Ratcliff and McKoon (2018) proposed integrated diffusion models for numerosity judgments in which a numerosity representation provides evidence used to drive the decision process. We extend this modeling framework to examine the interaction of non-numeric perceptual variables with numerosity by assuming that drift rate and non-decision time are functions of those variables. Four experiments were conducted with two different types of stimuli: a single array of intermingled blue and yellow dots in which both numerosity and dot area vary over trials and two side-by-side arrays of dots in which numerosity, dot area, and convex hull vary over trials. The tasks were to decide whether there were more blue or yellow dots (two experiments), more dots on which side, or which dots have a larger total area. Development of models started from the principled models in Ratcliff and McKoon (2018) and became somewhat ad hoc as we attempted to capture unexpected patterns induced by the conflict between numerosity and perceptual variables. In the three tasks involving numerosity judgments, the effects of the non-numeric variables were moderated by the number of dots. Under a high conflict, judgments were dominated by perceptual variables and produced an unexpected shift in the leading edge of the reaction time (RT) distributions. Although the resulting models were able to predict most of the accuracy and RT patterns, the models were not able to completely capture this shift in the RT distributions. However, when subjects judged area, numerosity affected perceptual judgments but there was no leading edge effect. Based on the results, it appears that the integrated diffusion models provide an effective framework to study the role of numerical and perceptual variables in numerosity tasks and their context-dependency.

中文翻译：

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使用扩散模型对数量和感知变量的相互作用进行建模

Ratcliff 和 McKoon (2018) 提出了用于数量判断的综合扩散模型，其中数量表示提供了用于驱动决策过程的证据。我们扩展了这个建模框架，通过假设漂移率和非决策时间是这些变量的函数来检查非数字感知变量与数量的相互作用。使用两种不同类型的刺激进行了四个实验：一个混合的蓝色和黄色点阵列，其中数量和点面积随试验而变化，以及两个并排的点阵列，其中数量、点面积和凸包因试验而异。任务是决定是否有更多的蓝色或黄色点（两个实验），哪一侧的点更多，或者哪些点的总面积更大。模型的开发从 Ratcliff 和 McKoon（2018 年）中的原则模型开始，随着我们试图捕捉由数量和感知变量之间的冲突引起的意外模式，模型变得有些临时。在涉及数量判断的三个任务中，非数字变量的影响通过点数来调节。在高度冲突下，判断由感知变量主导，并在反应时间 (RT) 分布的前沿产生了意想不到的变化。尽管生成的模型能够预测大部分准确度和 RT 模式，但这些模型无法完全捕捉 RT 分布的这种变化。然而，当受试者判断面积时，数量会影响知觉判断，但没有前沿效应。根据结果​​，