Title: Robust Inference under the Beta Regression Model with Application to Health Care Studies,
Abstract: Data on rates, percentages or proportions arise frequently in many different
applied disciplines like medical biology, health care, psychology and several
others. In this paper, we develop a robust inference procedure for the beta
regression model which is used to describe such response variables taking
values in $(0, 1)$ through some related explanatory variables. In relation to
the beta regression model, the issue of robustness has been largely ignored in
the literature so far. The existing maximum likelihood based inference has
serious lack of robustness against outliers in data and generate drastically
different (erroneous) inference in presence of data contamination. Here, we
develop the robust minimum density power divergence estimator and a class of
robust Wald-type tests for the beta regression model along with several
applications. We derive their asymptotic properties and describe their
robustness theoretically through the influence function analyses. Finite sample
performances of the proposed estimators and tests are examined through suitable
simulation studies and real data applications in the context of health care and
psychology. Although we primarily focus on the beta regression models with a
fixed dispersion parameter, some indications are also provided for extension to
the variable dispersion beta regression models with an application.