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An illustrated guide to context effects 上下文效果的图解指南
IF 1.8 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-08-01 DOI: 10.1016/j.jmp.2023.102790
Clintin P. Davis-Stober , A.A.J. Marley , William J. McCausland , Brandon M. Turner

Three context effects pertaining to stochastic discrete choice have attracted a lot of attention in Psychology, Economics and Marketing: the similarity effect, the compromise effect and the asymmetric dominance effect. Despite this attention, the existing literature is rife with conflicting definitions and misconceptions. We provide theorems relating different variants of each of the three context effects, and theorems relating the context effects to conditions on discrete choice probabilities, such as random utility, regularity, the constant ratio rule, and simple scalability, that may or may not hold for any given discrete choice model. We show how context effects at the individual level may or may not aggregate to context effects at the population level. Importantly, we offer this work as a guide for researchers to sharpen empirical tests and aid future development of choice models.

与随机离散选择相关的三种情境效应引起了心理学、经济学和市场营销学的广泛关注:相似性效应、妥协效应和不对称优势效应。尽管如此,现有的文献中充斥着相互矛盾的定义和误解。我们提供了与三种上下文效应的不同变体相关的定理,以及将上下文效应与离散选择概率的条件相关的定理,如随机效用、规律性、恒定比规则和简单可扩展性,这些定理可能适用于也可能不适用于任何给定的离散选择模型。我们展示了个体水平上的环境效应如何可能或可能不会汇总到群体水平上的环境效应。重要的是,我们提供这项工作,为研究人员提供指导,以提高实证检验和帮助未来发展的选择模型。
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引用次数: 0
A queueing model of visual search 视觉搜索的排队模型
IF 1.8 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-08-01 DOI: 10.1016/j.jmp.2023.102766
Yiqi Li , Martin Schlather , Edgar Erdfelder

Understanding how attentional resources are deployed in visual processing is a fundamental and highly debated topic. As an alternative to theoretical models of visual search that propose sequences of separate serial or parallel stages of processing, we suggest a queueing processing structure that entails a serial transition between parallel processing stages. We develop a continuous-time queueing model for standard visual search tasks to formalize and implement this notion. Specified as a finite-time, single-line, multiserver queueing system, the model accounts for both accuracy and response time (RT) data in visual search on a distributional level. It assumes two stages of processing. Visual stimuli first go through a massively parallel preattentive stage of feature encoding. They wait if necessary and then enter a limited-capacity attentive stage serially where multiple processing channels (“servers”) integrate features of several stimuli in parallel. A core feature of our model is the serial transition from the unlimited-capacity preattentive processing stage to the limited-capacity attentive processing stage. It enables asynchronous attentive processing of multiple stimuli in parallel and is more efficient than a simple chain of two successive, strictly parallel processing stages. The model accounts for response errors by means of two underlying mechanisms, namely, imperfect processing of the servers and, in addition, incomplete search adopted by the observer to maximize search efficiency under an accuracy constraint. For statistical inference, we develop a Monte-Carlo-based parameter estimation procedure, using maximum likelihood (ML) estimation for accuracy-related parameters and minimum distance (MD) estimation for RT-related parameters. We fit the model to two large empirical data sets from two types of visual search tasks. The model captures the accuracy rates almost perfectly and the observed RT distributions quite well, indicating a high explanatory power. The number of independent parallel processing channels that explain both data sets best was five. We also perform a Monte-Carlo model uncertainty analysis and show that the model with the correct number of parallel channels is selected for more than 90% of the simulated samples.

