Sufficient dimensions reduction in regressions with categorical predictors

In this article, we describe how the theory of sufficient dimension reduction, and a well-known inference method for it (sliced inverse regression), can be extended to regression analyses involving both quantitative and categorical predictor variables. As statistics faces an increasing need for effective analysis strategies for high-dimensional data, the results we present significantly widen the applicative scope of sufficient dimension reduction and open the way for a new class of theoretical and methodological developments.