🤖 AI Summary
This study addresses a critical yet previously unrecognized issue in observational causal inference: measurement-induced confounding, wherein latent variables—such as motivation or self-efficacy—are imperfectly measured, leading to biased estimates of adjusted causal effects. The authors formally identify and name this problem, moving beyond conventional two-stage adjustment approaches. They propose a novel Bayesian joint estimation framework that simultaneously models the latent variable’s measurement structure, the treatment assignment mechanism, and the potential outcomes model. This integrated approach effectively corrects bias in average treatment effect estimation and restores the nominal coverage of uncertainty intervals, thereby substantially enhancing the reliability of causal inferences drawn from observational data with error-prone proxies for unobserved confounders.
📝 Abstract
A critical assumption of observational studies is that all confounding variables must be known and sufficiently adjusted for to estimate causal effects. An implicit, and often overlooked, aspect of this assumption is that all confounding variables have been measured without error. In the social and medical sciences, latent traits such as motivation, self-efficacy, and ability measures are likely confounding variables. Because latent traits are not directly observable, conventional approaches to adjust for them in observational studies rely on collecting responses to individual items on a test or survey instrument and then adjust for sum scores, measurement model-derived ability estimates, or item responses directly. Through a process we describe as measurement induced confounding, we show that measurement error propagates through the estimation process and that current conventional approaches to adjusting for latent traits in observational studies produce biased estimates of the average treatment effect with incorrectly calibrated coverage properties. A critical implication of this finding is that current observational studies that attempt to adjust for latent confounding variables likely put forth biased causal estimates with incorrect uncertainty intervals. We show that measurement induced confounding can be resolved through a Bayesian Joint Estimation approach that simultaneously estimates the measurement model, the treatment assignment model, and the response model.