Li, Jianzhu, and Richard L. Valliant. 2009. "Survey weighted hat matrix and leverages." Survey Methodology, 35(1): 15-24.
Regression diagnostics are geared toward identifying individual points or groups of points that have an important influence on a fitted model. When fitting a model with survey data, the sources of influence are the response variable Y, the predictor variables X, and the survey weights, W. This article discusses the use of the hat matrix and leverages to identify points that may be influential in fitting linear models due to large weights or values of predictors. We also contrast findings that an analyst will obtain if ordinary least squares is used rather than survey weighted least squares to determine which points are influential.