Influence diagnostics in generalized symmetric linear models

Abstract

The aim of this paper is to introduce generalized symmetric linear models (GSLMs) in the same sense of generalized linear models (GLMs), in which a link function is defined to establish a relationship between the mean values of symmetric distributions and linear predictors. The class of symmetric distributions contains various distributions with lighter and heavier tails than normal and hence offers a more flexible basis for analyzing symmetric data. An iteratively reweighed least squares (IRLS) algorithm is derived to obtain maximum likelihood estimates. The local influence methodology is applied to study the sensitivity of the maximum likelihood estimates under some usual perturbation schemes, such as case-weight, response variable, continuous explanatory variable and scale parameter perturbations. We also discuss generalized leverage and residual analysis. Finally, an illustration is given in which the methodology developed in this paper is applied to a real data set.