Although a full understanding of how nonlinear regression works requires mastery of matrix algebra, the basic method is relatively easy to follow. Nevertheless, numerous studies have demonstrated that values obtained from hypothetical choices correlate with values obtained from actual rewards (see ).ĭescribing participant patterns of discounting presents numerous analytical challenges for researchers who are unfamiliar with advanced statistics because of reliance on nonlinear regression models. As the reader may surmise, the employment of hypothetical choice, as well as the use of verbal self-report, is a substantial deviation from the direct measurement techniques usually used in behavior-analytic studies. This methodology then is replicated across numerous delay values (i.e., the delay until the receipt of the LLR) to arrive at an understanding of the individual's preference for reward over time (the reader is encouraged to consult Madden & Johnson, 2010, for a lengthier discussion on discounting assessment methodology). This indifference point serves as an estimation of the subjective value of the LLR after some delay. The point at which an individual switches from choosing the LLR to the SSR is commonly termed the indifference point. Typically, hypothetical monetary choice paradigms feature a titrating series of choices between smaller sooner rewards (SSRs) and a larger later reward (LLR). The commonly used procedure for studying discounting is the administration of a series of hypothetical monetary choice trials (see Madden & Johnson, 2010). This behavioral interpretation of impulsivity has led to numerous advances in clinical issues such as increasing tolerance to reinforcement delay in individuals with acquired brain injury or autism ( ), as well as in the general assessment of impulsivity in children with attention deficit hyperactivity disorder (ADHD ), serious emotional disturbance (e.g., ), and severe problem behaviors (e.g., ). For instance, behavior analysts have come to define a form of impulsivity as preference for a smaller sooner reward, despite a larger delayed alternative being available (see ). Specifically, this operationalization of decision making is translated easily to issues concerning impulsivity and self-control. Analyses of delay discounting (the process by which delayed rewards have lower subjective values than sooner rewards of the same magnitude) have become increasingly popular due to their ability to allow researchers to investigate the temporal properties of reward for socially important problems (see Madden & Bickel, 2010). The goal of this technical article is to present researchers with a tutorial on how to conduct both nonlinear regression and area under the curve (AUC) estimations using Microsoft Office Excel 2010 and Excel for Mac 2011 (hereafter referred to simply as Excel) to analyze delay-discounting data.
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