On Diagnostics in Bell--Touchard Regression Models

Abstract

The Bell--Touchard regression model for count response variables was introduced recently in the statistical literature. This regression model for counts is, in some aspects, similar to the generalized linear model framework, and the mean response is related to covariates and unknown regression coefficients, which allows for parameter interpretation in terms of the response variable in its original scale. However, diagnostic methods for this class of regression models were not developed. In this paper, we fill this gap and propose a variety of diagnostic tools, such as leverage measures, global influence, normal curvatures of local influence under some perturbation schemes, and Pearson residuals. All diagnostic measures developed are applied in a real data set to analyze the fitted Bell--Touchard regression model in practice.