How to ask twenty questions and win: Machine learning tools for assessing preferences from small samples of willingness-to-pay prices

Subjective value has long been measured using binary choice experiments, yet responses like willingness-to-pay prices can be an effective and efficient way to assess individual differences risk preferences and value. Tony Marley’s work illustrated that dynamic, stochastic models permit meaningful inferences about cognition from process-level data on paradigms beyond binary choice, yet many of these models remain difficult to use because their likelihoods must be approximated from simulation. In this paper, we develop and test an approach that uses deep neural networks to estimate the parameters of otherwise-intractable behavioral models. Once trained, these networks allow for accurate and instantaneous parameter estimation. We compare different network architectures and show that they accurately recover true risk preferences related to utility, response caution, anchoring, and non-decision processes. To illustrate the usefulness of the approach, it was then applied to estimate model parameters for a large, demographically representative sample of U.S. participants who completed a 20-question pricing task — an estimation task that is not feasible with previous methods. The results illustrate the utility of machine-learning approaches for fitting cognitive and economic models, providing efficient methods for quantifying meaningful differences in risk preferences from sparse data.