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Ordered Beta Regression: A Parsimonious, Well-Fitting Model for Continuous Data with Lower and Upper Bounds

Published online by Cambridge University Press:  27 July 2022

Robert Kubinec Open the ORCID record for Robert Kubinec [Opens in a new window]
Robert Kubinec*
Affiliation:
Division of Social Sciences, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates. E-mail: rmk7@nyu.edu
*
Corresponding author Robert Kubinec
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Abstract

I propose a new model, ordered Beta regression, for continuous distributions with both lower and upper bounds, such as data arising from survey slider scales, visual analog scales, and dose–response relationships. This model employs the cut point technique popularized by ordered logit to fit a single linear model to both continuous (0,1) and degenerate [0,1] responses. The model can be estimated with or without observations at the bounds, and as such is a general solution for these types of data. Employing a Monte Carlo simulation, I show that the model is noticeably more efficient than ordinary least squares regression, zero-and-one-inflated Beta regression, rescaled Beta regression, and fractional logit while fully capturing nuances in the outcome. I apply the model to a replication of the Aidt and Jensen (2014, European Economic Review 72, 52–75) study of suffrage extensions in Europe. The model can be fit with the R package ordbetareg to facilitate hierarchical, dynamic, and multivariate modeling.

Keywords

Bayesian statisticslimited dependent variablesregression modeling
Type
Article
Information
Political Analysis , Volume 31 , Issue 4 , October 2023 , pp. 519 - 536
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of the Society for Political Methodology

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Footnotes

Edited by Jeff Gill

References

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Kubinec Dataset

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Supplementary material: PDF

Kubinec supplementary material

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