Model-Based Response Dimension Reduction

Functions for model-based response dimension reduction. Usual dimension reduction methods in multivariate regression focus on the reduction of predictors, not responses. The response dimension reduction is theoretically founded in Yoo and Cook (2008) . Later, three model-based response dimension reduction approaches are proposed in Yoo (2016) and Yoo (2019) . The method by Yoo and Cook (2008) is based on non-parametric ordinary least squares, but the model-based approaches are done through maximum likelihood estimation. For two model-based response dimension reduction methods called principal fitted response reduction and unstructured principal fitted response reduction, chi-squared tests are provided for determining the dimension of the response subspace.