Error-free milestones in error prone measurements
Abstract
A predictor variable or dose that is measured with substantial error may possess an error-free milestone, such that it is known with negligible error whether the value of the variable is to the left or right of the milestone. Such a milestone provides a basis for estimating a linear relationship between the true but unknown value of the error-free predictor and an outcome, because the milestone creates a strong and valid instrumental variable. The inferences are nonparametric and robust, and in the simplest cases, they are exact and distribution free. We also consider multiple milestones for a single predictor and milestones for several predictors whose partial slopes are estimated simultaneously. Examples are drawn from the Wisconsin Longitudinal Study, in which a BA degree acts as a milestone for sixteen years of education, and the binary indicator of military service acts as a milestone for years of service.
Keywords
Cite
@article{arxiv.0910.1233,
title = {Error-free milestones in error prone measurements},
author = {Dylan S. Small and Paul R. Rosenbaum},
journal= {arXiv preprint arXiv:0910.1233},
year = {2009}
}
Comments
Published in at http://dx.doi.org/10.1214/08-AOAS233 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)