FINDING RANK LEVERAGE SUBSETS IN REGRESSION

Rank leverage occurs when some linear combination of the parameters in a regression model is almost entirely estimated by a small subset of observations, a phenomenon that is closely related to the usual notation of leverage. Rank leverage subsets may be found from the eigenvalue decomposition of the matrix L = HS-1 H, where H denotes the hat matrix for the model, and S contains the diagonal elements of H. Each eigenvector for L, corresponding to a positive eigenvalue, defines a subset of observations, and a small subset indicates a problem of rank leverage. The results are comparable to those obtained by deletion techniques, but require less computation. The method may be derived via the eigenvalue decomposition of the matrix of correlations between observed and fitted values of the regression. The method works for both linear and generalized linear regression models.