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

Abstract

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.