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 brmsfit
r2_posterior(model, verbose = TRUE, ...)

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

# S3 method for 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.

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

Examples

library(performance)
if (require("rstanarm") && require("rstantools")) {
  model <- stan_glm(mpg ~ wt + cyl, data = mtcars, chains = 1, iter = 500, refresh = 0)
  r2_bayes(model)

  model <- stan_lmer(
    Petal.Length ~ Petal.Width + (1 | Species),
    data = iris,
    chains = 1,
    iter = 500,
    refresh = 0
  )
  r2_bayes(model)
}
#> Loading required package: rstantools
#> This is rstantools version 2.2.0
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: The largest R-hat is 1.07, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#r-hat
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
#> # Bayesian R2 with Compatibility Interval
#> 
#>   Conditional R2: 0.953 (95% CI [0.941, 0.961])
#>      Marginal R2: 0.821 (95% CI [0.702, 0.891])

if (require("BayesFactor")) {

  BFM <- generalTestBF(mpg ~ qsec + gear, data = mtcars, progress = FALSE)
  FM <- lmBF(mpg ~ qsec + gear, data = mtcars)

  r2_bayes(FM)
  r2_bayes(BFM[3])
  r2_bayes(BFM, average = TRUE) # across all models

  # with random effects:
  mtcars$gear <- factor(mtcars$gear)
  model <- lmBF(
    mpg ~ hp + cyl + gear + gear:wt,
    mtcars,
    progress = FALSE,
    whichRandom = c("gear", "gear:wt")
  )

  r2_bayes(model)
}
#> Loading required package: BayesFactor
#> Loading required package: coda
#> ************
#> Welcome to BayesFactor 0.9.12-4.3. If you have questions, please contact Richard Morey (richarddmorey@gmail.com).
#> 
#> Type BFManual() to open the manual.
#> ************
#> # Bayesian R2 with Compatibility Interval
#> 
#>   Conditional R2: 0.367 (95% CI [0.260, 0.633])
#>      Marginal R2: 0.209 (95% CI [2.871e-05, 0.500])

if (FALSE) {
if (require("brms")) {
  model <- brms::brm(mpg ~ wt + cyl, data = mtcars)
  r2_bayes(model)

  model <- brms::brm(Petal.Length ~ Petal.Width + (1 | Species), data = iris)
  r2_bayes(model)
}
}