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A zero-bounded model of operant demand
Journal of the Experimental Analysis of Behavior ( IF 2.7 ) Pub Date : 2021-02-15 , DOI: 10.1002/jeab.679
Shawn P Gilroy 1 , Brent A Kaplan 2 , Lindsay P Schwartz 3 , Derek D Reed 4 , Steven R Hursh 5
Affiliation  

Contemporary approaches for evaluating the demand for reinforcers use either the Exponential or the Exponentiated model of operant demand, both derived from the framework of Hursh and Silberberg (2008). This report summarizes the strengths and complications of this framework and proposes a novel implementation. This novel implementation incorporates earlier strengths and resolves existing shortcomings that are due to the use of a logarithmic scale for consumption. The Inverse Hyperbolic Sine (IHS) transformation is reviewed and evaluated as a replacement for the logarithmic scale in models of operant demand. Modeling consumption in the “log10-like” IHS scale reflects relative changes in consumption (as with a log scale) and accommodates a true zero bound (i.e., zero consumption values). The presence of a zero bound obviates the need for a separate span parameter (i.e., k) and the span of the model may be more simply defined by maximum demand at zero price (i.e., Q0). Further, this reformulated model serves to decouple the exponential rate constant (i.e., α) from variations in span, thus normalizing the rate constant to the span of consumption in IHS units and permitting comparisons when spans vary. This model, called the Zero-bounded Exponential (ZBE), is evaluated using simulated and real-world data. The direct reinstatement ZBE model showed strong correspondence with empirical indicators of demand and with a normalization of α (ZBEn) across empirical data that varied in reinforcing efficacy (dose, time to onset of peak effects). Future directions in demand curve analysis are discussed with recommendations for additional replication and exploration of scales beyond the logarithm when accommodating zero consumption data.

中文翻译:

操作需求的零界模型

当代评估强化物需求的方法使用操作性需求的指数或指数模型,两者均源自 Hursh 和 Silberberg(2008)的框架。本报告总结了该框架的优势和复杂性,并提出了一种新的实施方案。这种新颖的实现结合了早期的优势并解决了由于使用对数标度进行消费而导致的现有缺点。反双曲正弦 (IHS) 变换作为操作需求模型中对数标度的替代品进行了审查和评估。“log 10 ”中的消费建模-like” IHS 量表反映了消费的相对变化(如对数刻度)并适应真正的零界限(即零消费值)。零界限的存在消除了对单独的跨度参数(即,k)的需要,并且模型的跨度可以更简单地由零价格时的最大需求(即,Q 0)来定义。此外,这个重新制定的模型用于解耦指数速率常数(即,α) 来自跨度的变化,从而将速率常数标准化为 IHS 单位的消耗跨度,并允许在跨度变化时进行比较。该模型称为零界指数 (ZBE),使用模拟数据和真实数据进行评估。直接恢复 ZBE 模型与需求的经验指标和α (ZBEn)的标准化具有很强的对应性,这些经验数据在增强功效(剂量、达到峰值效应的时间)方面各不相同。讨论了需求曲线分析的未来方向,并提出了在适应零消费数据时对超出对数的尺度进行额外复制和探索的建议。
更新日期:2021-02-15
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