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

## 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()`

.

## 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