Effect Size Measures for Multilevel Models in Clinical Child and Adolescent Research: New R-Squared Methods and Recommendations

Abstract

Clinical psychologists studying child and adolescent populations commonly analyze hierarchically structured data via multilevel modeling (MLM). In clinical child and adolescent psychology, and in psychology more broadly, increasing emphasis is being placed on the reporting of effect size, such as R-squared (R2) measures of explained variance. In MLM, however, the literature on R2 had, until recently, suffered from several shortcomings: (a) the relations among existing measures were unknown, (b) methods for quantifying some types of explained variance were unavailable, (c) which (if any) measures should be used for model comparison was unclear, (d) most measures did not generalize to models with more than two levels, and (e) software to compute measures was unavailable. The purpose of this article is to summarize recent methodological developments that resolved these issues and encourage the use of MLM R2 in practice. We provide a nontechnical discussion of how the issues have been resolved and demonstrate how the new measures and methods can be implemented, highlighting their utility with an empirical example. We first consider a two-level MLM for a single hypothesized model in which we examine emotional response to social situations as a predictor of maladaptive self-cognitions, demonstrating the various ways we can quantify explained variance. We then discuss and demonstrate the use of R2 for model comparison, and discuss the extension to models with more than two levels. Last, we discuss new free software that researchers can use to compute measures and produce associated graphics.