Model-based effect sizes for multilevel linear regression coefficients [Author Accepted Manuscript]

Effect size reporting assists broader audiences in understanding the practical implications of a study’s results beyond statistical significance. However, effect sizes for multilevel model (MLM) coefficients are less often reported, potentially because there are currently no frameworks that can be used the same way for all fixed effects coefficients in a model. In this paper we introduce two model-based effect sizes (ESs) for 2-level hierarchical linear regression model coefficients: standardized mean difference (d) and unique variance-explained (sr2). We demonstrate their efficacy via simulation across a wide range of conditions and provide two real-data examples (one cross-sectional and one longitudinal) along with a new R package ‘MLMES’ that implements code easily for users. Thereafter we discuss practical recommendations, limitations, and future extensions for using MLM coefficient ESs.