Error-free milestones in error prone measurements

TL;DR

This paper introduces a method leveraging error-free milestones in error-prone measurements to estimate linear relationships nonparametrically, using instrumental variables created by these milestones, with applications in longitudinal studies.

Contribution

It develops a robust, nonparametric approach utilizing error-free milestones as instrumental variables for error-prone predictors, including multiple and multivariate cases.

Findings

Method provides exact, distribution-free inferences in simple cases.

Applications include estimating effects of education and military service.

Approach is robust to measurement errors and applicable to real longitudinal data.

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.