Get variance components from random effects models

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 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 (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, σ²_f, is the variance of the matrix-multiplication β∗X (parameter vector by model matrix).

Random effects variance

The random effect variance, σ²_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.

Distribution-specific variance

The distribution-specific variance, σ²_d, 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, σ²_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.

Residual variance

The residual variance, σ²_ε, is simply σ²_d + σ²_e.

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 σ²_ε 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 
# }