A modified estimating equation approach to correcting for measurement error in regression

Abstract

SUMMARY A modified estimating equation approach is proposed to correct for measurement error in regression problems. We allow changing measurement error variances and covariances across units, allow the regressors to be fixed, allow estimation of the measurement error variances/covariances and account for uncertainty arising from this estimation, and explicitly model measurement error in the response. Multiple linear, quadratic, Poisson, and logistic regression are considered in detail and it is seen that some previously developed estimators arise as special cases from the proposed approach. A small simulation study is presented for logistic regression.