Regression diagnostics for survey data

Diagnostics for linear regression models are included as options in Stata and many other statistical packages and are now readily available to analysts. However, these tools are generally aimed at ordinary or weighted least-squares regression and do not account for stratification, clustering, and survey weights that are features of datasets collected in complex sample surveys. The ordinary least-squares diagnostics can mislead users because the variances of model parameter estimates will usually be estimated incorrectly by the standard procedures. The variance or standard-error estimates are an intimate part of many diagnostics. In this presentation, I summarize research that has been done to extend some of the existing diagnostics to complex survey data. Among the linear regression techniques I cover are leverages, DFBETAS, DFFITS, the forward search method for identifying influential points, and collinearity diagnostics, like variance inflation factors and variance decompositions.