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.
Usage
get_variance(
x,
component = c("all", "fixed", "random", "residual", "distribution", "dispersion",
"intercept", "slope", "rho01", "rho00"),
verbose = TRUE,
...
)
get_variance_residual(x, verbose = TRUE, ...)
get_variance_fixed(x, verbose = TRUE, ...)
get_variance_random(x, verbose = TRUE, tolerance = 1e-05, ...)
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, ...)
Arguments
- x
A mixed effects model.
- component
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.- verbose
Toggle off warnings.
- ...
Currently not used.
- tolerance
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()
.
Value
A list with following elements:
var.fixed
, variance attributable to the fixed effectsvar.random
, (mean) variance of random effectsvar.residual
, residual variance (sum of dispersion and distribution)var.distribution
, distribution-specific variancevar.dispersion
, variance due to additive dispersionvar.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)
Details
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).
Fixed effects variance
The fixed effects variance, σ2f, is the variance of the matrix-multiplication β∗X (parameter vector by model matrix).
Random effects variance
The random effect variance, σ2i, represents the mean random effect variance of the model. Since this variance reflect 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.
Distribution-specific variance
The distribution-specific variance,
σ2d,
depends on the model family. For Gaussian models, it is
σ2 (i.e.
sigma(model)^2
). For models with binary outcome, it is
\(\pi^2 / 3\) for logit-link, 1
for probit-link, and \(\pi^2 / 6\)
for cloglog-links. Models from Gamma-families use \(\mu^2\) (as obtained
from family$variance()
). For all other models, the distribution-specific
variance is based on lognormal approximation, \(log(1 + var(x) / \mu^2)\)
(see Nakagawa et al. 2017). The expected variance of a zero-inflated
model is computed according to Zuur et al. 2012, p277.
Variance for the additive overdispersion term
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
.
Random intercept variance
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.
Random slope variance
The random slope variance (τ11)
is obtained from VarCorr()
. This measure is only available
for mixed models with random slopes.
Random slope-intercept correlation
The random slope-intercept correlation
(ρ01)
is obtained from VarCorr()
. This measure is only available
for mixed models with random intercepts and slopes.
Note
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 experimental and may not work for all models.
References
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., 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
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.
Examples
# \dontrun{
library(lme4)
data(sleepstudy)
m <- lmer(Reaction ~ Days + (1 + Days | Subject), data = sleepstudy)
get_variance(m)
#> $var.fixed
#> [1] 908.9534
#>
#> $var.random
#> [1] 1698.084
#>
#> $var.residual
#> [1] 654.94
#>
#> $var.distribution
#> [1] 654.94
#>
#> $var.dispersion
#> [1] 0
#>
#> $var.intercept
#> Subject
#> 612.1002
#>
#> $var.slope
#> Subject.Days
#> 35.07171
#>
#> $cor.slope_intercept
#> Subject
#> 0.06555124
#>
get_variance_fixed(m)
#> var.fixed
#> 908.9534
get_variance_residual(m)
#> var.residual
#> 654.94
# }