理解注意力资源是如何在视觉处理中部署的是一个基本的和高度争议的话题。作为视觉搜索理论模型的替代方案,我们提出了一种排队处理结构,它需要在并行处理阶段之间进行串行转换。我们为标准视觉搜索任务开发了一个连续时间排队模型来形式化和实现这一概念。该模型被指定为有限时间、单行、多服务器排队系统,在分布级别上考虑可视化搜索中的准确性和响应时间(RT)数据。它采用两个处理阶段。视觉刺激首先经历大量平行的特征编码前注意阶段。如果有必要,它们会等待,然后依次进入一个容量有限的专注阶段,在这个阶段,多个处理通道(“服务器”)并行地整合多个刺激的特征。该模型的一个核心特征是从无限容量的预注意加工阶段到有限容量的注意加工阶段的连续过渡。它能并行地对多个刺激进行异步注意处理,比两个连续的、严格并行的处理阶段的简单链更有效。该模型通过两种潜在的机制来解释响应误差,即服务器的不完全处理和观察者在精度约束下为最大化搜索效率而采取的不完全搜索。对于统计推断,我们开发了一种基于蒙特卡罗的参数估计程序,对精度相关参数使用最大似然(ML)估计,对rt相关参数使用最小距离(MD)估计。我们将模型拟合到来自两种类型的视觉搜索任务的两个大型经验数据集。该模型几乎完美地捕获了准确率,并且观察到的RT分布相当好,表明具有很高的解释力。能够最好地解释两个数据集的独立并行处理通道的数量是5个。我们还进行了蒙特卡罗模型不确定性分析,结果表明,90%以上的模拟样本选择了具有正确并行通道数的模型。
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引用次数: 0
Modal preference structures 模态偏好结构
IF 1.8 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-08-01 DOI: 10.1016/j.jmp.2023.102791
Davide Carpentiere , Alfio Giarlotta , Stephen Watson

A total preorder is a transitive and complete binary relation on a set. A modal preference structure of rank n is a string composed of 2 to the exponent n binary relations on a set such that there is a family of total preorders that gives all relations by taking intersections and unions. Total preorders are structures of rank zero, NaP-preferences (Giarlotta and Greco, 2013) are structures of rank one, and GNaP-preferences (Carpentiere et al., 2022) are structures of rank two. We characterize modal preference structures of any rank by properties of transitive coherence and mixed completeness. Moreover, we show how to construct structures of a given rank from others of lower rank. Modal preference structures arise in economics and psychology, in the process of aggregating hierarchical judgements of groups of agents, where each of the n coordinates represents a feature/stage of the decision procedure.

全预序是集合上的传递完备二元关系。一个n阶的模态偏好结构是一个由2 ^ n个二进制关系组成的字符串,在一个集合上,有一组总预购,通过取交集和并集给出所有关系。总预订量为0级结构,NaP-preferences (Giarlotta and Greco, 2013)为1级结构,GNaP-preferences (Carpentiere et al., 2022)为2级结构。利用传递相干性和混合完备性对任意阶的模态偏好结构进行了刻画。此外,我们展示了如何从其他低秩的结构中构造给定秩的结构。模态偏好结构出现在经济学和心理学中,在聚合主体群体的层次判断过程中,其中每个n个坐标代表决策过程的一个特征/阶段。
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引用次数: 0
Special issue on knowledge structures: Theoretical developments and applications 知识结构专题:理论发展与应用
IF 1.8 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-06-01 DOI: 10.1016/j.jmp.2023.102773
Jürgen Heller
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引用次数: 0
Diffusion models with time-dependent parameters: An analysis of computational effort and accuracy of different numerical methods 具有时变参数的扩散模型:不同数值方法的计算量和精度分析
IF 1.8 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-06-01 DOI: 10.1016/j.jmp.2023.102756
Thomas Richter , Rolf Ulrich , Markus Janczyk

Drift-diffusion models have become valuable tools in many fields of contemporary psychology and the neurosciences. The present study compares and analyzes different methods (i.e., stochastic differential equation, integral method, Kolmogorov equations, and matrix method) to derive the first-passage time distribution predicted by these models. First, these methods are compared in their accuracy and efficiency. In particular, we address non-standard problems, for example, models with time-dependent drift rates or time-dependent thresholds. Second, a mathematical analysis and a classification of these methods is provided. Finally, we discuss their strengths and caveats.

