Hierarchical Maximum Likelihood Parameter Estimation for Cumulative Prospect Theory: Improving the Reliability of Individual Risk Parameter Estimates

An individual’s tolerance of risk can be quantified by using decision models with tuned parameters that maximally fit a set of risky choices the individual has made. A goal of this model fitting procedure is to identify parameters that correspond to stable underlying risk preferences. These preferences can be modeled as an individual difference, indicating a particular decision maker’s tastes and willingness to accept risk. Using hierarchical statistical methods, we show significant improvements in the reliability of individual risk preference parameter estimates over other common methods for cumulative prospect theory. This hierarchical procedure uses population-level information (in addition to an individual’s choices) to break “ties” (or near ties) in the fit quality for sets of possible risk preference parameters. By breaking these statistical ties in a sensible way, researchers can avoid overfitting choice data and thus more resiliently measure individual differences in people’s risk preferences.