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

## Usage

r2_nakagawa(
model,
by_group = FALSE,
tolerance = 1e-05,
ci = NULL,
iterations = 100,
...
)

## 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().

ci

Confidence resp. credible interval level. For icc() and r2(), confidence intervals are based on bootstrapped samples from the ICC resp. R2 value. See iterations.

iterations

Number of bootstrap-replicates when computing confidence intervals for the ICC or R2.

...

Arguments passed down to brms::posterior_predict().

## 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 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).

• Conditional R2: takes both the fixed and random effects into account.

• Marginal R2: considers only the variance of the fixed effects.

The contribution of random effects can be deduced by subtracting the marginal R2 from the conditional R2 or by computing the icc().

## References

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

• Johnson, P. C. D. (2014). Extension of Nakagawa and 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., and 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., and 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
#>