Compute a Bayesian version of R-squared or LOO-adjusted R-squared for regression models.

# S3 method for stanreg
bayes_R2(object, ..., re.form = NULL)

# S3 method for stanreg
loo_R2(object, ...)

Arguments

object	A fitted model object returned by one of the rstanarm modeling functions. See `stanreg-objects`.
...	Currently ignored.
re.form	For models with group-level terms, `re.form` is passed to `posterior_epred` if specified.

Value

A vector of R-squared values with length equal to the posterior sample size (the posterior distribution of R-squared).

References

Andrew Gelman, Ben Goodrich, Jonah Gabry, and Aki Vehtari (2018). R-squared for Bayesian regression models. The American Statistician, to appear. DOI: 10.1080/00031305.2018.1549100. (Journal, Preprint, Notebook)

Examples

fit <- stan_glm(
  mpg ~ wt + cyl,
  data = mtcars,
  QR = TRUE,
  chains = 2,
  refresh = 0
)
rsq <- bayes_R2(fit)
print(median(rsq))
#> [1] 0.814778
hist(rsq)

loo_rsq <- loo_R2(fit)
#> Warning: Some Pareto k diagnostic values are slightly high. See help('pareto-k-diagnostic') for details.
print(median(loo_rsq))
#> [1] 0.7951127

# multilevel binomial model
if (!exists("example_model")) example(example_model)
print(example_model)
#> stan_glmer
#>  family:       binomial [logit]
#>  formula:      cbind(incidence, size - incidence) ~ size + period + (1 | herd)
#>  observations: 56
#> ------
#>             Median MAD_SD
#> (Intercept) -1.5    0.6  
#> size         0.0    0.0  
#> period2     -1.0    0.3  
#> period3     -1.1    0.3  
#> period4     -1.5    0.5  
#> 
#> Error terms:
#>  Groups Name        Std.Dev.
#>  herd   (Intercept) 0.77    
#> Num. levels: herd 15 
#> 
#> ------
#> * For help interpreting the printed output see ?print.stanreg
#> * For info on the priors used see ?prior_summary.stanreg
median(bayes_R2(example_model))
#> [1] 0.7564278
median(bayes_R2(example_model, re.form = NA)) # exclude group-level
#> [1] 0.6226784