Condition indexes and variance decompositions for diagnosing collinearity in linear model analysis of survey data

Abstract

Collinearities among explanatory variables in linear regression models affect estimates from survey data just as they do in non-survey data. Undesirable effects are unnecessarily inflated standard errors, spuriously low or high t-statistics, and parameter estimates with illogical signs. The available collinearity diagnostics are not generally appropriate for survey data because the variance estimators they incorporate do not properly account for stratification, clustering, and survey weights. In this article, we derive condition indexes and variance decompositions to diagnose collinearity problems in complex survey data. The adapted diagnostics are illustrated with data based on a survey of health characteristics.