Measurement Error and Nonlinear Confounding: Structural Equation Modeling Versus Double Machine Learning

Abstract

A latent confounder measured by fallible indicators can be adjusted for with structural equation modeling (SEM), which corrects measurement error but requires a specified functional form, or with double machine learning (DML), which learns the form but ignores measurement error. We derive both population biases and the crossover reliability, the composite reliability above which DML with the indicators or their mean as inputs is less biased than linear SEM; it depends on the nonlinear share of confounding and falls when covariates predict the confounder. A 46-condition Monte Carlo study confirmed both biases and the predicted ordering. With gradient boosting, learning the conditional means raised the DML bias by up to 0.05 and moved the finite-sample crossover upward. A quadratic SEM was unbiased when its form was correct and removed two thirds of the linear-SEM bias under a saturating nonlinearity but little of it under a cubic one.