Correcting data for measurement error in generalized linear models

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Abstract
This paper discusses a general strategy for reducing measurement-error-induced bias in statistical models. It is assumed that the measurement error is unbiased with a known variance although no other distributional assumptions on the measurement-error are employed, Using a preliminary fit of the model to the observed data, a transformation of the variable measured with error is estimated. The transformation is constructed so that the estimates obtained by refitting the model to the ‘corrected’ data have smaller bias, Whereas the general strategy can be applied in a number of settings, this paper focuses on the problem of covariate measurement error in generalized linear models, Two estimators are derived and their effectiveness at reducing bias is demonstrated in a Monte Carlo study.

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