Discounting: A practical guide to multilevel analysis of choice data

Multilevel modeling provides the ability to simultaneously evaluate the discounting of individuals and groups by examining choices between smaller sooner and larger later rewards. A multilevel logistic regression approach is advocated in which sensitivity to relative reward magnitude and relative delay are considered as separate contributors to choice. Examples of how to fit choice data using multilevel logistic models are provided to help researchers in the adoption of these methods.     

Children's Sensitivity to Cost and Reward in Decision Making across Distinct Domains of Probability,Effort, and Delay

Many behavioral paradigms used to study individuals' decision‐making tendencies do not capture the decision components that contribute to behavioral outcomes, such as differentiating decisions driven toward a reward from decisions driven away from a cost. This study tested a novel decision‐making task in a sample of 403 children (age 9 years) enrolled in an ongoing longitudinal study. The task consisted of three blocks representing distinct cost domains (delay, probability, and effort), wherein children were presented with a deck of cards, each of which consisted of a reward and a cost. Children elected whether to accept or skip the card at each trial. Reward–cost pairs were selected by using an adaptive algorithm to strategically sample the decision space in the fewest number of trials. Using person‐specific regression models, decision preferences were quantified for each cost domain with respect to general tolerance (intercept), as well as parameters estimating the effect of incremental increases in reward or cost on the probability of accepting a card. Results support the relative independence of decision‐making tendencies across cost domains, with moderate correlations observed between tolerance for delay and effort. Specific decision parameters showed unique associations with cognitive and behavioral measures including executive function, academic motivation, anxiety, and hyperactivity. Evidence indicates that sensitivity to reward is an important factor in incentivizing decisions to work harder or wait longer. Dissociating the relative contributions of reward and cost sensitivity in multiple domains may facilitate the identification of heterogeneity in suboptimal decision making. Copyright © 2017 John Wiley & Sons, Ltd.     

Discounting model selection with area‐based measures: A case for numerical integration

A novel method for analyzing delay discounting data is proposed. This newer metric, a model‐based Area Under Curve (AUC) combining approximate Bayesian model selection and numerical integration, was compared to the point‐based AUC methods developed by Myerson, Green, and Warusawitharana (2001) and extended by Borges, Kuang, Milhorn, and Yi (2016). Using data from computer simulation and a published study, comparisons of these methods indicated that a model‐based form of AUC offered a more consistent and statistically robust measurement of area than provided by using point‐based methods alone. Beyond providing a form of AUC directly from a discounting model, numerical integration methods permitted a general calculation in cases when the Effective Delay 50 (ED50) measure could not be calculated. This allowed discounting model selection to proceed in conditions where data are traditionally more challenging to model and measure, a situation where point‐based AUC methods are often enlisted. Results from simulation and existing data indicated that numerical integration methods extended both the area‐based interpretation of delay discounting as well as the discounting model selection approach. Limitations of point‐based AUC as a first‐line analysis of discounting and additional extensions of discounting model selection were also discussed.     

Impulsive choice and pre‐exposure to delays: iv. effects of delay‐ and immediacy‐exposure training relative to maturational changes in impulsivity

Impulsive choice describes preference for smaller, sooner rewards over larger, later rewards. Excessive delay discounting (i.e., rapid devaluation of delayed rewards) underlies some impulsive choices, and is observed in many maladaptive behaviors (e.g., substance abuse, gambling). Interventions designed to reduce delay discounting may provide therapeutic gains. One such intervention provides rats with extended training with delayed reinforcers. When compared to a group given extended training with immediate reinforcers, delay‐exposed rats make significantly fewer impulsive choices. To what extent is this difference due to delay‐exposure training shifting preference toward self‐control or immediacy‐exposure training (the putative control group) shifting preference toward impulsivity? The current study compared the effects of delay‐ and immediacy‐exposure training to a no‐training control group and evaluated within‐subject changes in impulsive choice across 51 male Wistar rats. Delay‐exposed rats made significantly fewer impulsive choices than immediacy‐exposed and control rats. Between‐group differences in impulsive choice were not observed in the latter two groups. While delay‐exposed rats showed large, significant pre‐ to posttraining reductions in impulsive choice, immediacy‐exposed and control rats showed small reductions in impulsive choice. These results suggest that extended training with delayed reinforcers reduces impulsive choice, and that extended training with immediate reinforcers does not increase impulsive choice.     

