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Autores principales: Kim, Mingang, Koffarnus, Mikhail N., Franck, Christopher T
Formato: Preprint
Publicado: 2024
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Acceso en línea:https://arxiv.org/abs/2404.18000
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author Kim, Mingang
Koffarnus, Mikhail N.
Franck, Christopher T
author_facet Kim, Mingang
Koffarnus, Mikhail N.
Franck, Christopher T
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2404_18000
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Thinking inside the bounds: Improved error distributions for indifference point data analysis and simulation via beta regression using common discounting functions
Kim, Mingang
Koffarnus, Mikhail N.
Franck, Christopher T
Methodology
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.
title Thinking inside the bounds: Improved error distributions for indifference point data analysis and simulation via beta regression using common discounting functions
topic Methodology
url https://arxiv.org/abs/2404.18000