Biometrics

this article we introduce a method that, like regression calibration, involves substitution of an estimated value for X in the regression model, but in which the first and second moments of the substituted value are consistent estimates of the first and second moments of X. Because of this central property, we call the method "moment reconstruction." One important advantage of the moment reconstruction approach is that it retains the simplicity of regression calibration, allowing use of standard software, while providing consistent estimation in nonlinear models, when covariates are normally distributed (see below). Other methods, such as corrected score methods (e.g., Huang andW ang, 2001) and full likelihood methods (e.g., Schafer, 1993), provide consistent estimation in more general situations, but require specialized software for implementation. A second advantage of the method is that it enables direct estimation of other regression model parameters such as the residual variance or classification error rates (see our example). A third advantage of the method is that it remains valid under certain types of differential measurement error, unlike other methods currently proposed for use in nonlinear model