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,
ci_method = NULL,
verbose = TRUE,
...
)
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 isNA
), decrease the tolerance-level. See alsocheck_singularity()
.- ci
Confidence resp. credible interval level. For
icc()
andr2()
, confidence intervals are based on bootstrapped samples from the ICC resp. R2 value. Seeiterations
.- iterations
Number of bootstrap-replicates when computing confidence intervals for the ICC or R2.
- ci_method
Character string, indicating the bootstrap-method. Should be
NULL
(default), in which caselme4::bootMer()
is used for bootstrapped confidence intervals. However, if bootstrapped intervals cannot be calculated this was, tryci_method = "boot"
, which falls back toboot::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 optionci_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.- verbose
Toggle warnings and messages.
- ...
Arguments passed down to
brms::posterior_predict()
.
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.