Risk preferences impose a hidden distortion on measures of choice impulsivity

Abstract

Measuring temporal discounting through the use of intertemporal choice tasks is now the gold standard method for quantifying human choice impulsivity (impatience) in neuroscience, psychology, behavioral economics, public health and computational psychiatry. A recent area of growing interest is individual differences in discounting levels, as these may predispose to (or protect from) mental health disorders, addictive behaviors, and other diseases. At the same time, more and more studies have been dedicated to the quantification of individual attitudes towards risk, which have been measured in many clinical and non-clinical populations using closely related techniques. Economists have pointed to interactions between measurements of time preferences and risk preferences that may distort estimations of the discount rate. However, although becoming standard practice in economics, discount rates and risk preferences are rarely measured simultaneously in the same subjects in other fields, and the magnitude of the imposed distortion is unknown in the assessment of individual differences. Here, we show that standard models of temporal discounting -such as a hyperbolic discounting model widely present in the literature which fails to account for risk attitudes in the estimation of discount rates- result in a large and systematic pattern of bias in estimated discounting parameters. This can lead to the spurious attribution of differences in impulsivity between individuals when in fact differences in risk attitudes account for observed behavioral differences. We advance a model which, when applied to standard choice tasks typically used in psychology and neuroscience, provides both a better fit to the data and successfully de-correlates risk and impulsivity parameters. This results in measures that are more accurate and thus of greater utility to the many fields interested in individual differences in impulsivity.

Fig 1. RA and ITC task design.

A (top): RA task design, the safe and lottery options are simultaneously displayed during the decision phase. A green dot cues the response time. A yellow square provides feedback on the choice entered. A variable inter-trial interval (ITI) follows. A (bottom): ITC task design, the immediate and delayed options simultaneously displayed during the decision phase. The offer disappears and a white dot cues the response time. A white check mark provides feedback on the choice entered. A variable ITI ensues. For a description of the choice set (see S1A and S1B Fig). B (left): distribution of natural logarithm of risk attitude parameter (ln(α)) across all subjects and all sessions. B (right): distribution of natural logarithm of discount parameter (ln(κ)) estimated from the LH model across all subjects and all sessions.

Fig 2. Model comparison.

A: cross-validated log likelihood (LL) comparison of model LH against model NLH. Each dot corresponds to data from a single subject’s session. B: LL comparison of model LE against model NLE. Panel C, LL comparison of model NLE against model NLH. Shaded areas for panels A and B correspond to sessions for which the nonlinear utility models fit the data better than the linear utility models. C: Shaded area corresponds to sessions for which the NLH model fit the data better than the NLE model. D: average difference in LL across all sessions between model NLH and model LH (dark color), between model NLE and model LE (intermediate color) and, between model NLH and model NLE (light color), black bars indicate S.E.M.

Fig 3. A systematic bias in discount parameters.

A: comparison of estimated discount parameters from model LH against model NLH for each subject’s sessions presented as natural logarithm of discount parameter (ln(κ)). B: discount parameter bias computed as difference between the natural log of estimated parameters from model LH against model NLH (ln(κ)LH − ln(κ)NLH), plotted as a function of the corresponding risk attitude parameter (α), dark dots represent data from each of our subjects’ sessions, gray dots represent simulated data. C: difference of goodness of fit (LL from NLH—LL from LH) between NLH and LH model as a function of the absolute value of the natural logarithm of α (|ln(α)|), risk neutrality here is 0 and any value above 0 is either risk averse or risk seeking. Spearman correlation: rho = 0.297, p < 0.01. Shaded area corresponds to the sessions for which model NLH fit the data better than model LH. D: correlation between the natural logarithm of the risk attitude parameter (ln(α)) and the natural logarithm of the discount parameter and model NLH (dark color).