Collinearity diagnostics in generalized linear models fitted with survey data
Articles and reports: 12-001-X202500200004Description: The class of generalized linear models (GLM) is a flexible generalization of ordinary least squares regression that allows the linear model to be related to the response variable via a link function and assumes the magnitude of the variance of each measurement to be a function of its predicted value. Multicollinearity in GLMs can inflate variances of the estimated coefficients and cause poor prediction in certain regions of the regression space. It may also cause a nonsignificant Wald statistic even when the predictors are highly predictive in a model of the family of GLMs. Little previous research has closely investigated the diagnostics of multicollinearity in GLMs, especially when complex survey data are used. In this paper, we develop variance inflation factors (VIFs) that measure the amount that the variance of a parameter estimator is increased due to multicollinearity in GLMs. We also extend VIFs and condition indexes to apply to complex survey data, accounting for design features, e.g. weights, clusters, and strata. Illustrations of these methods are given using data from a household survey of health and nutrition. Issue Number: 2025002Author(s): Liao, Dan; Valliant, RichardMain Product:Survey Methodology
