Repeated Probit Regression When Covariates Are Measured With Error

• Published in: Biometrics Vol. 55; no. 2; pp. 403 - 409
• Main Authors: Follmann, Dean A., Hunsberger, Sally A., Albert, Paul S.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.06.1999; International Biometric Society
• Subjects: Bias; Biometrics; Biometry; Child; children; Covariance matrices; diet; Diet, Fat-Restricted - adverse effects; equations; Error rates; Errors-in-variables; Fat intake; Humans; Hypercholesterolemia - diet therapy; Likelihood Functions; Linear Models; Linear regression; Maximum likelihood estimation; Measurement error; Models, Statistical; Nutritional Requirements; Probit regression; Random effects models; Randomized Controlled Trials as Topic - statistics & numerical data; Regression Analysis; Safety; School age children; statistical models; Statistical variance; Zinc
• ISSN: 0006-341X; 1541-0420
• DOI: 10.1111/j.0006-341X.1999.00403.x

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 the correlated binary responses conditional on the linear mixed model estimates is fit to the repeated binary data using generalized estimating equations. The approach is demonstrated using nutrient safety data from the Diet Intervention of School Age Children (DISC) study.