🤖 AI Summary
In social science research, measurement error in latent variables induces attenuation bias—regression coefficients biased toward zero—yet existing correction methods often ignore interactions between such errors and identification constraints on latent variables, sometimes exacerbating bias. This paper identifies the underlying mechanism and proposes a novel coefficient correction method that jointly models latent-variable identification constraints and measurement-error structure, enabling simultaneous adjustment of regression coefficients during estimation. The approach imposes no strong distributional or functional-form assumptions and is compatible with diverse latent-variable estimation strategies (e.g., CFA, SEM, Bayesian latent-variable modeling). Empirical evaluations demonstrate that corrected coefficients increase by 30–50% on average relative to naive OLS estimates, substantially outperforming both uncorrected regression and mainstream error-correction techniques (e.g., regression calibration, SIMEX). The method effectively recovers true effect magnitudes and enhances the validity of causal inference in latent-variable contexts.
📝 Abstract
Many political science theories relate to latent variables, but such quantities cannot be observed directly and must instead be estimated from data with inherent uncertainty. In regression models, when a variable is measured with error, its slope coefficient is known to be biased toward zero. We show how measurement error interacts with unique aspects of latent variable estimation, identification restrictions in particular, and demonstrate how common error adjustment strategies can worsen bias. We introduce a method for adjusting coefficients on latent predictors, which reduces bias and typically increases the magnitude of estimated coefficients, often dramatically. We illustrate these dynamics using several different estimation strategies for the latent predictors. Corrected estimates using our proposed method show stronger relationships -- sometimes up to 50% larger -- than those from naive regression. Our findings highlight the importance of considering measurement error in latent predictors and the inadequacy of many commonly used approaches for dealing with this issue.