Plot frequentist and Bayesian estimates together — frequentist_bayesian

Presents the estimates from a frequentist model and a Bayesian model on one plot, in the first two colours of the colourblind-safe depictr_palette(): brand blue for the frequentist estimates and orange for the Bayesian ones, whether the Bayesian side is drawn from draws or from summaries.

Usage

frequentist_bayesian_plot(
  frequentist,
  bayesian,
  conf_level = 0.95,
  labels = NULL,
  interaction = c("times", "asterisk", "colon", "space"),
  intercept = TRUE,
  facet = TRUE,
  scales = c("free", "fixed"),
  note_frequentist_no_prior = FALSE,
  vertical_line_at_x = 0,
  title = NULL,
  subtitle = NULL,
  x_lab = "Estimate",
  caption = NULL,
  ...
)

Arguments

frequentist: A frequentist model (e.g. from lm, glm or lmerTest::lmer) or a tidy data frame of estimates.
bayesian: A Bayesian model, a posterior draws object, a draws matrix/data frame, a tidy data frame of posterior summaries or a summary matrix such as brms::fixef() returns.
conf_level: Level of the intervals the function computes: the confidence intervals of a frequentist model and, when bayesian holds draws, the outer credible interval of each posterior (see Details). A single number strictly between 0 and 1.
labels, interaction, intercept: See compare_models(). On both paths, an unnamed labels vector takes the frequentist terms first, then any that only the Bayesian input holds. intercept defaults to TRUE here.
facet, scales: Layout controls. Because a Bayesian model almost always carries a large intercept alongside small slopes, the comparison defaults to a faceted, free-scaled layout (facet = TRUE): each term gets its own panel and free x-axis, so every posterior and its frequentist overlay stay legible. Pass facet = FALSE (or scales = "fixed") for the classic single shared-axis plot.
note_frequentist_no_prior: If TRUE, append "(no prior)" to the frequentist legend label, which is helpful when the title names the Bayesian prior.
vertical_line_at_x: Position of the vertical reference line (NA to omit).
title, subtitle, x_lab: Title, subtitle and x-axis label.
caption: Plot caption. The default (NULL) names the level of each source's intervals. Pass NA to omit the caption.
...: Further arguments passed to compare_models() on the summary path (ignored on the distribution path).

Value

A ggplot2::ggplot object.

Details

When bayesian carries posterior draws (a brms/rstanarm fit, a posterior draws object, a draws matrix, or a long/wide draws data frame), the full posterior distribution is drawn per term (a 'ggdist' half-eye) and the frequentist point and confidence interval is overlaid at the same position. When bayesian is only a table of posterior summaries, the function shows the familiar two-source forest plot via compare_models(). It reads tidy columns (term, estimate, conf.low, conf.high), the Estimate, Q2.5 and Q97.5 of the matrix brms::fixef() returns, and the l-95% CI and u-95% CI of summary(fit)$fixed.

Terms are aligned by their canonical display label, so the brms-style b_ prefix is reconciled automatically against the frequentist term names. Draws are read as in posterior_plot(), so a draws object holding b_ parameters keeps only those, and two terms that would share a label are an error. With draws, only the terms both sides share are drawn, and a message names any dropped, such as a sigma in the posterior. The forest plot of summaries draws every term of either input.

conf_level is the level of every interval the function computes. For a frequentist model, that is its confidence interval. For posterior draws, it is the outer of the equal-tailed credible intervals drawn beneath each half-eye, so the two sources are compared at one level. The inner interval is 66%, drawn only when conf_level exceeds 0.66 so that it stays the narrower of the two. A table of estimates keeps the interval limits it holds, at whatever level they were computed. By default, a caption names the level of each source's intervals or says that they are as supplied.

Examples

# Summary path: a tidy "Bayesian" summary as a data frame. The summary here
# stands in for a regularised posterior, so a weakly informative prior pulls
# each estimate toward zero and narrows its interval; a real posterior would
# come from the model fit rather than from arithmetic on the frequentist one.
freq <- lm(life_satisfaction ~ stress + sleep_hours + exercise_days,
           data = wellbeing_survey)
bayes <- tidy_estimates(freq)
bayes$estimate <- bayes$estimate * 0.9
half <- (bayes$conf.high - bayes$conf.low) / 2 * 0.8
bayes$conf.low <- bayes$estimate - half
bayes$conf.high <- bayes$estimate + half
frequentist_bayesian_plot(freq, bayes,
                          title = "Frequentist vs. Bayesian estimates")


# Distribution path: simulated posterior draws (one column per term) drawn as
# full posteriors with the frequentist point + CI overlaid.
set.seed(1)
co <- coef(freq)
draws <- as.data.frame(lapply(co, function(m) rnorm(400, m, abs(m) * 0.1 + 0.05)))
names(draws) <- names(co)
frequentist_bayesian_plot(freq, draws,
                          title = "Posterior with frequentist overlay")