Using Dimension-Reduction Subspaces to Identify Important Inputs in Models of Physical Systems

Graphical methods based on dimension-reduction subspaces for regression problems (Cook 1994) may be useful for studying the relative importance of inputs in computer models of physical systems. Sliced inverse regression (Li 1991), principal Hessian directions (Li 1992), ceres plots (Cook 1993), and inverse response plots (Cook and Weisberg 1994) are recent methods that can identify characteristics of dimension-reduction subspaces and facilitate graphical analyses of the important variables. These methods work well in the problem under consideration and may serve as important graphical methodology more generally, particularly when combined into a single paradigm for graphical regression analysis.