On choosing optimal response transformations for dimension reduction

It has previously been shown that response transformations can be very effective in improving dimension reduction outcomes for a continuous response. The choice of transformation used can make a big difference in the visualization of the response versus the dimension reduced regressors. In this article, we provide an automated approach for choosing parameters of transformation functions to seek optimal results. A criterion based on an influence measure between dimension reduction spaces is utilized for choosing the optimal parameter value of the transformation. Since influence measures can be time-consuming for large data sets, two efficient criteria are also provided. Given that a different transformation may be suitable for each direction required to form the subspace, we also employ an iterative approach to choosing optimal parameter values. Several simulation studies and a real data example highlight the effectiveness of the proposed methods.