Variance inflation factors in the analysis of complex survey data

Survey data are often used to fit linear regression models. The values of covariates used in modeling are not controlled as they might be in an experiment. Thus, collinearity among the covariates is an inevitable problem in the analysis of survey data. Although many books and articles have described the collinearity problem and proposed strategies to understand, assess and handle its presence, the survey literature has not provided appropriate diagnostic tools to evaluate its impact on regression estimation when the survey complexities are considered. We have developed variance inflation factors (VIFs) that measure the amount that variances of parameter estimators are increased due to having non-orthogonal predictors. The VIFs are appropriate for survey-weighted regression estimators and account for complex design features, e.g., weights, clusters, and strata. Illustrations of these methods are given using a probability sample from a household survey of health and nutrition.