed. We found that these original Ames rooms are 3D-to-3D perspective transformations of rectangular illusory rooms. Based on this analysis, we also developed a computational model that can construct a generalized Ames room that has a hexahedral shape with some free parameters that quantitatively control (i) the size and aspect-ratio of a rectangular illusory room, (ii) the amount of distortion of the Ames room from a rectangular room, and (iii) the viewpoint of an observer. This model was implemented as a computational program so that an Ames room can be constructed in a VR space. Note that the transformations of the Ames rooms can be applied to an arbitrary 3D scene and that they can be regarded as members of a subset of 3D-to-3D perspective transformations. Any perspective transformation in this subset distorts the 3D scene in such a way that the retinal image of the distorted scene, when seen from a specific viewpoint, is identical to the retinal image of the initial scene, when seen from a specific viewpoint. These generalizations allow us to control the conditions of an Ames room systematically with more flexibility when we study this illusion.
{"title":"Understanding the geometrical properties of an Ames room and controlling it systematically and quantitatively","authors":"Vladislav Myrov , Elena Gorina , Kristina Vodorezova , Maria Dvoeglazova , Ekaterina Koshmanova , Elena S. Gorbunova , Tadamasa Sawada","doi":"10.1016/j.jmp.2024.102885","DOIUrl":"10.1016/j.jmp.2024.102885","url":null,"abstract":"<div><div>Within an Ames room, the perceived size of objects, such as people, changes dynamically when the objects move about within the room. The shape of the Ames room is not actually rectangular but it is perceived to be rectangular. Unfortunately, the geometrical properties of the Ames room have often been misunderstood, and rooms that have different shapes are also referred to as “Ames rooms” in many articles. In this study, the geometrical properties of the original Ames rooms constructed by Adelbert Ames, Jr. were analyzed and the generalization of the Ames room was discussed. We found that these original Ames rooms are 3D-to-3D perspective transformations of rectangular illusory rooms. Based on this analysis, we also developed a computational model that can construct a generalized Ames room that has a hexahedral shape with some free parameters that quantitatively control (i) the size and aspect-ratio of a rectangular illusory room, (ii) the amount of distortion of the Ames room from a rectangular room, and (iii) the viewpoint of an observer. This model was implemented as a computational program so that an Ames room can be constructed in a VR space. Note that the transformations of the Ames rooms can be applied to an arbitrary 3D scene and that they can be regarded as members of a subset of 3D-to-3D perspective transformations. Any perspective transformation in this subset distorts the 3D scene in such a way that the retinal image of the distorted scene, when seen from a specific viewpoint, is identical to the retinal image of the initial scene, when seen from a specific viewpoint. These generalizations allow us to control the conditions of an Ames room systematically with more flexibility when we study this illusion.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"123 ","pages":"Article 102885"},"PeriodicalIF":2.2,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142423771","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 : 2024-10-08DOI: 10.1016/j.jmp.2024.102886
Gaurav Suri, Kenneth R. Paap
Self-control is core to human well-being. However, the lack of a well-specified, computationally tractable framework related to self-control makes it difficult to clarify underlying mechanisms, interpret relevant empirical phenomena, or develop interventions helpful in promoting self-control. To help address this gap, we invite consideration of the Comparison with Goal States Model (CGSM) for self-control. The CGSM amplifies activations related to available options whose representations are similar to representations of relevant goals and diminishes activations related to available options whose representations are dissimilar to representations of relevant goals. For example, influenced by healthy eating goals, the CGSM would amplify activations related to an apple and diminish activations related to a cookie, leading to an eventual preference for the apple, even though the cookie might be initially preferred. The CGSM successfully explicates observations related to reaction time in food choice, dynamics reflected in mouse-tracking trajectories, and showcases a mechanism by which hyperbolic discount curves in temporal discounting contexts might emerge. We use the CGSM to propose theoretical constraints on the nature of self-control and describe how multiple strategies have the potential to promote self-control.
