Schütt Heiko H, Harmeling Stefan, Macke Jakob H, Wichmann Felix A
Neural Information Processing Group, University of Tübingen, Tübingen, Germany; Department of Psychology, Universität of Potsdam, Potsdam, Germany; Graduate School for Neural and Behavioural Sciences IMPRS, Tübingen, Germany.
Institut für Informatik, Heinrich-Heine-Universität Düsseldorf, Germany.
Vision Res. 2016 May;122:105-123. doi: 10.1016/j.visres.2016.02.002. Epub 2016 May 2.
The psychometric function describes how an experimental variable, such as stimulus strength, influences the behaviour of an observer. Estimation of psychometric functions from experimental data plays a central role in fields such as psychophysics, experimental psychology and in the behavioural neurosciences. Experimental data may exhibit substantial overdispersion, which may result from non-stationarity in the behaviour of observers. Here we extend the standard binomial model which is typically used for psychometric function estimation to a beta-binomial model. We show that the use of the beta-binomial model makes it possible to determine accurate credible intervals even in data which exhibit substantial overdispersion. This goes beyond classical measures for overdispersion-goodness-of-fit-which can detect overdispersion but provide no method to do correct inference for overdispersed data. We use Bayesian inference methods for estimating the posterior distribution of the parameters of the psychometric function. Unlike previous Bayesian psychometric inference methods our software implementation-psignifit 4-performs numerical integration of the posterior within automatically determined bounds. This avoids the use of Markov chain Monte Carlo (MCMC) methods typically requiring expert knowledge. Extensive numerical tests show the validity of the approach and we discuss implications of overdispersion for experimental design. A comprehensive MATLAB toolbox implementing the method is freely available; a python implementation providing the basic capabilities is also available.
心理测量函数描述了诸如刺激强度等实验变量如何影响观察者的行为。从实验数据估计心理测量函数在心理物理学、实验心理学和行为神经科学等领域中起着核心作用。实验数据可能表现出显著的过度离散，这可能是由于观察者行为的非平稳性导致的。在这里，我们将通常用于心理测量函数估计的标准二项式模型扩展为贝塔二项式模型。我们表明，使用贝塔二项式模型即使在表现出显著过度离散的数据中也能够确定准确的可信区间。这超越了经典的过度离散拟合优度测量方法，后者可以检测到过度离散，但没有提供对过度离散数据进行正确推断的方法。我们使用贝叶斯推理方法来估计心理测量函数参数的后验分布。与以前的贝叶斯心理测量推理方法不同，我们的软件实现——psignifit 4——在自动确定的边界内对后验进行数值积分。这避免了使用通常需要专业知识的马尔可夫链蒙特卡罗（MCMC）方法。广泛的数值测试表明了该方法的有效性，并且我们讨论了过度离散对实验设计的影响。一个实现该方法的综合MATLAB工具箱可免费获得；也有一个提供基本功能的Python实现。
