B0783
Title: Beyond Beta regression: Modelling percentages and fractions in the presence of boundary observations
Authors: Ioannis Kosmidis - University College London (United Kingdom) [presenting]
Anyi Zou - University of Warwick (United Kingdom)
Abstract: One important limitation of regression models that are based on the Beta distribution is that they are not applicable when at least one of the observed responses is either zero or one - in such scenarios the likelihood function is either $+\infty$ or $-\infty$. The relevant approaches in the literature focus on either the adjustment of the boundary observations by small constants so that the adjusted responses end up in $(0,1)$, or the use of a discrete-continuous mixture of a Beta distribution and point masses at zero and/or one. The former approach suffers from the arbitrariness of choosing the additive adjustment. On the other hand the latter approach, despite of being natural in some applications, gives a ``special'' interpretation at the values of zero and/or one relative to observations in $(0,1)$, and hence it cannot be a general solution to the problem. An extension of the Beta regression model is considered that can naturally accommodate zero and one observations, that avoids the special treatment of such values, and such that it has the usual Beta regression model as a special case. Fitting and inferential procedures for the new model are presented and its usefulness is demonstrated by applications.
