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The Impact of Correlated and/or Interacting Predictor Omission on Estimated Regression Coefficients in Linear Regression

  • Emily NystromEmail author
  • Julia L. Sharp
  • William C. BridgesJr.
Original Article
  • 17 Downloads

Abstract

We examine cases of predictor omission defined by the relationship between the set of omitted predictor(s) and a set of remaining predictor(s), both of which are included in the full model. We consider a wider range of omitted predictors than previously studied by systematically accounting for both interaction and correlation between the included and the omitted predictors. Our study highlights the impact of predictor omission on the resulting estimated regression coefficients and their squared standard errors. Theoretical and simulated results are presented to illustrate the impact of predictor omission among cases of interaction and correlation. In our simulated results, bias diverged as correlation increased from zero to one. On its own, interaction amplified bias, but the impact of interaction was worse when combined with correlation. Overall, our discussions surround the known problem of predictor omission with a rigorous framework to quantify bias in the included predictor’s estimated regression coefficient and squared standard error.

Keywords

Correlation Interaction Model misspecification Linear regression Predictor omission 

Mathematics Subject Classification

62J05 

Notes

Compliance with Ethical Standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Copyright information

© Grace Scientific Publishing 2019

Authors and Affiliations

  1. 1.School of Mathematical and Statistical SciencesClemson UniversityClemsonUSA
  2. 2.Department of StatisticsColorado State UniversityFort CollinsUSA

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