McDowell J J, Wixted J T
Department of Psychology, Emory University, Atlanta, Georgia 30322.
J Exp Anal Behav. 1988 Jan;49(1):143-69. doi: 10.1901/jeab.1988.49-143.
The mathematical theory of linear systems, which has been used successfully to describe behavior maintained by variable-interval schedules, is extended to describe behavior maintained by variable-ratio schedules. The result of the analysis is a pair of equations, one of which expresses response rate on a variable-ratio schedule as a function of the mean ratio requirement (n) that the schedule arranges. The other equation expresses response rate on a variable-ratio schedule as a function of reinforcement rate. Both equations accurately describe existing data from variable-ratio schedules. The theory accounts for two additional characteristics of behavior maintained by variable-ratio schedules; namely, the appearance of strained, two-valued (i.e., zero or very rapid) responding at large ns, and the abrupt cessation of responding at a boundary n. The theory also accounts for differences between behavior on variable-interval and variable-ratio schedules, including (a) the occurrence of strained responding on variable-ratio but not on variable-interval schedules, (b) the abrupt cessation of responding on occurrence of higher response rates on variable-ratio than on variable-interval schedules. Furthermore, given data from a series of variable-interval schedules and from a series of concurrent variable-ratio variable-interval schedules, the theory permits quantitative prediction of many properties of behavior on single-alternative variable-ratio schedules. The linear system theory's combined account of behavior on variable-interval and variable-ratio schedules is superior to existing versions of six other mathematical theories of variable-interval and variable-ratio responding.
线性系统的数学理论已成功用于描述由可变间隔时间表维持的行为，现被扩展以描述由可变比率时间表维持的行为。分析结果是一组方程，其中一个方程将可变比率时间表上的反应率表示为该时间表所安排的平均比率要求（n）的函数。另一个方程将可变比率时间表上的反应率表示为强化率的函数。这两个方程都准确地描述了来自可变比率时间表的现有数据。该理论解释了由可变比率时间表维持的行为的另外两个特征；即在较大的n值时出现紧张的、二值化（即零或非常快速）的反应，以及在边界n处反应突然停止。该理论还解释了可变间隔和可变比率时间表上行为的差异，包括（a）可变比率时间表上出现紧张反应而可变间隔时间表上不出现，（b）可变比率时间表上反应率高于可变间隔时间表时反应突然停止。此外，给定来自一系列可变间隔时间表和一系列并发可变比率 - 可变间隔时间表的数据，该理论允许对单选项可变比率时间表上行为的许多属性进行定量预测。线性系统理论对可变间隔和可变比率时间表上行为的综合解释优于其他六种关于可变间隔和可变比率反应的数学理论的现有版本。
