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Problems with products? Control strategies for models with interaction and quadratic effects

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  • Beiser-McGrath, Janina
  • Beiser-McGrath, Liam F.

Abstract

Models testing interactive and quadratic hypotheses are common in Political Science but control strategies for these models have received little attention. Common practice is to simply include additive control variables, without relevant product terms, into models with interaction or quadratic terms. In this paper, we show in Monte Carlos that interaction terms can absorb the effects of other un-modeled interaction and non-linear effects and analogously, that included quadratic terms can reflect omitted interactions and non-linearities. This problem even occurs when included and omitted product terms do not share any constitutive terms. We show with Monte Carlo experiments that regularized estimators, the adaptive Lasso, Kernel Regularized Least Squares (KRLS), and Bayesian Additive Regression Trees (BART) can prevent the misattribution of interactive/quadratic effects, minimize the problems of efficiency loss and overfitting, and have low false-positive rates. We illustrate how inferences drawn can change when relevant product terms are used in the control strategy using a recent paper. Implementing the recommendations of this paper would increase the reliability of conditional and non-linear relationships estimated in many papers in the literature.

Suggested Citation

  • Beiser-McGrath, Janina & Beiser-McGrath, Liam F., 2020. "Problems with products? Control strategies for models with interaction and quadratic effects," LSE Research Online Documents on Economics 117235, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:117235
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    File URL: http://eprints.lse.ac.uk/117235/
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    References listed on IDEAS

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    3. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    4. Hainmueller, Jens & Hazlett, Chad, 2014. "Kernel Regularized Least Squares: Reducing Misspecification Bias with a Flexible and Interpretable Machine Learning Approach," Political Analysis, Cambridge University Press, vol. 22(2), pages 143-168, April.
    5. Brambor, Thomas & Clark, William Roberts & Golder, Matt, 2006. "Understanding Interaction Models: Improving Empirical Analyses," Political Analysis, Cambridge University Press, vol. 14(1), pages 63-82, January.
    6. Hainmueller, Jens & Mummolo, Jonathan & Xu, Yiqing, 2019. "How Much Should We Trust Estimates from Multiplicative Interaction Models? Simple Tools to Improve Empirical Practice," Political Analysis, Cambridge University Press, vol. 27(2), pages 163-192, April.
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    Cited by:

    1. Beiser-McGrath, Liam & Busemeyer, Marius R., 2023. "Carbon inequality and support for carbon taxation," LSE Research Online Documents on Economics 120925, London School of Economics and Political Science, LSE Library.

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    More about this item

    Keywords

    Interaction effects; machine learning; model misspecification; non-linear effects; replication;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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