Local Influence of Predictors in Multiple Linear Regression

Local influence diagnostics can be used to assess the influence of predictor values in multiple linear regression. For n observations and k regressors, an eigenanalysis of an nk x nk matrix is required to assess the influence on the estimated coefficients. We provide the analytic expressions for the eigenvectors and show that they are easily computed, describe influence on the parameter estimates of a principal components regression, and are related to leverage, outliers, and added-variables plots. The results indicate that multicollinearity and overfitting contribute to a fitted model's sensitivity, leading to strategies for model assessment and selection.