An overview of Bayesian reasoning in the analysis of delay‐discounting data

Statistical inference (including interval estimation and model selection) is increasingly used in the analysis of behavioral data. As with many other fields, statistical approaches for these analyses traditionally use classical (i.e., frequentist) methods. Interpreting classical intervals and p‐values correctly can be burdensome and counterintuitive. By contrast, Bayesian methods treat data, parameters, and hypotheses as random quantities and use rules of conditional probability to produce direct probabilistic statements about models and parameters given observed study data. In this work, we reanalyze two data sets using Bayesian procedures. We precede the analyses with an overview of the Bayesian paradigm. The first study reanalyzes data from a recent study of controls, heavy smokers, and individuals with alcohol and/or cocaine substance use disorder, and focuses on Bayesian hypothesis testing for covariates and interval estimation for discounting rates among various substance use disorder profiles. The second example analyzes hypothetical environmental delay‐discounting data. This example focuses on using historical data to establish prior distributions for parameters while allowing subjective expert opinion to govern the prior distribution on model preference. We review the subjective nature of specifying Bayesian prior distributions but also review established methods to standardize the generation of priors and remove subjective influence while still taking advantage of the interpretive advantages of Bayesian analyses. We present the Bayesian approach as an alternative paradigm for statistical inference and discuss its strengths and weaknesses.     

Contingency tracking during unsignaled delayed reinforcement: Effects of delay duration and d‐amphetamine

In two experiments, the role of the response–reinforcer relation in maintaining low‐rate responding under unsignaled delay conditions was investigated. In both experiments pecking by pigeons on one response key, denoted the relevant key, was reinforced under an unsignaled delay‐of‐reinforcement procedure (defined as tandem variable‐interval (VI) differential‐reinforcement‐of‐other behavior [DRO] schedule). Responding on a second key, denoted the irrelevant key, had no programmed consequences. Between sessions, the location of the relevant key varied (after one, two, or three sessions) pseudorandomly. In Experiment 1, the delay (DRO) duration was manipulated parametrically. Overall, proportional relevant‐key response rates (relevant‐key response rates / [relevant‐key response rates + irrelevant key response rates]) increased across 3‐session sequences in which the relevant key remained in the same location and decreased as the DRO duration was changed systematically (2, 5, and 10 s). In Experiment 2, acute administration of d‐amphetamine increased proportional relevant‐key response rates during 1‐day sequences for only the DRO 5‐s duration, and results over 3‐day sequences, once a discrimination had already been established, were inconsistent. Results support that the response–reinforcer relation is the primary determinant of responding, and such discriminations are relatively resistant to disruption or potentiation by behaviorally active doses of d‐amphetamine.     

Response rate correlates with indifference points in a delay‐discounting procedure

To study how effort affects reward value, we replicated Fortes, Vasconcelos and Machado's (2015) study using an adjusting‐delay task. Nine pigeons chose between a standard alternative that gave access to 4 s of food, after a 10 s delay, and an adjusting‐delay alternative that gave access to 12 s of food after a delay that changed dynamically with the pigeons' choices, decreasing when they preferred the standard alternative, and increasing when they preferred the adjusting alternative. The delay value at which preference stabilized defined the indifference point, a measure of reward value. To manipulate effort across phases, we varied the response rate required during the delay of the standard alternative. Results showed that a) the indifference point increased in the higher‐response‐rate phases, suggesting that reward value decreased with effort, and b) in the higher‐response‐rate phases, response rate in the standard alternative was linearly related to the indifference point. We advance several conceptions of how effort may change perceived delay or amount and thereby affect reward value.     

Effects of delayed time‐out on problem behavior of preschool children

Time‐out is a common negative punishment procedure in home and school settings. Although prior studies have shown time‐out is effective, more research is needed on its effects when implementation is imperfect. We evaluated delays to time‐out with 4 preschool children who engaged in some combination of aggression, property destruction, and rule breaking. Target behavior decreased for all subjects exposed to delayed time‐out, with 3 of 4 subjects displaying low levels of target behavior even when time‐out was delayed by 90‐120 s. These data suggest delayed time‐out might be effective in situations in which a caregiver or teacher cannot implement time‐out immediately.     

