Odic Darko, Im Hee Yeon, Eisinger Robert, Ly Ryan, Halberda Justin
Department of Psychology, University of British Columbia, 2136 West Mall, Vancouver, British Columbia, V6T 1Z4, Canada.
Johns Hopkins University, Baltimore, MD, USA.
Behav Res Methods. 2016 Jun;48(2):445-62. doi: 10.3758/s13428-015-0600-5.
A simple and popular psychophysical model-usually described as overlapping Gaussian tuning curves arranged along an ordered internal scale-is capable of accurately describing both human and nonhuman behavioral performance and neural coding in magnitude estimation, production, and reproduction tasks for most psychological dimensions (e.g., time, space, number, or brightness). This model traditionally includes two parameters that determine how a physical stimulus is transformed into a psychological magnitude: (1) an exponent that describes the compression or expansion of the physical signal into the relevant psychological scale (β), and (2) an estimate of the amount of inherent variability (often called internal noise) in the Gaussian activations along the psychological scale (σ). To date, linear slopes on log-log plots have traditionally been used to estimate β, and a completely separate method of averaging coefficients of variance has been used to estimate σ. We provide a respectful, yet critical, review of these traditional methods, and offer a tutorial on a maximum-likelihood estimation (MLE) and a Bayesian estimation method for estimating both β and σ [PsiMLE(β,σ)], coupled with free software that researchers can use to implement it without a background in MLE or Bayesian statistics (R-PsiMLE). We demonstrate the validity, reliability, efficiency, and flexibility of this method through a series of simulations and behavioral experiments, and find the new method to be superior to the traditional methods in all respects.
一个简单且流行的心理物理学模型——通常被描述为沿着有序内部量表排列的重叠高斯调谐曲线——能够准确描述人类和非人类在大多数心理维度（如时间、空间、数量或亮度）的大小估计、生成和再现任务中的行为表现和神经编码。该模型传统上包括两个参数，它们决定了物理刺激如何转化为心理量值：（1）一个指数，用于描述物理信号在相关心理量表中的压缩或扩展（β），以及（2）对沿心理量表的高斯激活中固有变异性（通常称为内部噪声）量的估计（σ）。迄今为止，对数-对数图上的线性斜率传统上用于估计β，而一种完全独立的平均方差系数方法已被用于估计σ。我们对这些传统方法进行了中肯但批判性的综述，并提供了一个关于最大似然估计（MLE）和用于估计β和σ的贝叶斯估计方法[PsiMLE(β,σ)]的教程，同时提供了免费软件，研究人员无需MLE或贝叶斯统计背景即可使用该软件来实现它（R-PsiMLE）。我们通过一系列模拟和行为实验证明了该方法的有效性、可靠性、效率和灵活性，并发现新方法在各方面都优于传统方法。
