Standard nonlinear regression is commonly used when modeling indifference points due to its ability to closely follow observed data, resulting in a good model fit. However, standard nonlinear regression currently lacks a reasonable distribution-based framework for indifference points, which limits its ability to adequately describe the inherent variability in the data. Software commonly assumes data follow a normal distribution with constant variance. However, typical indifference points do not follow a normal distribution or exhibit constant variance. To address these limitations, this paper introduces a class of nonlinear beta regression models that offers excellent fit to discounting data and enhances simulation-based approaches. This beta regression model can accommodate popular discounting functions. This work proposes three specific advances. First, our model automatically captures non-constant variance as a function of delay. Second, our model improves simulation-based approaches since it obeys the natural boundaries of observable data, unlike the ordinary assumption of normal residuals and constant variance. Finally, we introduce a scale-location-truncation trick that allows beta regression to accommodate observed values of zero and one. A comparison between beta regression and standard nonlinear regression reveals close agreement in the estimated discounting rate k obtained from both methods.

翻译：标准非线性回归因其能够紧密拟合观测数据而常用于无差异点建模，从而获得良好的模型拟合效果。然而，当前标准非线性回归缺乏适用于无差异点的合理分布框架，这限制了其充分描述数据内在变异性的能力。常用软件通常假设数据服从方差恒定的正态分布，但典型的无差异点既不服从正态分布，也不具有恒定方差。为克服这些局限，本文提出了一类非线性Beta回归模型，该模型能出色地拟合贴现数据并增强基于模拟的研究方法。此Beta回归模型可兼容多种常用贴现函数。本研究提出了三项具体进展：首先，我们的模型能自动捕捉方差随延迟变化的非恒定特性；其次，由于模型遵循观测数据的自然边界，相比常规的正态残差与恒定方差假设，它能改进基于模拟的研究方法；最后，我们引入了尺度-位置-截断技巧，使Beta回归能够兼容取值为0和1的观测数据。通过比较Beta回归与标准非线性回归发现，两种方法得到的贴现率k估计值高度吻合。