Consumer choices with variations in item price, delay, and opportunity cost.

Tversky and Kahneman (1981) told participants to imagine they were at a store about to purchase an item. They were asked if they would be willing to drive 20 min to another store to receive a $5 discount on the item's price. Most participants were willing, but only when the original price of the item was small ($15); when the original price was relatively large ($125), most said they would not drive 20 min for a $5 discount. We examined this framing effect in 296 participants, but instead used a psychophysical-adjustment procedure to obtain quantitative estimates of the discount required with different (a) item prices, (b) delays until the item's receipt, and (c) opportunity costs (in "driving" vs. "delivery" tasks). We systematically replicated Tversky and Kahneman's results, but also extended them by showing a substantial influence of opportunity costs on the consumer discounts required. A behavioral model of delay discounting-additive-utility theory-accounted for 97% of the variance in these consumer discounts.

Tests of an indifference rule in variable-delay and double-reward choice procedures with humans.

Four hundred and fifty participants were recruited from Amazon Mechanical Turk across 3 experiments to test the predictions of a hyperbolic discounting equation in accounting for human choices involving variable delays or multiple rewards (Mazur, 1984, 1986). In Experiment 1, participants made hypothetical choices between 2 monetary alternatives, 1 consisting of a fixed delay and another consisting of 2 delays of equal probability (i.e., a variable-delay procedure). In Experiment 2, participants made hypothetical monetary choices between a single, immediate reward and 2 rewards, 1 immediate and 1 delayed (i.e., a double-reward procedure). Experiment 3 also used a double-reward procedure, but with 2 delayed rewards. Participants in all 3 experiments also completed a standard delay-discounting task. Finally, 3 reward amounts were tested in each type of task ($100, $1000, and $5000). In the double-reward conditions (Experiments 2 and 3), the results were in good qualitative and quantitative agreement with Mazur's model (1984, 1986). In contrast, when participants made choices involving variable delays (Experiment 1), there was relatively poor qualitative and quantitative agreement with this model. These results, along with our previous findings, suggest the structure of questions in hypothetical tasks with humans can be a strong determinant of the choice pattern.

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.

Human choices between variable and fixed rewards in hypothetical variable-delay and double-reward discounting procedures.

Prior research has shown that nonhumans show an extreme preference for variable- over fixed-delays to reinforcement. This well-established preference for variability occurs because a reinforcer's strength or "value" decreases according to a curvilinear function as its delay increases. The purpose of the present experiments was to investigate whether this preference for variability occurs with human participants making hypothetical choices. In three experiments, participants recruited from Amazon Mechanical Turk made choices between variable and fixed monetary rewards. In a variable-delay procedure, participants repeatedly chose between a reward delivered either immediately or after a delay (with equal probability) and a reward after a fixed delay (Experiments 1 and 2). In a double-reward procedure, participants made choices between an alternative consisting of two rewards, one delivered immediately and one after a delay, and a second alternative consisting of a single reward delivered after a delay (Experiments 1 and 3). Finally, all participants completed a standard delay-discounting task. Although we observed both curvilinear discounting and magnitude effects in the standard discounting task, we found no consistent evidence of a preference for variability-as predicted by two prominent models of curvilinear discounting (i.e., a simple hyperbola and a hyperboloid)-in our variable-delay and double-reward procedures. This failure to observe a preference for variability may be attributed to the hypothetical, rule-governed nature of choices in the present study. In such contexts, participants may adopt relatively simple strategies for making more complex choices.

Automating Scoring of Delay Discounting for the 21- and 27-Item Monetary Choice Questionnaires.

Delay discounting describes the process wherein rewards lose value as a function of their delayed receipt; how quickly rewards lose value is termed the rate of delay discounting. Rates of delay discounting are robust predictors of much behavior of societal importance. One efficient approach to obtaining a human subject's rate of delay discounting is via the 21- and 27-item Monetary Choice Questionnaires, brief dichotomous choice tasks that assess preference between small immediate and larger delayed monetary outcomes. Unfortunately, the scoring procedures for the Monetary Choice Questionnaires are rather complex, which may serve as a barrier to their use. This report details a freely available Excel-based spreadsheet tool that automatically scores Monetary Choice Questionnaire response sets, using both traditional and contemporary/advanced approaches. An overview of the Monetary Choice Questionnaire and its scoring algorithm is provided. We conclude with general considerations for using the spreadsheet tool.

