Generalised least squares with ignored errors in variables.

We present data, both real and simulated, that show generalized least squares (GLS) estimation, intended to account for correlated response error structure, can produce gross biasing in regression parameter estimates under misspecified models with ignored errors in explanatory-variable measurements. The bias, and its subsequent effect on mean squared error (MSE), can be much more severe than the apparently less appropriate ordinary least squares (OLS) estimator. This article provides a theoretical basis for these effects by deriving expressions for the bias and MSE for the general GLS estimator through Taylor-series expansions. The results are compared with simulations for two specific weight matrices and applied to a dataset relating atmospheric pollutant levels in Los Angeles with average recorded wind speed. We show that the bias (with subsequent implications for the MSE) is always worse for the exponential correlation model with equally spaced explanatory-variable observations and present a simple test to decide a preference for OLS or GLS in practice