Modeling probability and additive summation for detection across multiple mechanisms under the assumptions of signal detection theory
Modeling probability and additive summation for detection across multiple mechanisms under the assumptions of signal detection theory
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DOI：
10.1167/15.5.1
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发表时间：
2015-01-01
影响因子：
1.8
通讯作者：
Schmidtmann, Gunnar
中科院分区：
文献类型：
--
作者：
Kingdom, Frederick A. A.;Baldwin, Alex S.;Schmidtmann, Gunnar
许多研究已经调查了多种刺激如何结合在一起才能达到阈值。广义地讲，这可以以两种方式发生：加法求和(AS)，其中来自不同刺激的输入在单一机制中相加；或者概率求和(PS)，其中不同刺激由单独的机制独立地检测。传统上，PS是在高阈值理论(HTT)下建模的；然而，测试表明HTT是不正确的，信号检测理论(SDT)是建模求和的更好框架。然而，在SDT下对PS的等价物进行建模相对复杂，导致许多研究人员使用蒙特卡罗模拟进行预测。对于强度相等或不相等的情况，我们推导出了利用数值积分来预测在SDT下假设PS的多个刺激的正确检测比例的公式。这两个公式都是通用的，用于计算Q监测机构中具有M个备选方案、n个刺激的强迫选择任务的性能，每个受试者都受到一个指数为S的非线性传感器。我们展示了概率(和加性)求和公式如何被用来模拟心理测量函数，当与威布尔函数拟合时，它对阈值和心理测量函数斜率作为S、n和Q的函数的变化做出特征预测。我们还展示了如何使用双目求和实验的数据来直接将这些公式与真实的心理测量函数拟合，并展示了如何获得S的估计并检验双目求和是否更符合PS或AS。使用Palamedes工具箱中新添加的软件功能，可以很容易地应用此处描述的方法。
Many studies have investigated how multiple stimuli combine to reach threshold. There are broadly speaking two ways this can occur: additive summation (AS) where inputs from the different stimuli add together in a single mechanism, or probability summation (PS) where different stimuli are detected independently by separate mechanisms. PS is traditionally modeled under high threshold theory (HTT); however, tests have shown that HTT is incorrect and that signal detection theory (SDT) is the better framework for modeling summation. Modeling the equivalent of PS under SDT is, however, relatively complicated, leading many investigators to use Monte Carlo simulations for the predictions. We derive formulas that employ numerical integration to predict the proportion correct for detecting multiple stimuli assuming PS under SDT, for the situations in which stimuli are either equal or unequal in strength. Both formulas are general purpose, calculating performance for forced-choice tasks with M alternatives, n stimuli, in Q monitored mechanisms, each subject to a non-linear transducer with exponent s. We show how the probability (and additive) summation formulas can be used to simulate psychometric functions, which when fitted with Weibull functions make signature predictions for how thresholds and psychometric function slopes vary as a function of s, n, and Q. We also show how one can fit the formulas directly to real psychometric functions using data from a binocular summation experiment, and show how one can obtain estimates of s and test whether binocular summation conforms more to PS or AS. The methods described here can be readily applied using software functions newly added to the Palamedes toolbox.