Understanding different types of repeatability and intra-class correlation for an analysis of biological variation

Shinichi Nakagawa , David F Westneat, Ayumi Mizuno , Yimen Gerardo Araya Ajoy, Ned A Dochtermann, Kate Laskowski, Joel L Pick, Denis Réale, Coralie Williams , Jonathan Wright, Holger Schielzeth

Repeatability (more generally known as intraclass correlation) represents an important quantity of interest in many scientific fields. It represents a metric for summarizing variance decomposition to identify sources of variation in an outcome of interest (e.g. organismal traits). The estimation of variance components is often achieved through linear mixed-effect models or their extension, generalized linear mixed-effect models. Here, we review variants of calculating repeatabilities from mixed-effects models for a variety of conditions and applications. We also recommend which variant might be appropriate under what conditions, focusing on behavioural biology/ecology examples. However, the decision is ultimately with the researcher, since it depends upon their research question, and there is no one-size-fits-all solution. We also highlight the importance of the scope of inference, which affects how repeatabilities are used and interpreted. We recommend transparent reporting of statistical results, including all variance components, which are the building blocks of repeatability. This review aims to assist empiricists in choosing an appropriate repeatability variant and interpretation concerning their questions and scope of inference.