Bias Reduction in Standard Errors for Linear and Generalized Linear Models with Multi-Stage Samples

Linearization and the jackknife are widely used to estimate standard errors for the coefficients of linear regression models fit to multi-stage samples. For some designs, linearization estimators can have large negative bias, while the jackknife has a correspondingly large positive bias. 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 iid, the BRL estimator is unbiased. The BRL method applies to samples with nonconstant 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. Simulation study results show that BRL standard errors combined with the Satterthwaite approximation to determine the reference distribution yield tests with Type I error rates near nominal values.