@article{ref1,
title="Thinking inside the bounds: improved error distributions for indifference point data analysis and simulation via beta regression using common discounting functions",
journal="Perspectives on behavior science",
year="2024",
author="Kim, Mingang and Koffarnus, Mikhail N. and Franck, Christopher T.",
volume="47",
number="2",
pages="417-433",
abstract="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 0 and 1. A comparison between beta regression and standard nonlinear regression reveals close agreement in the estimated discounting rate k obtained from both methods.<p /> <p>Language: en</p>",
language="en",
issn="2520-8969",
doi="10.1007/s40614-024-00410-8",
url="http://dx.doi.org/10.1007/s40614-024-00410-8"
}