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-08,
ci = NULL,
iterations = 100,
ci_method = NULL,
null_model = NULL,
approximation = "lognormal",
model_component = NULL,
verbose = TRUE,
...
)A list with the conditional and marginal R2 values.
A mixed effects model.
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 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().
Confidence resp. credible interval level. For icc(), r2(), and
rmse(), confidence intervals are based on bootstrapped samples from the
ICC, R2 or RMSE value. See iterations.
Number of bootstrap-replicates when computing confidence intervals for the ICC, R2, RMSE etc.
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 way, 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.
Optional, a null model to compute the random effect variances,
which is passed to insight::get_variance(). Usually only required if
calculation of r-squared or ICC fails when null_model is not specified. If
calculating the null model takes longer and you already have fit the null
model, you can pass it here, too, to speed up the process.
Character string, indicating the approximation method
for the distribution-specific (observation level, or residual) variance. Only
applies to non-Gaussian models. Can be "lognormal" (default), "delta" or
"trigamma". For binomial models, the default is the theoretical
distribution specific variance, however, it can also be
"observation_level". See Nakagawa et al. 2017, in particular supplement
2, for details.
For models that can have a zero-inflation component,
specify for which component variances should be returned. If NULL or
"full" (the default), both the conditional and the zero-inflation component
are taken into account. If "conditional", only the conditional component is
considered.
Toggle warnings and messages.
Arguments passed down to lme4::bootMer() or boot::boot()
for bootstrapped ICC, R2, RMSE etc.; for variance_decomposition(),
arguments are passed down to brms::posterior_predict().
The single variance components that are required to calculate the marginal
and conditional r-squared values are calculated using the insight::get_variance()
function. The results are validated against the solutions provided by
Nakagawa et al. (2017), in particular examples shown in the Supplement 2
of the paper. Other model families are validated against results from the
MuMIn package. This means that the r-squared values returned by r2_nakagawa()
should be accurate and reliable for following mixed models or model families:
Bernoulli (logistic) regression
Binomial regression (with other than binary outcomes)
Poisson and Quasi-Poisson regression
Negative binomial regression (including nbinom1, nbinom2 and nbinom12 families)
Gaussian regression (linear models)
Gamma regression
Tweedie regression
Beta regression
Ordered beta regression
Following model families are not yet validated, but should work:
Zero-inflated and hurdle models
Beta-binomial regression
Compound Poisson regression
Generalized Poisson regression
Log-normal regression
Skew-normal regression
Extracting variance components for models with zero-inflation part is not straightforward, because it is not definitely clear how the distribution-specific variance should be calculated. Therefore, it is recommended to carefully inspect the results, and probably validate against other models, e.g. Bayesian models (although results may be only roughly comparable).
Log-normal regressions (e.g. lognormal() family in glmmTMB or gaussian("log"))
often have a very low fixed effects variance (if they were calculated as
suggested by Nakagawa et al. 2017). This results in very low ICC or
r-squared values, which may not be meaningful.
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().
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. tools:::Rd_expr_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. tools:::Rd_expr_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_nakagawa(model, by_group = TRUE)
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