A New Family of Regression Models for $[0,1]$ Outcome Data: Expanding the Palette

Abstract: Beta regression is a popular methodology when the outcome variable $y$ is on the open interval $(0,1)$. When $y$ is in the closed interval $[0,1]$, it is commonly accepted that beta regression is inapplicable. Instead, common solutions are to use augmented beta regression or censoring models or else to subjectively rescale the endpoints to allow beta regression. We provide an attractive new approach with a family of models that treats the entirety of $y\in[0,1]$ in a single model without rescaling or the need for the complications of augmentation or censoring. This family provides the interpretational convenience of a single straightforward model for the expectation of $y \in [0,1]$ over its entirety. We establish the conditions for the existence of a unique MLE and then examine this new family of models from both maximum-likelihood and Bayesian perspectives. We successfully apply the models to employment data in which augmented beta regression was difficult due to data separation. We also apply the models to healthcare panel data that were originally examined by way of rescaling.