View Submission - CRONOSMDA2019

A0270
**Title: **Infinite mixtures of beta regression models for bounded-domain variables
**Authors: **Ioannis Kosmidis - University of Warwick and The Alan Turing Institute (United Kingdom) **[presenting]**

Achim Zeileis - University of Innsbruck (Austria)

**Abstract: **Beta regression is a useful tool for modelling bounded-domain continuous response variables, such as proportions, rates fractions and concentration indices. One important limitation of beta regression models is that they do not apply when at least one of the observed responses is on the boundary --- in such scenarios the likelihood function is simply 0 regardless of the value of the parameters. The relevant approaches in the literature focus on either the transformation of the observations by small constants so that the transformed responses end up in the support of the beta distribution, or the use of a discrete-continuous mixture of a beta distribution and point masses at either or both of the boundaries. The former approach suffers from the arbitrariness of choosing the additive adjustment. The latter approach gives a ``special'' interpretation to the boundary observations relative to the non-boundary ones, and requires the specification of an appropriate regression structure for the hurdle part of the overall model, generally leading to complicated models. We rethink of the problem and present an alternative model class that leverages the flexibility of the beta distribution, can naturally accommodate boundary observations and preserves the parsimony of beta regression, which is a limiting case. Likelihood-based estimation and inferential procedures for the new model are presented, and its usefulness is illustrated by applications.

Achim Zeileis - University of Innsbruck (Austria)