Bayesian R2

Compute R2 for Bayesian models. For mixed models (including a random part), it additionally computes the R2 related to the fixed effects only (marginal R2). While r2_bayes() returns a single R2 value, r2_posterior() returns a posterior sample of Bayesian R2 values.

Usage

r2_bayes(model, robust = TRUE, ci = 0.95, verbose = TRUE, ...)

r2_posterior(model, ...)

# S3 method for class 'brmsfit'
r2_posterior(model, verbose = TRUE, ...)

# S3 method for class 'stanreg'
r2_posterior(model, verbose = TRUE, ...)

# S3 method for class 'BFBayesFactor'
r2_posterior(model, average = FALSE, prior_odds = NULL, verbose = TRUE, ...)

Arguments

model

A Bayesian regression model (from brms, rstanarm, BayesFactor, etc).

robust

Logical, if TRUE, the median instead of mean is used to calculate the central tendency of the variances.

ci

Value or vector of probability of the CI (between 0 and 1) to be estimated.

verbose

Toggle off warnings.

...

Arguments passed to r2_posterior().

average

Compute model-averaged index? See bayestestR::weighted_posteriors().

prior_odds

Optional vector of prior odds for the models compared to the first model (or the denominator, for BFBayesFactor objects). For data.frames, this will be used as the basis of weighting.

Value

A list with the Bayesian R2 value. For mixed models, a list with the Bayesian R2 value and the marginal Bayesian R2 value. The standard errors and credible intervals for the R2 values are saved as attributes.

Details

r2_bayes() returns an "unadjusted" R2 value. See r2_loo() to calculate a LOO-adjusted R2, which comes conceptually closer to an adjusted R2 measure.

For mixed models, the conditional and marginal R2 are returned. The marginal R2 considers only the variance of the fixed effects, while the conditional R2 takes both the fixed and random effects into account. Technically, since r2_bayes() relies on rstantools::bayes_R2(), the "marginal" R2 calls bayes_R2(re.form = NA), while the "conditional" R2 calls bayes_R2(re.form = NULL). The re.form argument is passed to rstantools::posterior_epred(), which is internally called in bayes_R2().

Note that for "marginal" and "conditional", we refer to the wording suggested by Nakagawa et al. 2017. Thus, we don't use the term "marginal" in the sense that the random effects are integrated out, but are "ignored".

r2_posterior() is the actual workhorse for r2_bayes() and returns a posterior sample of Bayesian R2 values.

References

• Gelman, A., Goodrich, B., Gabry, J., and Vehtari, A. (2018). R-squared for Bayesian regression models. The American Statistician, 1–6. doi:10.1080/00031305.2018.1549100

• Nakagawa, S., Johnson, P. C. D., and 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.

Examples

library(performance)
# \donttest{
model <- suppressWarnings(rstanarm::stan_glm(
  mpg ~ wt + cyl,
  data = mtcars,
  chains = 1,
  iter = 500,
  refresh = 0,
  show_messages = FALSE
))
r2_bayes(model)
#> # Bayesian R2 with Compatibility Interval
#> 
#>   Conditional R2: 0.811 (95% CI [0.681, 0.884])

model <- suppressWarnings(rstanarm::stan_lmer(
  Petal.Length ~ Petal.Width + (1 | Species),
  data = iris,
  chains = 1,
  iter = 500,
  refresh = 0
))
r2_bayes(model)
#> # Bayesian R2 with Compatibility Interval
#> 
#>   Conditional R2: 0.954 (95% CI [0.951, 0.957])
#>      Marginal R2: 0.387 (95% CI [0.174, 0.611])
# }

# \donttest{
model <- suppressWarnings(brms::brm(
  mpg ~ wt + cyl,
  data = mtcars,
  silent = 2,
  refresh = 0
))
r2_bayes(model)
#> # Bayesian R2 with Compatibility Interval
#> 
#>   Conditional R2: 0.826 (95% CI [0.757, 0.855])

model <- suppressWarnings(brms::brm(
  Petal.Length ~ Petal.Width + (1 | Species),
  data = iris,
  silent = 2,
  refresh = 0
))
r2_bayes(model)
#> # Bayesian R2 with Compatibility Interval
#> 
#>   Conditional R2: 0.955 (95% CI [0.951, 0.957])
#>      Marginal R2: 0.382 (95% CI [0.173, 0.597])
# }