I have the following output from a mixed effects model. I want to talk about how much variation is explained by the model. Is the variance under random effects corresponding to residuals (note: here trial is the random effect) the variation explained? i.e. 58.6 % or is there another way to infer this
REML criterion at convergence: 71.9
Scaled residuals:
Min 1Q Median 3Q Max
-1.82579 -0.59620 0.04897 0.62629 1.54639
Random effects:
Groups Name Variance Std.Dev.
trial (Intercept) 0.06008 0.2451
Residual 0.58633 0.7974
Number of obs: 60, groups: trial, 30
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 1.5522 0.2684 12.6610 13.233 0.09888
drugantho 0.8871 0.1753 14.0000 1.043 0.31601
interventionadded 0.2513 0.2553 14.0000 -1.276 0.32436 **
sexmale 3.0026 0.6466 15.0000 4.066 0.00021
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
No, the Residual variance is the exactly the variance of the residual random errors, i.e. the unexplained variance.
As far as I know, there isn't a single, unanimously accepted way of computing a coefficient of determination for mixed-effects model analogous to (and with all the properties of) the R^2 of the simpler linear model case. The reasons are discussed here, where it is also provided a simple/crude recipe for estimating the fraction of variance explained by the model
r2.corr.mer <- function(m) {
lmfit <- lm(model.response(model.frame(m)) ~ fitted(m))
summary(lmfit)$r.squared
}