Identifying regression outliers and mixtures graphically

Regressions in practice can include outliers and other unknown subpopulation structures. For example, mixtures of regressions occur if there is an omitted categorical predictor, like gender or location, and different regressions occur within each category. The theory of regression graphics based on central subspaces can be used to construct graphical solutions to long-standing problems of this type. It is argued that in practice the central subspace automatically expands to incorporate outliers and regression mixtures. Thus methods of estimating the central subspace can be used to identify these phenomena, without specifying a model. Examples illustrating the power of the theory are presented.