Shake, Rattle and Roll: Some Pertubation Diagnostics for Linear Regression

Keywords: regression diagnostics, SVD

Abstract: Many tools exist for diagnosing potential or actual difficulties that may arise in multiple linear regression computations. We propose an approach that involves the addition of perturbations in the observation or variable space. These additions are developed from the singular value decomposition of the actual data, and the diagnostics were devised in the hope of aiding users with particular data sets. All three perturbations that we propose involve the addition of information to the data. This contrasts with jackknife and bootstrap methods that can be viewed, along with many other diagnostics, as deletion perturbations.

Many tools exist for diagnosing potential or actual difficulties that may arise in multiple linear regression computations. We propose an approach that involves the addition of perturbations in the observation or variable space. These additions are developed from the singular value decomposition of the actual data, and the diagnostics were devised in the hope of aiding users with particular data sets. All three perturbations that we propose involve the addition of information to the data. This contrasts with jackknife and bootstrap methods that can be viewed, along with many other diagnostics, as deletion perturbations.