Delay discounting is associated with treatment response among cocaine-dependent outpatients.

Delay discounting (DD) describes the rate at which reinforcers lose value as the temporal delay to their receipt increases. Steeper discounting has been positively associated with vulnerability to substance use disorders, including cocaine use disorders. In the present study, we examined whether DD of hypothetical monetary reinforcers is associated with the duration of cocaine abstinence achieved among cocaine-dependent outpatients. Participants were 36 adults who were participating in a randomized controlled trial examining the efficacy of voucher-based contingency management (CM) using low-magnitude (N = 18) or high-magnitude (N = 18) voucher monetary values. DD was associated with the number of continuous weeks of cocaine abstinence achieved, even after adjusting for treatment condition during the initial 12-week, t(33) = 2.48, p = .045 and entire recommended 24-week of treatment, t(33) = 2.40, p = .022. Participants who exhibited steeper discounting functions achieved shorter periods of abstinence in the Low-magnitude voucher condition (12-week: t(16) = 2.48, p = .025; 24-week: t(16) = 2.68, p = .017), but not in the High-magnitude voucher condition (12-week: t(16) = 0.51, p = .618; 24-week: t(16) = 1.08, p = .298), although the interaction between DD and treatment condition was not significant (12-week: t(32) = -1.12, p = .271; 24-week: t(32) = -0.37, p = .712). These results provide further evidence on associations between DD and treatment response and extend those observations to a new clinical population (i.e., cocaine-dependent outpatients), while also suggesting that a more intensive intervention like the High-magnitude CM condition may diminish this negative relationship between DD and treatment response.

A Quantitative Analysis and Natural History of B. F. Skinner's Coauthoring Practices.

This paper describes and analyzes B. F. Skinner's coauthoring practices. After identifying his 35 coauthored publications and 27 coauthors, we analyze his coauthored works by their form (e.g., journal articles) and kind (e.g., empirical); identify the journals in which he published and their type (e.g., data-type); describe his overall and local rates of publishing with his coauthors (e.g., noting breaks in the latter); and compare his coauthoring practices with his single-authoring practices (e.g., form, kind, journal type) and with those in the scientometric literature (e.g., majority of coauthored publications are empirical). We address these findings in the context of describing the natural history of Skinner's coauthoring practices. Finally, we describe some limitations in our methods and offer suggestions for future research.

On the scaling interpretation of exponents in hyperboloid models of delay and probability discounting.

Previously, we (McKerchar et al., 2009) showed that two-parameter hyperboloid models (Green and Myerson, 2004; Rachlin, 2006) provide significantly better fits to delay discounting data than simple, one-parameter hyperbolic and exponential models. Here, we extend this effort by comparing fits of the two-parameter hyperboloid models to data from a larger sample of participants (N=171) who discounted probabilistic as well as delayed rewards. In particular, we examined the effects of amount on the exponents in the two hyperboloid models of delay and probability discounting in order to evaluate key theoretical predictions of the standard psychophysical scaling interpretation of these exponents. Both the Rachlin model and the Green and Myerson model provided very good fits to delay and probability discounting of both small and large amounts at both the group and individual levels (all R(2)s>.97 at the group level; all median R(2)s>.92 at the individual level). For delay discounting, the exponent in both models did not vary as a function of delayed amount, consistent with the psychophysical scaling interpretation. For probability discounting, however, the exponent in both models increased as the probabilistic amount increased-a finding inconsistent with the scaling interpretation.

A comparison of four models of delay discounting in humans.

The present study compared four prominent models of delay discounting: a one-parameter exponential decay, a one-parameter hyperbola [Mazur, J.E., 1987. An adjusting procedure for studying delayed reinforcement. In: Commons, M.L., Mazur, J.E., Nevin, J.A., Rachlin, H. (Eds.), Quantitative Analyses of Behavior: The Effect of Delay and of Intervening Events on Reinforcement Value, vol. 5. Erlbaum, Hillsdale, NJ, pp. 55-73], a two-parameter hyperboloid in which the denominator is raised to a power [Green, L., Myerson, J., 2004. A discounting framework for choice with delayed and probabilistic rewards. Psychol. Bull. 130, 769-792], and a two-parameter hyperbola in which delay is raised to a power [Rachlin, H., 2006. Notes on discounting. J. Exp. Anal. Behav. 85, 425-435]. Sixty-four college undergraduates made choices between hypothetical monetary rewards, one immediate and one delayed, and the fit of the four models to their data was assessed. All four equations accounted for a large proportion of the variance at both the group and the individual levels, but the exponents of both two-parameter models were significantly less than 1.0 at the group level, and frequently so at the individual level. Taken together, these results strongly suggest that more than one parameter is needed to accurately describe delay discounting by humans. Notably, both the Rachlin and the Green and Myerson models accounted for more than 99% of the variance at the group level and for 96% of the variance in the median individual. Because both models provide such good descriptions of the data, model selection will need to be based on other grounds.

