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
#>
```