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Compute the marginal and conditional r-squared value for mixed effects models with complex random effects structures.


r2_nakagawa(model, by_group = FALSE, tolerance = 1e-05)



A mixed effects model.


Logical, if TRUE, returns the explained variance at different levels (if there are multiple levels). This is essentially similar to the variance reduction approach by Hox (2010), pp. 69-78.


Tolerance for singularity check of random effects, to decide whether to compute random effect variances for the conditional r-squared or not. Indicates up to which value the convergence result is accepted. When r2_nakagawa() returns a warning, stating that random effect variances can't be computed (and thus, the conditional r-squared is NA), decrease the tolerance-level. See also check_singularity().


A list with the conditional and marginal R2 values.


Marginal and conditional r-squared values for mixed models are calculated based on Nakagawa et al. 2017. For more details on the computation of the variances, see ?insight::get_variance.

The marginal r-squared considers only the variance of the fixed effects, while the conditional r-squared takes both the fixed and random effects into account. The random effect variances are actually the mean random effect variances, thus the r-squared value is also appropriate for mixed models with random slopes or nested random effects (see Johnson 2014).


  • Hox, J. J. (2010). Multilevel analysis: techniques and applications (2nd ed). New York: Routledge.

  • Johnson, P. C. D. (2014). Extension of Nakagawa & Schielzeth’s R2 GLMM to random slopes models. Methods in Ecology and Evolution, 5(9), 944–946. doi:10.1111/2041-210X.12225

  • Nakagawa, S., & Schielzeth, H. (2013). A general and simple method for obtaining R2 from generalized linear mixed-effects models. Methods in Ecology and Evolution, 4(2), 133–142. doi:10.1111/j.2041-210x.2012.00261.x

  • Nakagawa, S., Johnson, P. C. D., & Schielzeth, H. (2017). The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded. Journal of The Royal Society Interface, 14(134), 20170213. doi:10.1098/rsif.2017.0213


if (require("lme4")) {
  model <- lmer(Sepal.Length ~ Petal.Length + (1 | Species), data = iris)
  r2_nakagawa(model, by_group = TRUE)
#> # Explained Variance by Level
#> Level   |     R2
#> ----------------
#> Level 1 |  0.569
#> Species | -0.853