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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 class 'merMod'
  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 class 'glmmTMB'
  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 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.


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)


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).


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.

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 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.

Distribution-specific (observation level) 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 by default based on lognormal approximation, \(log(1 + var(x) / \mu^2)\) (see Nakagawa et al. 2017). Other approximation methods can be specified with the approximation argument. 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.

Residual variance

The residual variance, σ2ε, is simply σ2d + σ2e.

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.


  • 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.


# \donttest{
m <- lmer(Reaction ~ Days + (1 + Days | Subject), data = sleepstudy)

#> $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 
#> var.fixed 
#>  908.9534 
#> var.residual 
#>       654.94 
# }