Let say I've ran this linear regression:

`lm_mtcars <- lm(mpg ~ wt + vs, mtcars) `

I can use `anova()`

to see the amount of variance in the dependent variable accounted for by the two predictors:

`anova(lm_mtcars) Analysis of Variance Table Response: mpg Df Sum Sq Mean Sq F value Pr(>F) wt 1 847.73 847.73 109.7042 2.284e-11 *** vs 1 54.23 54.23 7.0177 0.01293 * Residuals 29 224.09 7.73 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 `

Lets say I now add a random intercept for `cyl`

:

`library(lme4) lmer_mtcars <- lmer(mpg ~ wt + vs + (1 | cyl), mtcars) summary(lmer_mtcars) Linear mixed model fit by REML ['lmerMod'] Formula: mpg ~ wt + vs + (1 | cyl) Data: mtcars REML criterion at convergence: 148.8 Scaled residuals: Min 1Q Median 3Q Max -1.67088 -0.68589 -0.08363 0.48294 2.16959 Random effects: Groups Name Variance Std.Dev. cyl (Intercept) 3.624 1.904 Residual 6.784 2.605 Number of obs: 32, groups: cyl, 3 Fixed effects: Estimate Std. Error t value (Intercept) 31.4788 2.6007 12.104 wt -3.8054 0.6989 -5.445 vs 1.9500 1.4315 1.362 Correlation of Fixed Effects: (Intr) wt wt -0.846 vs -0.272 0.006 `

The variance accounted for by each fixed effect now drops because the random intercept for `cyl`

is now accounting for some of the variance in `mpg`

:

`anova(lmer_mtcars) Analysis of Variance Table Df Sum Sq Mean Sq F value wt 1 201.707 201.707 29.7345 vs 1 12.587 12.587 1.8555 `

But in `lmer_mtcars`

, how can I tell what proportion of the variance is being accounted for by `wt`

, `vs`

and the random intecept for `cyl`

?

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#### Best Answer

You can use `MuMIn`

package and its `r.squaredGLMM()`

function which will give you 2 approximated r-squared values based on Nakagawa & Schielzeth (2012) and Johnson (2014):

Marginal R^2 is the proportion of variance explained by the fixed effects alone.

Conditional R^2 is the proportion of variance explained by the fixed and random effects jointly.

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