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 R2s \u3e .97 at the group level; all median R2s \u3e .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 interpretatio

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

This is the published version, reproduced here with permission from the publisher. This article is also available electronically form http://www.ncbi.nlm.nih.gov/pubmed/22532732.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

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, 1987), a two-parameter hyperboloid in which the denominator is raised to a power (Green and Myerson, 2004), and a two-parameter hyperbola in which delay is raised to a power (Rachlin, 2006). 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

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

Rationale—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. Objectives—In the present study, we examined whether DD of hypothetical monetary reinforcers is associated with the duration of cocaine abstinence achieved among cocainedependent outpatients. Methods—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. Results—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 Lowmagnitude 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). Conclusions—These results provide further evidence on associations between DD and treatment response and extend those observations to a new clinical population (i.e., cocainedependent outpatients), while also suggesting that a more intensive intervention like the Highmagnitude 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

Functional analysis and treatment of breath holding maintained by nonsocial reinforcement.

A functional analysis showed that breath holding exhibited by a 16-year-old boy with mental retardation occurred independent of social consequences. Assessment results of the existing treatment procedure-a verbal reprimand-were used to design a treatment package that reduced the behavior to low levels across 7 months

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