Department of Family and Community Medicine.
Department of Statistics.
Psychol Addict Behav. 2023 Feb;37(1):57-71. doi: 10.1037/adb0000889. Epub 2022 Nov 28.
Howard Rachlin wrote extensively on how value diminishes in a hyperbolic form, and he contributed to understanding choice processes between different commodities as a molar pattern of behavior. The field of behavioral economic demand has been dominated by exponential decay functions, indicating that decreases in consumption of a commodity are best fit by exponential functions. Because of the success of Rachlin's equation at describing how hyperbolic decay affects the value of a commodity across various factors (e.g., delay, probability, social distance), we attempted to extend his equation to behavioral economic demand data for alcohol and opioids.
Rachlin's discounting equation was applied to estimate consumption on alcohol purchase task data and nonhuman drug demand data. We compared results of his equation to the exponentiated demand equation using both a mixed-effects modeling approach and a two-stage approach.
Rachlin's equation provided better fits to consumption data than the exponentiated equation for both mixed-effects and two-stage modeling. We also found that traditional demand metrics, such as , can be derived analytically when using Rachlin's equation. Certain metrics derived from Rachlin's equation appeared to be related to clinical covariates in ways similar to the exponentiated equation.
Rachlin's equation better described demand data than did the exponentiated equation, indicating that demand for a commodity may decrease hyperbolically rather than exponentially. Other benefits of his equation are that it does not have the same pitfalls as the current exponential equations and is relatively straightforward in its conceptualization when applied to demand data. (PsycInfo Database Record (c) 2023 APA, all rights reserved).
霍华德·雷奇林（Howard Rachlin）广泛研究了价值如何呈双曲线形式减少的问题，并为理解不同商品之间的选择过程做出了贡献，他将其视为行为的摩尔模式。行为经济需求领域一直以指数衰减函数为主导，这表明商品消费的减少最适合用指数函数来拟合。由于 Rachlin 方程在描述双曲线衰减如何影响各种因素（例如，延迟、概率、社会距离）下商品价值方面取得了成功，我们试图将他的方程扩展到酒精和阿片类药物的行为经济需求数据中。
Rachlin 的折扣方程被应用于估计酒精购买任务数据和非人类药物需求数据中的消费。我们使用混合效应建模方法和两阶段方法，将他的方程与指数需求方程的结果进行了比较。
对于混合效应和两阶段建模， Rachlin 的方程都比指数方程更能拟合消费数据。我们还发现，当使用 Rachlin 的方程时，可以从分析中得出传统的需求指标，例如。从 Rachlin 的方程中得出的某些指标似乎与指数方程类似，与临床协变量有关。
Rachlin 的方程比指数方程更能描述需求数据，这表明商品的需求可能呈双曲线下降，而不是指数下降。他的方程的其他好处是，它没有当前指数方程的相同缺陷，并且在应用于需求数据时，其概念相对简单。（PsycInfo 数据库记录（c）2023 APA，保留所有权利）。
