Attenuation Bias with Latent Predictors

Abstract

Many core concepts in political science are latent and therefore can only be measured with error. Measurement error in a predictor attenuates slope coefficient estimates in regression, biasing them toward zero. We show that widely used strategies for correcting attenuation bias -- including instrumental variables and the method of composition -- are themselves biased when applied to latent regressors, sometimes even more than simple regression ignoring the measurement error altogether. We derive a correlation-based correction using split-sample measurement strategies. Rather than assuming a particular estimation strategy for the latent trait, our approach is modular and can be easily deployed with a wide variety of latent trait measurement strategies, including additive score, factor, or machine learning models, requiring no joint estimation while yielding consistent slopes under standard assumptions. Simulations and applications show stronger relationships after our correction, sometimes by as much as 50%. Open-source software implements the procedure. Results underscore that latent predictors demand tailored error correction; otherwise, conventional practice can exacerbate bias.