Use of a force-plate actometer for detecting and quantifying vertical leaping induced by amphetamine in BALB/cJ mice, but not in C57BL/6J, DBA/2J, 129X1/SvJ, C3H/HeJ, and CD-1 mice.

The force-plate actometer is a relatively new computer-based instrument with high temporal and spatial resolution that has been used to measure the behavioral effects of genetic restriction (e.g., inbred mice) and drugs (e.g., dopaminergic agonists and antagonists) on a variety of behaviors in rodents, including locomotor activity, stereotypies, tremor, and wall rearing. In the present study, the force-plate actometer was used to measure the differential effects of amphetamine-induced (10.0mg/kg) vertical leaping in five inbred mouse strains (BALB/cJ, C57BL/6J, DBA/2J, 129X1/SvJ, and C3H/HeJ) and one outbred stock (CD-1). Across a 13-day, five-injection procedure, mice of the BALB/cJ strain leaped an average of 82 times per 60-min session; the C57BL/6J, DBA/2J, 129X1/SvJ, C3H/HeJ strains and CD-1 stock always showed zero or near zero levels of vertical leaping following amphetamine treatment. The quantitative precision afforded by the force-plate actometer revealed that the mean duration of the leaps by the BALB/cJ strain was 0.18 second, and the corresponding peak force averaged 87.4 gram per leap, which was more than 400% of the average body weight of this strain. Although no evidence of behavioral sensitization was indicated for amphetamine's effects on vertical leaping, sensitization to amphetamine's effects on spatial confinement (i.e., bouts of low mobility) was observed in all mouse types. Results indicate that the force-plate actometer is an instrument well suited for detecting and quantifying both vertical leaping and collateral behaviors induced by amphetamine in mice.

Differential acquisition of lever pressing in inbred and outbred mice: comparison of one-lever and two-lever procedures and correlation with differences in locomotor activity.

Recent progress in mouse genetics has led to an increased interest in developing procedures for assessing mouse behavior, but relatively few of the behavioral procedures developed involve positively reinforced operant behavior. When operant methods are used, nose poking, not lever pressing, is the target response. In the current study differential acquisition of milk-reinforced lever pressing was observed in five inbred strains (C57BL/6J, DBA/2J, 129X1/SvJ, C3H/HeJ, and BALB/cJ) and one outbred stock (CD-1) of mice. Regardless of whether one or two levers (an "operative" and "inoperative" lever) were in the operant chamber, a concomitant variable-time fixed-ratio schedule of milk reinforcement established lever pressing in the majority of mice within two 120-min sessions. Substantial differences in lever pressing were observed across mice and between procedures. Adding an inoperative lever retarded acquisition in C57BL/6J, DBA/2J, 129X1/SvJ, and C3H/HeJ mice, but not in CD-1 and BALB/cJ mice. Locomotor activity was positively correlated with number of lever presses in both procedures. Analyses of durations of the subcomponents (e.g., time to move from hopper to lever) of operant behavior revealed further differences among the six types of mice. Together, the data suggest that appetitively reinforced lever pressing can be acquired rapidly in mice and that a combination of procedural, behavioral, and genetic variables contributes to this acquisition.

Effects of risperidone on destructive behavior of persons with developmental disabilities: III. Functional analysis.

Functional analyses were conducted during a double-blind, placebo-controlled study of the atypical antipsychotic medication risperidone with 13 individuals. Risperidone was effective in reducing destructive behavior (compared to placebo) for 10 participants. For 7 of these responders, an undifferentiated pattern of responding occurred across their baseline functional analysis conditions (i.e., a similar rate of responding across conditions), and risperidone treatment produced nonspecific reductions of their destructive behavior across functional analysis conditions. For the remaining 3 responders, a differentiated pattern of responding occurred across their baseline functional analysis conditions (i.e., an elevated rate of responding occurred in a specific condition), and risperidone treatment produced function-specific reductions of their destructive behavior.