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

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 cutpoint 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 this type 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, re-scaled beta regression and fractional logit while fully capturing nuances in the outcome. I apply the model to a replication of the Aidt and Jensen (2012) study of suffrage extensions in Europe. The model can be fit with the R package `ordbetareg` to facilitate hierarchical, dynamic and multivariate modeling.