Sufficient dimension reduction in multivariate regressions with categorical predictors

In this paper, we present a novel sufficient dimension reduction method for multivariate regressions with categorical predictors. We adopt ideas from a previous work byChiaromonte et al. (2002) who proposed sufficient dimension reduction in regressions with categorical predictors and the work by Li et al. (2008) who proposed the projective-resampling idea to multivariate response problems. In addition, we incorporate a variable selection procedure. Simulation studies show the efficacy of our method. We present a real data analysis through our proposed method to discover new association between personal characteristics and dietary factors which influence plasma beta-carotene and retinol levels in human serum.