In the well-known multilevel modelling framework (McCulloch et al. Only when accounting for the correlation between clustered observations, correct statistical inferences can be made. Dependencies among observations in clusters can be expressed as a correlation, where positively correlated observations share similar information (Kenny and Judd 1986), and are not as informative as independent observations (Galbraith et al. In clustered data (e.g., hierarchical data, multilevel data) observations are associated, and not independently observed (Dorman 2008). The popularity of the linear mixed effects models (e.g., random effect models, multilevel models) is intuitively explained by the variety of different names under which the family of statistical models for clustered data are known. 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. We highlight the importance of understanding these phenomena through analysis of the data from Lamers, Bohlmeijer, Korte, and Westerhof (2015). When negative clustering effects are ignored, mixed effects models incorrectly assume that observations are independently distributed. We also demonstrate that ignoring a small negative correlation leads to deflated Type-I errors, invalid standard errors and confidence intervals in regression analysis. 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. Random effects in a mixed effects model can model a positive correlation among clustered observations but not a negative correlation. This assumption is not always true: individuals competing in a cluster for scarce resources are negatively correlated. However, this model has an ill-understood shortcoming: it assumes that observations within clusters are always positively correlated. The linear mixed effects model is an often used tool for the analysis of multilevel data.

Vif negative correlation examples