Bias reduction in standard errors for linear and generalized linear models with multi-stage samples - ARCHIVED

Linearization and the jack-knife method are widely used to estimate standard errors for the coefficients of linear regression models fit to multi-stage samples. With few primary sampling units (PSUs) or when a few PSUs have high leverage, linearization estimators can have large negative bias, while the jack-knife method has a correspondingly large positive bias. We characterize the design factors that produce large biases in these standard error estimators. In this technical paper, we propose an alternative estimator, bias reduced linearization (BRL), based on residuals adjusted to better approximate the covariance of the true errors.

When errors are independently and identically distributed (iid), the BRL estimator is unbiased. The BRL method applies to stratified samples with non-constant selection weights and to generalized linear models such as logistic regression. We also discuss BRL standard error estimators for generalized estimating equation models that explicitly model the dependence among observations from the same PSU in data from complex sample designs. Simulation study results show that BRL standard errors are combined with the Satterthwaite approximation to determine the reference distribution yield tests with Type I error rates near nominal values. We contrast our method with alternatives proposed by Kott (1994 and 1996) and Mancl and DeRouen (2001).