Fixed and random effects models: making an informed choice

Andrew Bell*, Malcolm Fairbrother, Kelvyn Jones

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

237 Citations (Scopus)
230 Downloads (Pure)


This paper assesses the options available to researchers analysing multilevel (including longitudinal) data, with the aim of supporting good methodological decision-making. Given the confusion in the literature about the key properties of fixed and random effects (FE and RE) models, we present these models’ capabilities and limitations. We also discuss the within-between RE model, sometimes misleadingly labelled a ‘hybrid’ model, showing that it is the most general of the three, with all the strengths of the other two. As such, and because it allows for important extensions—notably random slopes—we argue it should be used (as a starting point at least) in all multilevel analyses. We develop the argument through simulations, evaluating how these models cope with some likely mis-specifications. These simulations reveal that (1) failing to include random slopes can generate anti-conservative standard errors, and (2) assuming random intercepts are Normally distributed, when they are not, introduces only modest biases. These results strengthen the case for the use of, and need for, these models.

Original languageEnglish
Pages (from-to)1051-1074
Number of pages24
JournalQuality and Quantity
Issue number2
Early online date7 Aug 2018
Publication statusPublished - 15 Mar 2019


  • Fixed effects
  • Hybrid models
  • Multilevel models
  • Mundlak
  • Random effects
  • Within and between effects


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