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Machine Learning Predictions as Regression Covariates

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  • Fong, Christian
  • Tyler, Matthew

Abstract

In text, images, merged surveys, voter files, and elsewhere, data sets are often missing important covariates, either because they are latent features of observations (such as sentiment in text) or because they are not collected (such as race in voter files). One promising approach for coping with this missing data is to find the true values of the missing covariates for a subset of the observations and then train a machine learning algorithm to predict the values of those covariates for the rest. However, plugging in these predictions without regard for prediction error renders regression analyses biased, inconsistent, and overconfident. We characterize the severity of the problem posed by prediction error, describe a procedure to avoid these inconsistencies under comparatively general assumptions, and demonstrate the performance of our estimators through simulations and a study of hostile political dialogue on the Internet. We provide software implementing our approach.

Suggested Citation

  • Fong, Christian & Tyler, Matthew, 2021. "Machine Learning Predictions as Regression Covariates," Political Analysis, Cambridge University Press, vol. 29(4), pages 467-484, October.
  • Handle: RePEc:cup:polals:v:29:y:2021:i:4:p:467-484_3
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    Cited by:

    1. Gordon Burtch & Edward McFowland III & Mochen Yang & Gediminas Adomavicius, 2023. "EnsembleIV: Creating Instrumental Variables from Ensemble Learners for Robust Statistical Inference," Papers 2303.02820, arXiv.org.
    2. Benjamin Lu & Jia Wan & Derek Ouyang & Jacob Goldin & Daniel E. Ho, 2024. "Quantifying the Uncertainty of Imputed Demographic Disparity Estimates: The Dual Bootstrap," NBER Chapters, in: Race, Ethnicity, and Economic Statistics for the 21st Century, National Bureau of Economic Research, Inc.
    3. Mochen Yang & Edward McFowland & Gordon Burtch & Gediminas Adomavicius, 2022. "Achieving Reliable Causal Inference with Data-Mined Variables: A Random Forest Approach to the Measurement Error Problem," INFORMS Joural on Data Science, INFORMS, vol. 1(2), pages 138-155, October.
    4. Laura Battaglia & Timothy Christensen & Stephen Hansen & Szymon Sacher, 2024. "Inference for Regression with Variables Generated from Unstructured Data," Papers 2402.15585, arXiv.org, revised May 2024.

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