Covariate Measurement Error in Generalized Linear Models

Abstract

The EM algorithm is used to obtain estimators of regression coefficients for generalized linear models with canonical link when normally distributed covariates are masked by normally distributed measurement errors. By casting the true covariates as 'missing data', the EM procedure suggests an iterative scheme in which each cycle consists of an E-step, requiring the computation of approximate first and second conditional moments of the true covariates given the observed data, followed by an M-step in which regression parameters are updated by iteratively reweighted least squares based on these approxima tions. The proposed procedure is compared numerically with the exact maximum likeli hood solution, obtained by using Gaussian quadrature instead of the approximations in the E-step of the EM algorithm, and with alternative estimators for simple logistic regression with measurement error. The results for the proposed procedure are encouraging.