Solved – Proportion of variance in dependent variable accounted for by predictors in a mixed effects model

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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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