Repeated probit regression when covariates are measured with error

This paper develops a model for repeated binary regression when a covariate is measured with error. The model allows for estimating the effect of the true value of the covariate on a repeated binary response. The choice of a probit link for the effect of the error-free covariate, coupled with normal measurement error for the error-free covariate, results in a probit model after integrating over the measurement error distribution. We propose a two -stage estimation procedure where, in the first stage, a linear mixed model is used to fit the repeated covariate. In the second stage, a model for th e correlated binary responses conditional on the linear mixed model estimat es is fit to the repeated binary data using generalized estimating equation s. The approach is demonstrated using nutrient safety data from the Diet In tervention of School Age Children (DISC) study.