Quality & Quantity

, Volume 51, Issue 3, pp 1359–1379 | Cite as

Spurious relationships arising from aggregate variables in linear regression

  • David J. ArmorEmail author
  • Chenna Reddy Cotla
  • Thomas Stratmann


Linear regressions that use aggregated values from a group variable such as a school or a neighborhood are commonplace in the social sciences. This paper uses Monte Carlo methods to demonstrate that aggregated variables produce spurious relationships with other dependent and independent variables in a model even when there are no underlying relationships among those variables. The size of the spurious relationships (or postulated effects) increases as the number of observations per group decreases. Although this problem is remedied by including the individual-level variable in the regression, the problem has not been discussed in the methodological literature. Accordingly, studies using aggregate variables must be interpreted with caution if the individual-level measurements are not available.


Aggregated variables Contextual effects Monte Carlo Linear regression Spurious correlation 


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • David J. Armor
    • 1
    Email author
  • Chenna Reddy Cotla
    • 2
  • Thomas Stratmann
    • 3
  1. 1.School of Policy, Government, and International AffairsGeorge Mason UniversityArlingtonUSA
  2. 2.Interdisciplinary Center for Economic Science (ICES)George Mason UniversityFairfaxUSA
  3. 3.Department of EconomicsGeorge Mason UniversityFairfaxUSA

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