{"title":"A computational account of self-control","authors":"Gaurav Suri, Kenneth R. Paap","doi":"10.1016/j.jmp.2024.102886","DOIUrl":"10.1016/j.jmp.2024.102886","url":null,"abstract":"<div><div>Self-control is core to human well-being. However, the lack of a well-specified, computationally tractable framework related to self-control makes it difficult to clarify underlying mechanisms, interpret relevant empirical phenomena, or develop interventions helpful in promoting self-control. To help address this gap, we invite consideration of the Comparison with Goal States Model (CGSM) for self-control. The CGSM amplifies activations related to available options whose representations are similar to representations of relevant goals and diminishes activations related to available options whose representations are dissimilar to representations of relevant goals. For example, influenced by healthy eating goals, the CGSM would amplify activations related to an apple and diminish activations related to a cookie, leading to an eventual preference for the apple, even though the cookie might be initially preferred. The CGSM successfully explicates observations related to reaction time in food choice, dynamics reflected in mouse-tracking trajectories, and showcases a mechanism by which hyperbolic discount curves in temporal discounting contexts might emerge. We use the CGSM to propose theoretical constraints on the nature of self-control and describe how multiple strategies have the potential to promote self-control.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"123 ","pages":"Article 102886"},"PeriodicalIF":2.2,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142423769","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}
Pub Date : 2024-09-27DOI: 10.1016/j.jmp.2024.102884
Manuel Villarreal, Michael D. Lee
We introduce a new framework for measuring the dynamics of category learning using Coupled Hidden Markov Models (CHMMs). The key assumptions of the framework are that people maintain a latent assignment of every stimulus to a category, and that they can update the assignments for all stimuli whenever they encounter any stimulus. These assumptions contrast with many existing accounts of category learning, which either do not allow for what is learned about one stimulus to influence the category association of others, or allow only for indirect influence. The CHMM framework allows tailored models to be developed for specific category learning tasks, taking as input the stimulus sequence and category responses people make, and producing as output inferences about the underlying dynamics of category assignments and the mechanics of the response processes. We demonstrate the framework by applying it to a categorization task considered by Lee and Navarro (2002), showing how the model measures the change in participants’ latent category assignments as they learn the category structure. We conclude by discussing potential applications of the CHMM framework to category learning situations involving prior knowledge, changing category structures, and category learning tasks that involve the consideration of multiple stimuli at one time.
我们介绍了一种使用耦合隐马尔可夫模型（CHMMs）测量类别学习动态的新框架。该框架的关键假设是，人们将每个刺激物都归入一个类别，而且每当遇到任何刺激物时，他们都能更新所有刺激物的归属。这些假设与许多现有的类别学习论述形成鲜明对比，后者要么不允许所学到的关于一个刺激物的知识影响其他刺激物的类别关联，要么只允许间接影响。CHMM框架允许为特定的类别学习任务开发量身定制的模型，将刺激序列和人们做出的类别反应作为输入，并将类别分配的基本动态和反应过程的机制作为输出推论。我们将该框架应用于 Lee 和 Navarro（2002 年）所考虑的分类任务，展示了该模型如何测量参与者在学习类别结构时潜在类别分配的变化。最后，我们将讨论 CHMM 框架在涉及先验知识、不断变化的类别结构以及同时考虑多个刺激的类别学习任务中的潜在应用。
{"title":"A Coupled Hidden Markov Model framework for measuring the dynamics of categorization","authors":"Manuel Villarreal, Michael D. Lee","doi":"10.1016/j.jmp.2024.102884","DOIUrl":"10.1016/j.jmp.2024.102884","url":null,"abstract":"<div><div>We introduce a new framework for measuring the dynamics of category learning using Coupled Hidden Markov Models (CHMMs). The key assumptions of the framework are that people maintain a latent assignment of every stimulus to a category, and that they can update the assignments for all stimuli whenever they encounter any stimulus. These assumptions contrast with many existing accounts of category learning, which either do not allow for what is learned about one stimulus to influence the category association of others, or allow only for indirect influence. The CHMM framework allows tailored models to be developed for specific category learning tasks, taking as input the stimulus sequence and category responses people make, and producing as output inferences about the underlying dynamics of category assignments and the mechanics of the response processes. We demonstrate the framework by applying it to a categorization task considered by Lee and Navarro (2002), showing how the model measures the change in participants’ latent category assignments as they learn the category structure. We conclude by discussing potential applications of the CHMM framework to category learning situations involving prior knowledge, changing category structures, and category learning tasks that involve the consideration of multiple stimuli at one time.</div></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"123 ","pages":"Article 102884"},"PeriodicalIF":2.2,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142327333","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}
Pub Date : 2024-09-16DOI: 10.1016/j.jmp.2024.102883
Konstantinos V. Katsikopoulos
The priority heuristic is a lexicographic semi-order for choosing between gambles. It has merits such as predicting, out-of-sample, people's majority choice more accurately than benchmarks such as prospect theory, having been axiomatized, and logically implying major violations of expected utility theory. The heuristic has shortcomings too, such as failing to account for individual differences and intricate choice patterns, and predicting less accurately than various model ensembles and neural networks in some environments. This note focuses on an important purported shortcoming of the heuristic, that it cannot produce valuations of gambles. I point out that the certainty equivalent of a gamble for the priority heuristic is known and suggest that this fact can be used to enhance the scope of the heuristic. Indeed, by making simple auxiliary assumptions and calculations, I demonstrate that the priority heuristic can explain the Saint Petersburg paradox and the equity premium puzzle, and to do so arguably more parsimoniously and plausibly than standard approaches.
