Rage Against the Mean – A Review of Distributional Regression Approaches

Abstract Distributional regression models that overcome the traditional focus on relating the conditional mean of the response to explanatory variables and instead target either the complete conditional response distribution or more general features thereof have seen increasing interest in the past decade. The current state of distributional regression will be discussed, with a particular focus on the four most prominent model classes: (i) generalized additive models for location, scale and shape, (ii) conditional transformation models and distribution regression, (iii) density regression, and (iv) quantile and expectile regression. Characteristics of the different distributional regression approaches will be provided to establish a structured overview on the similarities and differences with respect to the required assumptions on the conditional response distribution, theoretical properties, and the availability of software implementations. In addition, challenges arising in the interpretability of distributional regression models will be discussed and all four approaches will be illustrated with an application analyzing determinants of income distributions from the German Socio-Economic Panel (GSOEP).