  Standard nonlinear regression is commonly used when modeling indifference
points due to its ability to closely follow observed data, resulting in a good
model fit. However, standard nonlinear regression currently lacks a reasonable
distribution-based framework for indifference points, which limits its ability
to adequately describe the inherent variability in the data. Software commonly
assumes data follow a normal distribution with constant variance. However,
typical indifference points do not follow a normal distribution or exhibit
constant variance. To address these limitations, this paper introduces a class
of nonlinear beta regression models that offers excellent fit to discounting
data and enhances simulation-based approaches. This beta regression model can
accommodate popular discounting functions. This work proposes three specific
advances. First, our model automatically captures non-constant variance as a
function of delay. Second, our model improves simulation-based approaches since
it obeys the natural boundaries of observable data, unlike the ordinary
assumption of normal residuals and constant variance. Finally, we introduce a
scale-location-truncation trick that allows beta regression to accommodate
observed values of zero and one. A comparison between beta regression and
standard nonlinear regression reveals close agreement in the estimated
discounting rate k obtained from both methods.
