Generalized least squares with ignored errors in variables

We present data, both real and simulated, that show generalized least squar es (GLS) estimation, intended to account for correlated response error stru cture, can produce gross biasing in regression parameter estimates under mi sspecified models with ignored errors in explanatory-variable measurements. The bias, and its subsequent effect on mean squared error (MSE), can be mu ch more severe than the apparently less appropriate ordinary least squares (OLS) estimator. This article provides a theoretical basis for these effect s by deriving expressions for the bias and MSE for the general GLS estimato r through Taylor-series expansions. The results are compared with simulatio ns for two specific weight matrices and applied to a dataset relating atmos pheric pollutant levels in Los Angeles with average recorded wind speed. We show that the bias (with subsequent implications for the MSE) is always wo rse for the exponential correlation model with equally spaced explanatory-v ariable observations and present a simple test to decide a preference for O LS or GLS in practice.