Nakagawa's R2 for mixed modelsSource:
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, ci = NULL, iterations = 100, ci_method = NULL, verbose = TRUE, ... )
A mixed effects model.
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
Number of bootstrap-replicates when computing confidence intervals for the ICC or R2.
Character string, indicating the bootstrap-method. Should be
NULL(default), in which case
lme4::bootMer()is used for bootstrapped confidence intervals. However, if bootstrapped intervals cannot be calculated this was, try
ci_method = "boot", which falls back to
boot::boot(). This may successfully return bootstrapped confidence intervals, but bootstrapped samples may not be appropriate for the multilevel structure of the model. There is also an option
ci_method = "analytical", which tries to calculate analytical confidence assuming a chi-squared distribution. However, these intervals are rather inaccurate and often too narrow. It is recommended to calculate bootstrapped confidence intervals for mixed models.
Toggle warnings and messages.
Arguments passed down to
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
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.
model <- lme4::lmer(Sepal.Length ~ Petal.Length + (1 | Species), data = iris) r2_nakagawa(model) #> # R2 for Mixed Models #> #> Conditional R2: 0.969 #> Marginal R2: 0.658 r2_nakagawa(model, by_group = TRUE) #> # Explained Variance by Level #> #> Level | R2 #> ---------------- #> Level 1 | 0.569 #> Species | -0.853 #>