Thinking inside the bounds: Improved error distributions for indifference point data analysis and simulation via beta regression using common discounting functions

Mingang Kim; Mikhail N. Koffarnus; Christopher T Franck

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arXiv · 2404.18000

Thinking inside the bounds: Improved error distributions for indifference point data analysis and simulation via beta regression using common discounting functions

Mingang Kim·Mikhail N. Koffarnus·Christopher T Franck

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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 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.

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BibTeX RIS

Mingang Kim, Mikhail N. Koffarnus, Christopher T Franck. 2024-06-06. Thinking inside the bounds: Improved error distributions for indifference point data analysis and simulation via beta regression using common discounting functions. https://arxiv.org/abs/2404.18000

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