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AbstractProbability predictions are essential to inform decision making across many fields. Ideally, probability predictions are (i) well calibrated, (ii) accurate, and (iii) bold, that is, spread out enough to be informative for decision making. However, there is a fundamental tension between calibration and boldness, since calibration metrics can be high when predictions are overly cautious, that is, non-bold. The purpose of this work is to develop a Bayesian model selection-based approach to assess calibration, and a strategy for boldness-recalibration that enables practitioners to responsibly embolden predictions subject to their required level of calibration. Specifically, we allow the user to pre-specify their desired posterior probability of calibration, then maximally embolden predictions subject to this constraint. We demonstrate the method with a case study on hockey home team win probabilities and then verify the performance of our procedures via simulation. We find that very slight relaxation of calibration probability (e.g., from 0.99 to 0.95) can often substantially embolden predictions when they are well calibrated and accurate (e.g., widening hockey predictions’ range from 26%–78% to 10%–91%). [ABSTRACT FROM AUTHOR]

We propose a Bayesian model selection approach for generalized linear mixed models (GLMMs). We consider covariance structures for the random effects that are widely used in areas such as longitudinal studies, genome‐wide association studies, and spatial statistics. Since the random effects cannot be integrated out of GLMMs analytically, we approximate the integrated likelihood function using a pseudo‐likelihood approach. Our Bayesian approach assumes a flat prior for the fixed effects and includes both approximate reference prior and half‐Cauchy prior choices for the variances of random effects. Since the flat prior on the fixed effects is improper, we develop a fractional Bayes factor approach to obtain posterior probabilities of the several competing models. Simulation studies with Poisson GLMMs with spatial random effects and overdispersion random effects show that our approach performs favorably when compared to widely used competing Bayesian methods including deviance information criterion and Watanabe–Akaike information criterion. We illustrate the usefulness and flexibility of our approach with three case studies including a Poisson longitudinal model, a Poisson spatial model, and a logistic mixed model. Our proposed approach is implemented in the R package GLMMselect that is available on CRAN. [ABSTRACT FROM AUTHOR]

Delay discounting reflects the rate at which a reward loses its subjective value as a function of delay to that reward. Many models have been proposed to measure delay discounting, and many comparisons have been made among these models. We highlight the two‐parameter delay discounting model popularized by Howard Rachlin by demonstrating two key practical features of the Rachlin model. The first feature is flexibility; the Rachlin model fits empirical discounting data closely. Second, when compared with other available two‐parameter discounting models, the Rachlin model has the advantage that unique best estimates for parameters are easy to obtain across a wide variety of potential discounting patterns. We focus this work on this second feature in the context of maximum likelihood, showing the relative ease with which the Rachlin model can be utilized compared with the extreme care that must be used with other models for discounting data, focusing on two illustrative cases that pass checks for data validity. Both of these features are demonstrated via a reanalysis of discounting data the authors have previously used for model selection purposes. [ABSTRACT FROM AUTHOR]

Behavioral economics has been a fruitful area of research in substance use. Mathematical descriptions of how individuals temporally discount the value of a commodity have been correlated with substance use and mathematical descriptions of drug consumption decreasing as a function of price (i.e., demand) predict maladaptive substance use. While there is a logical assumption that temporal factors affect demand for a drug, little has been done to merge these models. Thus, the purpose of this study was to combine models of discounting and demand, extending Howard Rachlin's work and contributions to novel areas of study. Data from 85 participants from Amazon Mechanical Turk (MTurk) who completed a hypothetical cigarette purchase task that included price of and delay to cigarettes were analyzed. Multilevel modeling was used to determine descriptive accuracy of combined additive and multiplicative models of discounting and demand. Of the discounting models used in conjunction with the exponentiated demand equation, the Rachlin hyperboloid best described the delay dimension of consumption. The multiplicative version of the Rachlin equation applied to both delay and price outperformed other models tested. Therefore, existing models of discounting and demand can be extended to modeling consumption data from complex multidimensional experimental arrangements. [ABSTRACT FROM AUTHOR]