Age‐related differences in delay discounting: Immediate reward,reward magnitude,and social influence

Delay discounting refers to the tendency of individuals to subjectively devalue rewards that are to be received in the future, with high rates of delay discounting being associated with a variety of maladaptive life outcomes (e.g., unhealthy dietary and exercise behaviors). The current study explored the psychological and social processes involved in adult age‐related differences in delay discounting of monetary rewards. Younger adults exhibited higher levels of delay discounting than older adults. This increased level of patience in older adults was found whether smaller‐sooner rewards were to be received immediately or in the future. However, there was an interaction with reward magnitude, whereby younger adults exhibited higher levels of delay discounting for smaller reward magnitudes but not larger reward magnitudes. Social influence on delay discounting was investigated by having participants complete three phases of the delay‐discounting task: an individual precollaboration phase, a collaboration phase in age‐group‐matched dyads, and an individual postcollaboration phase. A convergence effect was observed in that dyad members' postcollaboration choices were significantly more similar compared to their baseline choices during the precollaboration phase. Moreover, levels of convergence were comparable between younger and older adults, suggesting age invariance in social influence on delay discounting. The current results demonstrate a degree of malleability in delay discounting that extends into older adulthood, making interventions targeting the construct a promising avenue for future research.     

回溯式时距估计的动态性及心理机制

时间流逝过程中, 回溯式时距估计动态性体现在短时延迟和长时发展两个方面。前者聚焦秒、分级的延迟, 将其归为背景变化或由目标时距引发的认知差异; 后者聚焦跨年龄(如婴儿、儿童到成年)的个体发展, 认为主要是信息加工速度的差异。最后, 从综合视角出发, 认为其动态性可能是由不同时距信息心理表征的差异造成的, 这体现时间认知的分段综合性。未来需以时间流逝的动态视角开展回溯式时距估计的心理表征研究, 深入探讨与目标时距紧密相关的计时策略在回溯式时距估计中的作用, 并扩展年龄、人格类型等个体差异方面的动态特征研究。     

更优更耐心：质量结果对跨期选择的影响

跨期选择以往的研究集中于金钱数量结果。基于维度加工的模型,本文探究了在跨期选择中,人们面对质量差异的结果（如今天的低配版手机还是六个月后的高配版手机）与相对应的金钱结果（如今天的5000元还是六个月后的6000元）的选择偏好差异。三个实验结果表明：人们面对质量结果（相比于金钱结果）的跨期选择表现得更耐心,而这种现象是由于人们面对选择时在结果维度差异感知不同所致。与金钱结果跨期选择相同,质量结果跨期选择的心理加工过程同样遵循维度间差异比较。本研究为基于维度的跨期选择模型提供了新的证据。     

Vocabulary and automatic attention: The relation between novel words and gaze dynamics in noun generalization

Words direct visual attention in infants, children, and adults, presumably by activating representations of referents that then direct attention to matching stimuli in the visual scene. Novel, unknown, words have also been shown to direct attention, likely via the activation of more general representations of naming events. To examine the critical issue of how novel words and visual attention interact to support word learning we coded frame-by-frame the gaze of 17- to 31-month-old children (n = 66, 38 females) while generalizing novel nouns. We replicate prior findings of more attention to shape when generalizing novel nouns, and a relation to vocabulary development. However, we also find that following a naming event, children who produce fewer nouns take longer to look at the objects they eventually select and make more transitions between objects before making a generalization decision. Children who produce more nouns look to the objects they eventually select more quickly following the naming event and make fewer looking transitions. We discuss these findings in the context of prior proposals regarding children's few-shot category learning, and a developmental cascade of multiple perceptual, cognitive, and word-learning processes that may operate in cases of both typical development and language delay.

Research Highlights

• Examined how novel words guide visual attention by coding frame-by-frame where children look when asked to generalize novel names.
• Gaze patterns differed with vocabulary size: children with smaller vocabularies attended to generalization targets more slowly and did more comparison than those with larger vocabularies.
• Demonstrates a relationship between vocabulary size and attention to object properties during naming.
• This work has implications for looking-based tests of early cognition, and our understanding of children's few-shot category learning.