On the scaling interpretation of exponents in hyperboloid models of delay and probability discounting |
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Authors: | Todd L McKerchar Leonard Green |
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Institution: | a Department of Psychology, Jacksonville State University, 700 Pelham Rd. North, Jacksonville, AL 36265, United States b Department of Psychology, Washington University, St. Louis, MO, United States |
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Abstract: | Previously, we (McKerchar et al., 2009) showed that two-parameter hyperboloid models (
Green and Myerson, 2004] and Rachlin, 2006]) provide significantly better fits to delay discounting data than simple, one-parameter hyperbolic and exponential models. Here, we extend this effort by comparing fits of the two-parameter hyperboloid models to data from a larger sample of participants (N = 171) who discounted probabilistic as well as delayed rewards. In particular, we examined the effects of amount on the exponents in the two hyperboloid models of delay and probability discounting in order to evaluate key theoretical predictions of the standard psychophysical scaling interpretation of these exponents. Both the Rachlin model and the Green and Myerson model provided very good fits to delay and probability discounting of both small and large amounts at both the group and individual levels (all R2s > .97 at the group level; all median R2s > .92 at the individual level). For delay discounting, the exponent in both models did not vary as a function of delayed amount, consistent with the psychophysical scaling interpretation. For probability discounting, however, the exponent in both models increased as the probabilistic amount increased—a finding inconsistent with the scaling interpretation. |
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Keywords: | Delay discounting Probability discounting Hyperboloid Model comparison Scaling Money Humans |
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