选择与坚持:跨期选择与延迟满足之比较

做出选择与坚持选择是决策活动的两个重要阶段。跨期选择源于经济学领域对成人对发生在不同时间点的结果"做出选择"过程的研究;延迟满足则源于心理学领域对儿童为获得未来较大收益而抵制当前诱惑的"坚持选择"过程的研究。二者均致力于研究与时间相关的决策活动,从不同视角关注个体的冲动性与自我控制,但鲜见学者对二者异同的系统比较。本文着重从研究方法、认知机制与神经基础入手探讨了二者的异同,冀为两个研究领域协同发展、共同促进人类远见的培养与实践提供科学的理论支持。     

延迟间隔和提取条件对短时错误记忆的影响

采用短时DRM迫选任务,探讨提取条件和延迟间隔对短时错误记忆的影响,以进一步考察短时错误记忆的产生机制。结果发现,短时错误记忆的产生主要源于提取时对存贮细节通达的缺失。在无有效提取线索的条件下,延迟间隔能够增加错误记忆率;而有效提取线索存在时,真实记忆痕迹的可通达性增加能够极大避免错误记忆的产生,延迟间隔的作用则不显著。该实验的结果是对错误记忆理论解释的一种补充。     

Reprint of “Co-occurring motor,language and emotional–behavioral problems in children 3–6 years of age”

PurposeDevelopmental Coordination Disorder (DCD) has been shown to co-occur with behavioral and language problems in school-aged children, but little is known as to when these problems begin to emerge, or if they are inherent in children with DCD. The purpose of this study was to determine if deficits in language and emotional–behavioral problems are apparent in preschool-aged children with movement difficulties.MethodTwo hundred and fourteen children (mean age 4 years 11 months, SD 9.8 months, 103 male) performed the Movement Assessment Battery for Children 2nd Edition (MABC-2). Children falling at or below the 16th percentile were classified as being at risk for movement difficulties (MD risk). Auditory comprehension and expressive communication were examined using the Preschool Language Scales 4th Edition (PLS-4). Parent-reported emotional and behavioral problems were assessed using the Child Behavior Checklist (CBCL).ResultsPreschool children with diminished motor coordination (n = 37) were found to have lower language scores, higher externalizing behaviors in the form of increased aggression, as well as increased withdrawn and other behavior symptoms compared with their typically developing peers.ConclusionsMotor coordination, language and emotional–behavioral difficulties tend to co-occur in young children aged 3–6 years. These results highlight the need for early intervention.     

Co-occurring motor,language and emotional–behavioral problems in children 3–6 years of age

PurposeDevelopmental Coordination Disorder (DCD) has been shown to co-occur with behavioral and language problems in school-aged children, but little is known as to when these problems begin to emerge, or if they are inherent in children with DCD. The purpose of this study was to determine if deficits in language and emotional–behavioral problems are apparent in preschool-aged children with movement difficulties.MethodTwo hundred and fourteen children (mean age 4 years 11 months, SD 9.8 months, 103 male) performed the Movement Assessment Battery for Children 2nd Edition (MABC-2). Children falling at or below the 16th percentile were classified as being at risk for movement difficulties (MD risk). Auditory comprehension and expressive communication were examined using the Preschool Language Scales 4th Edition (PLS-4). Parent-reported emotional and behavioral problems were assessed using the Child Behavior Checklist (CBCL).ResultsPreschool children with diminished motor coordination (n = 37) were found to have lower language scores, higher externalizing behaviors in the form of increased aggression, as well as increased withdrawn and other behavior symptoms compared with their typically developing peers.ConclusionsMotor coordination, language and emotional–behavioral difficulties tend to co-occur in young children aged 3–6 years. These results highlight the need for early intervention.     

Choice between single and multiple reinforcers in concurrent-chains schedules

Pigeons responded on concurrent-chains schedules with equal variable-interval schedules as initial links. One terminal link delivered a single reinforcer after a fixed delay, and the other terminal link delivered either three or five reinforcers, each preceded by a fixed delay. Some conditions included a postreinforcer delay after the single reinforcer to equate the total durations of the two terminal links, but other conditions did not include such a postreinforcer delay. With short initial links, preference for the single-reinforcer alternative decreased when a postreinforcer delay was present, but with long initial links, the postreinforcer delays had no significant effect on preference. In conditions with a postreinforcer delay, preference for the single-reinforcer alternative frequently switched from above 50% to below 50% as the initial links were lengthened. This pattern of results was consistent with delay-reduction theory (Squires & Fantino, 1971), but not with the contextual-choice model (Grace, 1994) or the hyperbolic value-added model (Mazur, 2001) as they have usually been applied. However, the hyperbolic value-added model could account for the results if its calculations were expanded to include reinforcers delivered in later terminal links. The implications of these findings for models of concurrent-chains performance are discussed.