bayes_R2: Bayesian R-squared

In tulpa: Templated Unified Library for Posterior Approximation in Bayesian Hierarchical Models

Bayesian R-squared

Description

Per posterior draw s, R2_s = Var_i(mu_si) / (Var_i(mu_si) + Var_res_s), where mu_si are the response-scale fitted means and Var_res_s is the family's residual variance averaged over observations (Gelman et al. 2019). The linear predictor is rebuilt per draw exactly as in posterior_predict() (fixed effects + random effects + offset at the training data).

Usage

bayes_R2(object, ...)

## S3 method for class 'tulpa_fit'
bayes_R2(
  object,
  ndraws = NULL,
  summary = TRUE,
  probs = c(0.025, 0.975),
  seed = NULL,
  ...
)

Arguments

object	A tulpa_fit object from tulpa().
...	Passed to methods.
ndraws	Number of posterior draws to use. Defaults to all stored draws, or 400 on the draw-free Laplace tier.
summary	Summarize the per-draw values (default TRUE).
probs	Quantiles reported by the summary (default 2.5% / 97.5%).
seed	Optional integer seed (RNG state is restored on exit), used by the Gaussian fixed-effect sampling on draw-free fits.

Value

With summary = TRUE (default) a one-row data frame with estimate (posterior median), std.error, and the probs quantiles; with summary = FALSE the vector of per-draw R^2 values.

References

Gelman, Goodrich, Gabry & Vehtari (2019). R-squared for Bayesian regression models. The American Statistician 73(3):307-309.

Examples

set.seed(1)
d <- data.frame(x = rnorm(200))
d$y <- rnorm(200, 2 * d$x, 1)
fit <- tulpa(y ~ x, data = d, family = "gaussian", mode = "laplace", phi = 1)
bayes_R2(fit)

tulpa documentation built on Oct. 19, 2026, 5:09 p.m.