Hi all, I know that R-squared values for mixed effects models are an area of active development / some controversy. I'm wondering if anyone could help me to understand how *conditional R-squared values*, as described by Nakagawa and Schielzeth (2013) and as implemented in the MuMIn (and piecewiseSEM) packages. In particular, my (very naive) thought was that the square root of the conditional r-squared value (my understanding: the r-squared value for both together the fixed and random effects) minus the marginal r-squared value (the r-squared value for only the fixed effects) would / could equal the ICC. Please excuse me if this is completely belying a very limited understanding. For example, for this example using the sleepstudy data, the conditional minus the marginal, or what I thought would represent something akin to the proportion of variance explained only by the random effects, or, in this example, .424. The intra-class correlation for the random intercept is .483. Can anyone help me clear about how these two values can (or could / whether they should) be related? library(lme4) library(MuMIn) library(sjstats) m1 <- lmer(Reaction ~ Days + (1 | Subject), sleepstudy) r_squared_vals <- MuMIn::r.squaredGLMM(m1) # Just the conditional r-squared value (conditional - marginal) r_squared_vals[2] - r_squared_vals[1] # .424 ICC_val <- sjstats::icc(fm1) # The intra-class correlation (ICC) for the ICC_val # 0.483 I ask in part because I'm interested in calculating the partial r-squared values using the r2glmm <https://www.google.com/search?q=r2glmm&oq=r2glmm&aqs=chrome.0.69i59j69i60l3.1051j0j7&sourceid=chrome&ie=UTF-8> package (and the r2beta() function) and am curious if there can be some similar proportion of variance explained interpretation for the random effects. Again, I'm sorry if this is not clear, obvious, or not a direction worth pursuing fo well-understood reasons. Thanks for considering! Josh
Joshua Rosenberg, Ph.D. Candidate Educational Psychology & Educational Technology Michigan State University http://jmichaelrosenberg.com [[alternative HTML version deleted]]