{"title":"Making valuations with the priority heuristic","authors":"Konstantinos V. Katsikopoulos","doi":"10.1016/j.jmp.2024.102883","DOIUrl":"10.1016/j.jmp.2024.102883","url":null,"abstract":"<div><p>The priority heuristic is a lexicographic semi-order for choosing between gambles. It has merits such as predicting, out-of-sample, people's majority choice more accurately than benchmarks such as prospect theory, having been axiomatized, and logically implying major violations of expected utility theory. The heuristic has shortcomings too, such as failing to account for individual differences and intricate choice patterns, and predicting less accurately than various model ensembles and neural networks in some environments. This note focuses on an important purported shortcoming of the heuristic, that it cannot produce valuations of gambles. I point out that the certainty equivalent of a gamble for the priority heuristic is known and suggest that this fact can be used to enhance the scope of the heuristic. Indeed, by making simple auxiliary assumptions and calculations, I demonstrate that the priority heuristic can explain the Saint Petersburg paradox and the equity premium puzzle, and to do so arguably more parsimoniously and plausibly than standard approaches.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"123 ","pages":"Article 102883"},"PeriodicalIF":2.2,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S002224962400052X/pdfft?md5=33d571a5e4e5b946fd089948c0769780&pid=1-s2.0-S002224962400052X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142233739","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}
Pub Date : 2024-09-12DOI: 10.1016/j.jmp.2024.102875
Luigi Burigana
Two theories of current interest and of mathematical and computational substance concerning knowledge assessment in education are discussed. These are the theory of knowledge structures and the theory of Bayesian networks as specifically related to educational assessment. In four separate sections, the two theories are compared by considering the sets of variables involved in their models, the set-theoretical and relational constructs defined on those variables, the probabilistic assumptions and properties, and the problems addressed by the theories in constructing their models. For the comparison, a common-base system of symbols and terms is adopted, which overcomes the peculiarities of expression in the corresponding streams of literature. This system gives us a better recognition of the similarities and differences between the two paradigms, and a precise appreciation of their arguments and abilities.
{"title":"Bayesian networks and knowledge structures in cognitive assessment: Remarks on basic comparable aspects","authors":"Luigi Burigana","doi":"10.1016/j.jmp.2024.102875","DOIUrl":"10.1016/j.jmp.2024.102875","url":null,"abstract":"<div><p>Two theories of current interest and of mathematical and computational substance concerning knowledge assessment in education are discussed. These are the theory of knowledge structures and the theory of Bayesian networks as specifically related to educational assessment. In four separate sections, the two theories are compared by considering the sets of variables involved in their models, the set-theoretical and relational constructs defined on those variables, the probabilistic assumptions and properties, and the problems addressed by the theories in constructing their models. For the comparison, a common-base system of symbols and terms is adopted, which overcomes the peculiarities of expression in the corresponding streams of literature. This system gives us a better recognition of the similarities and differences between the two paradigms, and a precise appreciation of their arguments and abilities.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"123 ","pages":"Article 102875"},"PeriodicalIF":2.2,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142171999","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 : 2024-08-28DOI: 10.1016/j.jmp.2024.102876
Gerhard Tutz
The Rasch model is the most prominent member of the class of latent trait models that are in common use. The main reason is that it can be considered as a measurement model that allows to separate person and item parameters, a feature that is referred to as invariance of comparisons or specific objectivity. It is shown that the property is not an exclusive trait of Rasch type models but is also found in alternative latent trait models. It is distinguished between separability in the theoretical measurement model and empirical separability with empirical separability meaning that parameters can be estimated without reference to the other group of parameters. A new type of pairwise estimator with this property is proposed that can be used also in alternative models. Separability is considered in binary models as well as in polytomous models.
{"title":"Invariance of comparisons: Separation of item and person parameters beyond Rasch models","authors":"Gerhard Tutz","doi":"10.1016/j.jmp.2024.102876","DOIUrl":"10.1016/j.jmp.2024.102876","url":null,"abstract":"<div><p>The Rasch model is the most prominent member of the class of latent trait models that are in common use. The main reason is that it can be considered as a measurement model that allows to separate person and item parameters, a feature that is referred to as invariance of comparisons or specific objectivity. It is shown that the property is not an exclusive trait of Rasch type models but is also found in alternative latent trait models. It is distinguished between separability in the theoretical measurement model and empirical separability with empirical separability meaning that parameters can be estimated without reference to the other group of parameters. A new type of pairwise estimator with this property is proposed that can be used also in alternative models. Separability is considered in binary models as well as in polytomous models.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"122 ","pages":"Article 102876"},"PeriodicalIF":2.2,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022249624000452/pdfft?md5=1dcee797a7b9847b792cd716bac6beb0&pid=1-s2.0-S0022249624000452-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142087886","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}
Pub Date : 2024-08-09DOI: 10.1016/j.jmp.2024.102868
Stephen W Link
Think about a thought. Easy to do but where does the thought come from? How is it created? Can it be measured? If so what in the mind is measured? This presentation describes a method for answering these basic questions. The answers derive from a new experimental method called Directly Measured Stimulus Differences (DMSD) and a new theory of mental measurement, a cybernetic process, for the creation of thought. The ideas of Prime Thought and Prime Mind are introduced.
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