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Comparison of multiplicative and additive hyperbolic and hyperboloid discounting models in delayed lotteries involving gains and losses.

ABSTRACT: Many day-to-day decisions may involve risky outcomes that occur at some delay after a decision has been made. We refer to such scenarios as delayed lotteries. Despite human choice often involves delayed lotteries, past research has primarily focused on decisions with delayed or risky outcomes. Comparatively, less research has explored how delay and probability interact to influence decisions. Within research on delayed lotteries, rigorous comparisons of models that describe choice from the discounting framework have not been conducted. We performed two experiments to determine how gain or loss outcomes are devalued when delayed and risky. Experiment 1 used delay and probability ranges similar to past research on delayed lotteries. Experiment 2 used individually calibrated delay and probability ranges. Ten discounting models were fit to the data using a genetic algorithm. Candidate models were derived from past research on discounting delayed or probabilistic outcomes. We found that participants' behavior was best described primarily by a three-parameter multiplicative model. Measures based on information criteria pointed to a solution in which only delay and probability were psychophysically scaled. Absolute measures based on residuals pointed to a solution in which amount, delay, and probability are simultaneously scaled. Our research suggests that separate scaling parameters for different discounting factors may not be necessary with delayed lotteries.

SUBMITTER: Bialaszek W

PROVIDER: S-EPMC7244164 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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Comparison of multiplicative and additive hyperbolic and hyperboloid discounting models in delayed lotteries involving gains and losses.

Białaszek Wojciech W Marcowski Przemysław P Cox David J DJ

PloS one 20200522 5

Many day-to-day decisions may involve risky outcomes that occur at some delay after a decision has been made. We refer to such scenarios as delayed lotteries. Despite human choice often involves delayed lotteries, past research has primarily focused on decisions with delayed or risky outcomes. Comparatively, less research has explored how delay and probability interact to influence decisions. Within research on delayed lotteries, rigorous comparisons of models that describe choice from the disco ...[more]

PMID: 32442186

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Project description:Additive and multiplicative regression models of habituation were compared regarding the fit to looking times from a habituation experiment with infants aged between 3 and 11 months. In contrast to earlier studies, the current study considered multiple probability distributions, namely Weibull, gamma, lognormal and normal distribution. In the habituation experiment the type of contrast between the habituation and the test trial was varied (luminance, color or orientation contrast), crossed with the number of habituation trials (1, 3, 5, or 7 habituation trials) and crossed with three age cohorts (4, 7, 10 months). The initial mean LT to dark stimuli (around 3.7 s) was considerably shorter than the mean LT to green and gray stimuli (around 5 s). Infants showed the strongest dishabituation to changes from dark to bright (luminance contrast) and weak-to-no dishabituation to a 90-degrees rotation of the gray stimuli (orientation contrast). The dishabituation was stronger after five and seven habituation trials, but the result was not statistically robust. The gamma distribution showed the best fit in terms of log-likelihood and mean absolute error and the best predictive performance. Furthermore, the gamma distribution showed small correlations between parameters relative to other models. The normal additive model showed an inferior fit and medium correlations between the parameters. In particular, the positive correlation between the initial looking time (LT) and the habituation rate was likely responsible for a different interpretation relative to the multiplicative models of the main effect of age on the habituation rate. Otherwise, the additive and multiplicative models provided similar statistical conclusions. The performance of the model versions without pooling and with partial pooling across participants (also called random-effects, multi-level or hierarchical models) were compared. The latter type of models showed worse data fit but more precise predictions and reduced correlations between the parameters. The performance of model variants with auto-regressive time structures were explored but showed considerably worse fit. The performance of quadratic models that allowed non-monotonic changes in LTs were investigated as well. However, when fitted with LT data, these models did not produce non-monotonic change in LTs. The study underscores the utility of partial-pooling models in terms of providing more accurate predictions. Further, it agrees with previous research in that a multiplicative LT model is preferable. Nevertheless, the current results suggest that the impact of the choice of an additive model on the statistical inference is less dramatic then previously assumed.

Project description:Choice bundling, in which a single choice produces a series of repeating consequences over time, increases valuation of delayed monetary and non-monetary gains. Interventions derived from this manipulation may be an effective method for mitigating the elevated delay discounting rates observed in cigarette smokers. No prior work, however, has investigated whether the effects of choice bundling generalize to reward losses. In the present study, an online panel of cigarette smokers (N = 302), recruited using survey firms Ipsos and InnovateMR, completed assessments for either monetary gains or losses (randomly assigned). In Step 1, participants completed a delay-discounting task to establish Effective Delay 50 (ED50), or the delay required for an outcome to lose half of its value. In Step 2, participants completed three conditions of an adjusting-amount task, choosing between a smaller, sooner (SS) adjusting amount and a larger, later (LL) fixed amount. The bundle size (i.e., number of consequences) was manipulated across conditions, where a single choice produced either 1 (control), 3, or 9 consequences over time (ascending/descending order counterbalanced). The delay to the first LL amount in each condition, as well as the intervals between all additional SS and LL amounts (where applicable), were set to individual participants' ED50 values from Step 1 to control for differences in discounting of gains and losses. Results from Step 1 showed significantly higher ED50 values (i.e., less discounting) for losses compared to gains (p < 0.001). Results from Step 2 showed that choice bundling significantly increased valuation of both LL gains and losses (p < 0.001), although effects were significantly greater for losses (p < 0.01). Sensitivity analyses replicated these conclusions. Future research should examine the potential clinical utility of choice bundling, such as development of motivational interventions that emphasize both the bundled health gains associated with smoking cessation and the health losses associated with continued smoking.

Dataset Information

Comparison of multiplicative and additive hyperbolic and hyperboloid discounting models in delayed lotteries involving gains and losses.

Publications

Comparison of multiplicative and additive hyperbolic and hyperboloid discounting models in delayed lotteries involving gains and losses.

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