To linearize or not to linearize: That is the Mazur delay discounting question

We consider the widely used Mazur hyperbolic delay discounting model. Our scientific contributions are two-fold. First, we provide a novel linearized version of the Mazur model that leads to an analytic estimator of the delay discount rate. Our novel estimator bypasses an outstanding problem: the instability in the numerical optimization to compute the nonlinear estimator. As a result, a simulation study shows that when compared to the conventional nonlinear estimator, our novel estimator more accurately estimates the discount rate. Second, we propose a linearized Mazur random effects model and develop a related F-test for the comparison of the impact of different experimental conditions on the delay discount rate. Because our approach does not suffer from numerical instability, all observations can be used in the computation of the F-statistic. As a result, when compared to the conventional approach, our F-test provides much higher statistical power to detect nonnull effect sizes. Analysis of a previously published dataset examining the effects of a brief intervention to reduce delay discounting provides empirical support for the utility of our proposed linearized methods.