The DARC Toolbox: automated, flexible, and efficient delayed and risky choice experiments using Bayesian adaptive design

Abstract

Delayed and risky choice (DARC) experiments are a cornerstone of research in psychology, behavioural economics and neuroeconomics. By collecting an agent's preferences between pairs of prospects we can characterise their preferences, investigate what affects them, and probe the underlying decision making mechanisms. We present a state-of-the-art approach and software toolbox allowing such DARC experiments to be run in a highly efficient way. Data collection is costly, so our toolbox automatically and adaptively generates pairs of prospects in real time to maximise the information gathered about the participant's behaviours. We demonstrate that this leads to improvements over alternative experimental paradigms. The key to realising our real time and automatic performance is a number of advances over current Bayesian adaptive design methodology. In particular, we derive an improved estimator for discrete output problems and design a novel algorithm for automating sequential adaptive design. We provide a number of pre-prepared DARC tools for researchers to use, but a key contribution is an adaptive experiment toolbox that can be extended to virtually any 2-alternative-choice task. In particular, to carry out custom adaptive experiments using our toolbox, the user need only encode their behavioural model and design space -both the subsequent inference and sequential design optimisation are automated for arbitrary models the user might write.

Temporal discounting does not influence body mass index

“…The methods used to estimate discount rates are also a potential limitation. While there are adaptive methods which give rise to more precise estimates (Du, Green, & Myerson, 2002;Frye, Galizio, Friedel, DeHart, & Odum, 2016;Vincent & Rainforth, 2018), these are currently not implemented in online internet based questionnaire settings, hence the reliance upon the simple fixed set of non-adaptive choices in the MCQ and WCQ. The penalty paid however is two-fold.…”

A systematic investigation into the reliability of inter-temporal choice model parameters

“…Although we believe the two data-generation procedures examined here are representative of the methods that are commonly used to estimate inter-temporal choice model parameters, there are other methods that warrant consideration in future work. One such method is the adaptive design optimization approach (Cavagnaro, Aranovich, Mcclure, Pitt, & Myung, 2016;Vincent & Rainforth, 2017). Adaptive design optimization involves updating parameter estimates in real time and generating items on the fly that maximize information gain.…”

Hunger increases delay discounting of food and non-food rewards

“…Delay discounting behaviour of participants was measured, in both control and fasted states using a Bayesian adaptive procedure (Vincent & Rainforth, 2018). There are many good adaptive methods of eliciting inter-temporal preferences but this approach is notable as it allows us to near-optimally maximise the precision of the estimates of discount rates for a given number of trials.…”

“…The delayed reward could take on 19 possible delays, approximately logarithmically spaced between 1 hour and 1 year. A full explanation of the methods and a comparison to other approaches is provided by (Vincent & Rainforth, 2018).…”