Multiple deletion diagnostics in beta regression models

Abstract

We consider the problem of identifying multiple outliers in a general class of beta regression models proposed by Ferrari and Cribari-Neto (J Appl Stat 31:799-815, 2004). The currently available single-case deletion diagnostic measures, e.g., the standardized weighted residual (SWR), the Cook-like distance (LD), etc., often fail to identify multiple outlying observations, because they suffer from the well-known problems of masking and swamping effects. In this article, we develop group deletion diagnostic measures, such as generalized SWR, generalized LD, generalized DFFITS and generalized DFBETAS, and suggest a simple procedure for identifying multiple outliers using these. The performance of the proposed methods is investigated through simulation studies and two practical examples.