This function extracts the different variance components of a mixed model and
returns the result as list. Functions like get_variance_residual(x) or
get_variance_fixed(x) are shortcuts for get_variance(x, component = "residual")
etc.
get_variance(x, ...)# S3 method for merMod
get_variance(
x,
component = c("all", "fixed", "random", "residual", "distribution", "dispersion",
"intercept", "slope", "rho01", "rho00"),
tolerance = 1e-08,
null_model = NULL,
approximation = "lognormal",
verbose = TRUE,
...
)
# S3 method for glmmTMB
get_variance(
x,
component = c("all", "fixed", "random", "residual", "distribution", "dispersion",
"intercept", "slope", "rho01", "rho00"),
model_component = NULL,
tolerance = 1e-08,
null_model = NULL,
approximation = "lognormal",
verbose = TRUE,
...
)
get_variance_residual(x, verbose = TRUE, ...)
get_variance_fixed(x, verbose = TRUE, ...)
get_variance_random(x, verbose = TRUE, tolerance = 1e-08, ...)
get_variance_distribution(x, verbose = TRUE, ...)
get_variance_dispersion(x, verbose = TRUE, ...)
get_variance_intercept(x, verbose = TRUE, ...)
get_variance_slope(x, verbose = TRUE, ...)
get_correlation_slope_intercept(x, verbose = TRUE, ...)
get_correlation_slopes(x, verbose = TRUE, ...)
A list with following elements:
var.fixed, variance attributable to the fixed effects
var.random, (mean) variance of random effects
var.residual, residual variance (sum of dispersion and distribution-specific/observation level variance)
var.distribution, distribution-specific (or observation level) variance
var.dispersion, variance due to additive dispersion
var.intercept, the random-intercept-variance, or between-subject-variance (τ00)
var.slope, the random-slope-variance (τ11)
cor.slope_intercept, the random-slope-intercept-correlation (ρ01)
cor.slopes, the correlation between random slopes (ρ00)
A mixed effects model.
Currently not used.
Character value, indicating the variance component that
should be returned. By default, all variance components are returned. The
distribution-specific ("distribution") and residual ("residual") variance
are the most computational intensive components, and hence may take a few
seconds to calculate.
Tolerance for singularity check of random effects, to decide
whether to compute random effect variances or not. Indicates up to which
value the convergence result is accepted. The larger tolerance is, the
stricter the test will be. See performance::check_singularity().
Optional, a null-model to be used for the calculation of
random effect variances. If NULL, the null-model is computed internally.
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.
Toggle off warnings.
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.
The fixed effects variance, σ2f, is the variance of the matrix-multiplication β∗X (parameter vector by model matrix).
The random effect variance, σ2i, represents the mean random effect variance of the model. Since this variance reflects the "average" random effects variance for mixed models, it is also appropriate for models with more complex random effects structures, like random slopes or nested random effects. Details can be found in Johnson 2014, in particular equation 10. For simple random-intercept models, the random effects variance equals the random-intercept variance.
The distribution-specific variance,
σ2d,
is the conditional variance of the response given the predictors , Var[y|x],
which depends on the model family.
Gaussian: For Gaussian models, it is
σ2 (i.e. sigma(model)^2).
Bernoulli: For models with binary outcome, it is
π2/3 for logit-link,
1 for probit-link, and π2/6
for cloglog-links.
Binomial: For other binomial models, the distribution-specific variance for Bernoulli models is used, divided by a weighting factor based on the number of trials and successes.
Gamma: Models from Gamma-families use μ2
(as obtained from family$variance()).
For all other models, the distribution-specific variance is by default
based on lognormal approximation,
log(1 + var(x) / μ2)
(see Nakagawa et al. 2017). Other approximation methods can be specified
with the approximation argument.
Zero-inflation models: The expected variance of a zero-inflated model is computed according to Zuur et al. 2012, p277.
The variance for the additive overdispersion term,
σ2e,
represents "the excess variation relative to what is expected from a certain
distribution" (Nakagawa et al. 2017). In (most? many?) cases, this will be
0.
The residual variance, σ2ε, is simply σ2d + σ2e.
The random intercept variance, or between-subject variance
(τ00), is obtained from
VarCorr(). It indicates how much groups or subjects differ from each other,
while the residual variance σ2ε
indicates the within-subject variance.
The random slope variance (τ11)
is obtained from VarCorr(). This measure is only available for mixed models
with random slopes.
The random slope-intercept correlation
(ρ01) is obtained from
VarCorr(). This measure is only available for mixed models with random
intercepts and slopes.
This function supports models of class merMod (including models from
blme), clmm, cpglmm, glmmadmb, glmmTMB, MixMod, lme, mixed,
rlmerMod, stanreg, brmsfit or wbm. Support for objects of class
MixMod (GLMMadaptive), lme (nlme) or brmsfit (brms) is
not fully implemented or tested, and therefore may not work for all models
of the aforementioned classes.
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 returned variance components 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 and nbinom2 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
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 (see
performance::icc() or performance::r2_nakagawa()).
This function returns different variance components from mixed models, which are needed, for instance, to calculate r-squared measures or the intraclass-correlation coefficient (ICC).
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. tools:::Rd_expr_doi("10.1111/2041-210X.12225")
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. tools:::Rd_expr_doi("10.1098/rsif.2017.0213")
Zuur, A. F., Savel'ev, A. A., & Ieno, E. N. (2012). Zero inflated models and generalized linear mixed models with R. Newburgh, United Kingdom: Highland Statistics.
# \donttest{
library(lme4)
data(sleepstudy)
m <- lmer(Reaction ~ Days + (1 + Days | Subject), data = sleepstudy)
get_variance(m)
get_variance_fixed(m)
get_variance_residual(m)
# }
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