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,
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, ...)

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)`var.distribution`

, distribution-specific variance`var.dispersion`

, variance due to additive dispersion`var.intercept`

, the random-intercept-variance, or between-subject-variance (τ_{00})`var.slope`

, the random-slope-variance (τ_{11})`cor.slope_intercept`

, the random-slope-intercept-correlation (ρ_{01})`cor.slopes`

, the correlation between random slopes (ρ_{00})

- 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()`

.

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).

The fixed effects variance, σ^{2}_{f},
is the variance of the matrix-multiplication β∗X
(parameter vector by model matrix).

The random effect variance, σ^{2}_{i},
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.

The distribution-specific variance,
σ^{2}_{d},
depends on the model family. For Gaussian models, it is
σ^{2} (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.

The variance for the additive overdispersion term,
σ^{2}_{e},
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, σ^{2}_{ε},
is simply σ^{2}_{d} + σ^{2}_{e}.

The random intercept variance, or *between-subject* variance
(τ_{00}),
is obtained from `VarCorr()`

. It indicates how much groups
or subjects differ from each other, while the residual variance
σ^{2}_{ε}
indicates the *within-subject variance*.

The random slope variance (τ_{11})
is obtained from `VarCorr()`

. This measure is only available
for mixed models with random slopes.

The random slope-intercept correlation
(ρ_{01})
is obtained from `VarCorr()`

. This measure is only available
for mixed models with random intercepts and slopes.

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.

```
if (FALSE) {
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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