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)

Arguments

model

A mixed effects model.

by_group

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

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().

Value

A list with the conditional and marginal R2 values.

Details

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).

References

  • 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

Examples

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