Fixed Effects, Random Effects, and Hybrid Models for Causal Analysis

  • Glenn FirebaughEmail author
  • Cody Warner
  • Michael Massoglia
Part of the Handbooks of Sociology and Social Research book series (HSSR)


Longitudinal data are becoming increasingly common in social science research. In this chapter, we discuss methods for exploiting the features of longitudinal data to study causal effects. The methods we discuss are broadly termed fixed effects and random effects models. We begin by discussing some of the advantages of fixed effects models over traditional regression approaches and then present a basic notation for the fixed effects model. This notation serves also as a baseline for introducing the random effects model, a common alternative to the fixed effects approach. After comparing fixed effects and random effects models – paying particular attention to their underlying assumptions – we describe hybrid models that combine attractive features of each. To provide a deeper understanding of these models, and to help researchers determine the most appropriate approach to use when analyzing longitudinal data, we provide three empirical examples. We also briefly discuss several extensions of fixed/random effects models. We conclude by suggesting additional literature that readers may find helpful.


Fixed Effect Random Effect Model Hybrid Model Fixed Effect Model Fixed Effect Estimate 
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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Glenn Firebaugh
    • 1
    Email author
  • Cody Warner
    • 2
  • Michael Massoglia
    • 3
  1. 1.Sociology and DemographyPennsylvania State UniversityUniversity ParkUSA
  2. 2.Sociology and Crime, Law and JusticePennsylvania State UniversityUniversity ParkUSA
  3. 3.Department of SociologyUniversity of Wisconsin-MadisonMadisonUSA

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