漂移扩散模型已经成为当代心理学和神经科学许多领域的宝贵工具。本研究比较和分析了不同的方法(即随机微分方程、积分法、Kolmogorov方程和矩阵法)来推导这些模型预测的首次通过时间分布。首先,对这些方法的准确性和效率进行了比较。特别是,我们解决了非标准问题,例如,具有时间相关漂移率或时间相关阈值的模型。其次,对这些方法进行了数学分析和分类。最后,我们讨论它们的优势和注意事项。
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引用次数: 3
Well-graded polytomous knowledge structures 良好分级的多面体知识结构
IF 1.8 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-06-01 DOI: 10.1016/j.jmp.2023.102770
Wen Sun , Jinjin Li , Zhaorong He , Xun Ge , Yidong Lin

Heller (2021) and Stefanutti et al. (2020) provided the mathematical foundation for the generalization of knowledge structure theory (KST) to polytomous items. Based on their works, the well-gradedness can be extended to polytomous knowledge structures. We propose the concepts of discriminative polytomous knowledge structure and well-graded polytomous knowledge structure. Then we show that every well-graded polytomous knowledge structure is discriminative. The basis of any polytomous knowledge space is formed by the collection of all the atoms. We discuss the sufficient and necessary conditions of polytomous knowledge structures to be well-graded polytomous knowledge spaces. Moreover, we provide an example to illustrate that a well-graded polytomous knowledge space is not necessarily a polytomous closure space.

Heller(2021)和Stefanutti等人。(2020)为知识结构理论(KST)推广到多面体项提供了数学基础。基于他们的工作,良好的等级性可以扩展到多面体知识结构。我们提出了判别多元体知识结构和良分多元体信息结构的概念。然后我们证明了每一个好分的多面体知识结构都是有判别性的。任何多面体知识空间的基础都是由所有原子的集合形成的。我们讨论了多模知识结构是良次多模知识空间的充要条件。此外,我们还提供了一个例子来说明一个好分次的多面体知识空间不一定是多面体闭合空间。
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引用次数: 2
Nondecomposable Item Response Theory models: Fundamental measurement in psychometrics 不可分解项目反应理论模型:心理测量学的基本测量方法
IF 1.8 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-06-01 DOI: 10.1016/j.jmp.2023.102772
Vithor Rosa Franco , Jacob Arie Laros , Marie Wiberg

The main aim of the current paper is to propose Item Response Theory (IRT) models derived from the nondecomposable measurement theories presented in Fishburn (1974). More specifically, we aim to: (i) present the theoretical basis of the Rasch model and its relations to psychophysics’ models of utility; (ii) give a brief exposition on the measurement theories presented in Fishburn (1974, 1975), some of which do not require an additive structure; and (iii) derive IRT models from these measurement theories, as well as Bayesian implementations of these models. We also present two empirical examples to compare how well these IRT models fit to real data. In addition to deriving new IRT models, we also discuss theoretical interpretations regarding the models’ capability of generating fundamental measures of the true scores of the respondents. The manuscript ends with prospects for future studies and practical implications.

本文的主要目的是根据Fishburn(1974)提出的不可分解测量理论,提出项目反应理论(IRT)模型。更具体地说,我们的目标是:(i)介绍Rasch模型的理论基础及其与心理物理学效用模型的关系;(ii)简要阐述Fishburn(19741975)提出的测量理论,其中一些理论不需要加性结构;以及(iii)从这些测量理论导出IRT模型以及这些模型的贝叶斯实现。我们还提供了两个实证例子来比较这些IRT模型与真实数据的拟合程度。除了推导新的IRT模型外,我们还讨论了关于模型生成受访者真实得分基本衡量标准的能力的理论解释。该手稿最后对未来的研究和实际意义进行了展望。
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引用次数: 0
Geometrical properties of a generalized cone and its 2D image 广义锥及其二维图像的几何性质
IF 1.8 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-06-01 DOI: 10.1016/j.jmp.2023.102765
Tadamasa Sawada , Zygmunt Pizlo

The generalized cone is a simple 3D shape that is produced by sweeping a planar cross-section along a curve. Many complex and articulated 3D objects can be represented by combining generalized cones. It has been shown that generalized cones play an important role in our visual system for perceiving the shapes of these objects and recognizing them. In this study, we analyzed the geometrical properties of generalized cones and their 2D images and found that there are invariant features in the images of the generalized cones under both 2D orthographic and perspective projections that facilitate the recovery of the 3D shapes of the cones from the images. We found that the 3D translational symmetry of generalized cones can be analyzed using tools designed for 3D mirror-symmetry.