Background: Cigarette smoking continues to be a major health concern and remains the leading preventable cause of death in the US. Recent efforts have been made to determine the potential health and policy benefits of reducing nicotine in combustible cigarettes. The degree to which changes in blood nicotine relate to measures of the abuse liability of reduced-nicotine cigarettes is unknown. The current study examined the relation between blood nicotine and behavioral economic demand measures of cigarettes differing in nicotine content.Methods: Using a within-subject design, participants smoked a single cigarette during each experimental session. Cigarettes included the participant's usual-brand cigarette and SPECTRUM investigational cigarette differing in nicotine level (mg of nicotine to g of tobacco; 15.8 mg/g, 5.2 mg/g, 2.4 mg/g, 1.3 mg/g, and 0.4 mg/g). During each session, blood was collected at multiple timepoints and behavioral economic demand was assessed. Nonlinear mixed-effects models were used to estimate differences in derived intensity (Q0) and change in elasticity (α).Results: Measures of blood nicotine decreased in an orderly fashion related to nicotine level and significantly predicted change in elasticity (α), but not derived intensity. No differences in demand parameters between the usual brand and 15.8mg/g cigarettes were observed. However, α was significantly higher (lower valuation) for 0.4mg/g than 15.8mg/g cigarettes.Conclusions: The lowest nicotine level (0.4mg/g) corresponded with the lowest abuse liability (α) compared to the full-strength control (15.8mg/g), with the 1.3mg/g level also resulting in low abuse liability.Implications: This is the first study examining the relative contributions of nicotine content in cigarettes and blood nicotine levels on the behavioral economic demand abuse liability of cigarettes ranging in nicotine content. Our results suggest blood nicotine and nicotine content both predict behavioral economic demand abuse liability. In addition, our results suggest a nicotine content of 1.3mg/g or lower may be effective at reducing cigarette uptake among first-time (naïve) smokers. Our results largely conform to previous findings suggesting a very low nicotine content cigarette maintains lower abuse liability than full-strength cigarettes. [ABSTRACT FROM AUTHOR]

Introduction: Cigarette smoking remains the leading preventable cause of death in the United States. Recent efforts have explored the potential health and policy benefits of reducing nicotine, an addictive component, in combustible cigarettes. To date, an experimental, prospective analysis directly comparing the effects of varying regulatory environments on purchases of multiple products has yet to be conducted. The present study compared real purchasing of conventional cigarettes, reduced-nicotine cigarettes, and a variety of other nicotine and tobacco products across a range of regulatory environments.Methods: Participants were assigned to one of five groups, each associated with a different nicotine level (mg of nicotine to g of tobacco) in SPECTRUM investigational cigarettes (15.8, 5.2, 2.4, 1.3, and 0.4 mg/g). Across sessions, participants made real purchases for nicotine/tobacco products in an Experimental Tobacco Marketplace. Each session corresponded with a distinct regulatory environment wherein different nicotine/tobacco products were available for purchase.Results: Our results suggest that the primary drivers of cigarette and nicotine purchasing are regulatory environment and the presence/absence of alternative nicotine and tobacco products. Perhaps surprisingly, nicotine level does not appear to be such a driver of purchasing behavior under these experimental conditions. Investigational cigarette purchasing is lowest when other preferred combustible products are available and highest when investigational cigarettes are the only combustible product available for purchase.Conclusions: If a reduced-nicotine policy is implemented, great care should be taken in determining and making available less-harmful nicotine/tobacco products as the availability of preferred combustible products may result in undesirable levels of purchasing.Implications: This is the first experimental study investigating different potential regulatory effects related to a reduced-nicotine policy by examining purchasing across a range of nicotine/tobacco products. Our results suggest the presence of affordable, highly preferred combustible products is likely to maintain tobacco purchasing at undesirable levels. To promote switching to less-harmful products, affordable alternate nicotine and tobacco products should be readily available. Finally, our results suggest that the availability of noncigarette products, not cigarette nicotine level, will most likely affect purchasing of reduced-nicotine cigarettes. [ABSTRACT FROM AUTHOR]