📝 SummarXiv

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, sometimes even more than simple regression ignoring the measurement error altogether. We derive appropriate bias correction methods using split-sample measurement strategies. Our approach is modular and can be easily deployed with additive score, factor, or machine learning models, requiring no joint estimation while yielding consistent slopes under standard assumptions. Simulations and applications -- political knowledge, democracy indices, and text-based sentiment -- show stronger relationships after correction, sometimes by 50 percent. Open-source software implements the procedure. Results underscore that latent predictors demand tailored error correction; otherwise, conventional practice can exacerbate bias.