Effect size measures for multilevel models: definition, interpretation, and TIMSS example

Abstract

Effect size reporting is crucial for interpretation of applied research results and for conducting meta-analysis. However, clear guidelines for reporting effect size in multilevel models have not been provided. This report suggests and demonstrates appropriate effect size measures including the ICC for random effects and standardized regression coefficients or $f^2$ for fixed effects. Following this, complexities associated with reporting $R^2$ as an effect size measure are explored, as well as appropriate effect size measures for more complex models including the three-level model and the random slopes model. An example using TIMSS data is provided.