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Researchers often mention the utility and need for R-squared measures of explained variance for multilevel models (MLMs). Although this topic has been addressed by methodologists, the MLM R-squared literature suffers from several shortcomings: (a) analytic relationships among existing measures have not been established so measures equivalent in the population have been redeveloped 2 or 3 times; (b) a completely full partitioning of variance has not been used to create measures, leading to gaps in the availability of measures to address key substantive questions; (c) a unifying approach to interpreting and choosing among measures has not been provided, leading to researchers' difficulty with implementation; and (d) software has inconsistently and infrequently incorporated available measures. We address these issues with the following contributions. We develop an integrative framework of R-squared measures for MLMs with random intercepts and/or slopes based on a completely full decomposition of variance. We analytically relate 10 existing measures from different disciplines as special cases of 5 measures from our framework. We show how our framework fills gaps by supplying additional total and level-specific measures that answer new substantive research questions. To facilitate interpretation, we provide a novel and integrative graphical representation of all the measures in the framework; we use it to demonstrate limitations of current reporting practices for MLM R-squareds, as well as benefits of considering multiple measures from the framework in juxtaposition. We supply and empirically illustrate an R function, r2MLM, that computes all measures in our framework to help researchers in considering effect size and conveying practical significance. (PsycINFO Database Record (c) 2019 APA, all rights reserved).
Rights et al. (Thu,) studied this question.