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

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
JournalPerspectives on Behavior Science
DOIs
StateAccepted/In press - 2024

Bibliographical note

Publisher Copyright:
© The Author(s) 2024.

ASJC Scopus subject areas

  • Social Psychology
  • Experimental and Cognitive Psychology
  • Clinical Psychology

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