Abstract : Sliced Inverse Regression (SIR) is an effective method for dimensionality reduction in high-dimensional regression
problems. However, the method has requirements on the distribution of the predictors that are hard to check since they depend on
unobserved variables. It has been shown that, if the distribution of the predictors is elliptical, then these requirements are satisfied.
In case of mixture models, the ellipticity is violated and in addition there is no assurance of a single underlying
regression model among the different components. Our approach clusterizes the predictors space to force the condition to hold on each
cluster and includes a merging technique to look for different underlying models in the data. A study on simulated data as well as two real
applications are provided. It appears that SIR, unsurprisingly, is not capable of dealing with a mixture of Gaussians involving different underlying models whereas our approach is able to correctly investigate the mixture.