广义圆锥体是一种简单的三维形状,它是通过沿曲线扫掠平面横截面而产生的。许多复杂和铰接的三维对象可以通过组合广义锥来表示。研究表明,广义锥在我们的视觉系统中扮演着重要的角色,可以感知这些物体的形状并识别它们。在本研究中,我们分析了广义锥及其二维图像的几何性质,发现在二维正投影和透视投影下,广义锥的图像中都存在不变特征,有助于从图像中恢复锥的三维形状。我们发现,广义锥的三维平移对称性可以使用为三维镜像对称设计的工具进行分析。
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引用次数: 0
Adjacencies on random ordering polytopes and flow polytopes 随机排序多面体和流动多面体上的邻接关系
IF 1.8 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-06-01 DOI: 10.1016/j.jmp.2023.102768
Jean-Paul Doignon , Kota Saito

The Multiple Choice Polytope (MCP) is the prediction range of a random utility model due to Block and Marschak(1960). Fishburn(1998) offers a nice survey of the findings on random utility models at the time. A complete characterization of the MCP is a remarkable achievement of Falmagne (1978). To derive a more enlightening proof of Falmagne Theorem, Fiorini(2004) assimilates the MCP with the flow polytope of some acyclic network. However, apart from a recognition of the facets by Suck(2002), the geometric structure of the MCP was apparently not much investigated. We characterize the adjacency of vertices and the adjacency of facets. Our characterization of the edges of the MCP helps understand recent findings in economics papers such as Chang, Narita and Saito(2022) and Turansick(2022). Moreover, our results on adjacencies also hold for the flow polytope of any acyclic network. In particular, they apply not only to the MCP, but also to three polytopes which Davis-Stober, Doignon, Fiorini, Glineur and Regenwetter (2018) introduced as extended formulations of the weak order polytope, interval order polytope and semiorder polytope (the prediction ranges of other models, see for instance Fishburn and Falmagne, 1989, and Marley and Regenwetter, 2017).

多选多点(MCP)是Block和Marschak(1960)提出的随机效用模型的预测范围。Fishburn(1998)对当时的随机实用新型的发现进行了很好的调查。对MCP的完整表征是Falmagne(1978)的一项非凡成就。为了得到Falmagne定理的更具启发性的证明,Fiorini(2004)将MCP与一些非循环网络的流多面体同化。然而,除了Suck(2002)对小平面的认识外,MCP的几何结构显然没有得到太多研究。我们刻画了顶点的邻接性和小平面的邻接性。我们对MCP边缘的描述有助于理解Chang、Narita和Saito(2022)以及Turansick(2022)等经济学论文中的最新发现。此外,我们关于邻接的结果也适用于任何非循环网络的流多面体。特别是,它们不仅适用于MCP,还适用于Davis Stober、Doignon、Fiorini、Glineur和Regenwetter(2018)引入的三个多面体,作为弱阶多面体、区间阶多面体和半阶多面体的扩展公式(其他模型的预测范围,见Fishburn和Falmagne,1989,以及Marley和Regenwitter,2017)。
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引用次数: 4
Stochastic choice with bounded processing capacity 具有有限处理能力的随机选择
IF 1.8 4区 心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-06-01 DOI: 10.1016/j.jmp.2023.102771
Thierry Marchant , Arunava Sen

We propose and characterize a class of stochastic decision functions for a decision-maker who has a capacity for processing at most k-alternatives at a time. When faced with a menu containing more than k alternatives, she randomly chooses a sub-menu of size k with uniform probability and selects the best alternative according to a strict ordering . For smaller menus, she chooses the best alternative according to .

我们为一个决策者提出并刻画了一类随机决策函数,该决策者一次处理最多k个备选方案。当面对包含k个以上备选方案的菜单时,她以均匀的概率随机选择一个大小为k的子菜单,并根据严格的排序选择最佳备选方案。对于较小的菜单,她根据≻选择最佳选择。
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引用次数: 2
期刊
Journal of Mathematical Psychology
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