Small and negative correlations among clustered observations: Limitations of the linear mixed effects model

Natalie M. Nielsen, Wouter A.C. Smink, Jean-Paul G.J.A. Fox*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
18 Downloads (Pure)

Abstract

The linear mixed effects model is an often used tool for the analysis of multilevel data. However, this model has an ill-understood shortcoming: it assumes that observations within clusters are always positively correlated. This assumption is not always true: individuals competing in a cluster for scarce resources are negatively correlated. Random effects in a mixed effects model can model a positive correlation among clustered observations but not a negative correlation. As negative clustering effects are largely unknown to the sheer majority of the research community, we conducted a simulation study to detail the bias that occurs when analysing negative clustering effects with the linear mixed effects model. We also demonstrate that ignoring a small negative correlation leads to deflated Type-I errors, invalid standard errors and confidence intervals in regression analysis. When negative clustering effects are ignored, mixed effects models incorrectly assume that observations are independently distributed. We highlight the importance of understanding these phenomena through analysis of the data from Lamers, Bohlmeijer, Korte, and Westerhof (2015). We conclude with a reflection on well-known multilevel modelling rules when dealing with negative dependencies in a cluster: negative clustering effects can, do and will occur and these effects cannot be ignored.
Original languageEnglish
Pages (from-to)51-77
Number of pages27
JournalBehaviormetrika
Volume48
Issue number1
Early online date24 Jan 2021
DOIs
Publication statusPublished - Jan 2021

Keywords

  • negative clustering effects
  • negative cluster correlation
  • negative ICC
  • covariance structure models
  • Linear Mixed Effects model

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