Beyond mean regression

Abstract

Usual exponential family regression models focus on only one designated quantity of the response distribution, namely the mean. While this entails easy interpretation of the estimated regression effects, it may often lead to incomplete analyses when more complex relationships are indeed present and also bears the risk of false conclusions about the significance/importance of covariates. We will therefore give an overview on extended types of regression models that allows us to go beyond mean regression. More specifically, we will consider generalized additive models for location, scale and shape as well as semiparametric quantile and expectile regression. We will review the basic properties of all three approaches and compare them with respect to the flexibility in terms of the supported types of predictor specification, the availability of software and the support for different types of inferential procedures. The considered model classes are illustrated using a data set on rents for flats in the City of Munich.