geom_smooth: Prediction interval and not confidence interval for se in the documentation

[herry23xet]

Hello,
if I use geom_smooth(), then an interval is shown in the standard se = TRUE, which does not have a constant width. Especially for linear estimates of slope parameters.
However, the documentation states that se is a confidence interval (https://ggplot2.tidyverse.org/reference/geom_smooth.html):

Display confidence interval around smooth? (TRUE by default, see level to control.)

However, this cannot be the case, as a confidence interval is always a fixed interval around the slope parameter.
What geom_smooth() shows, however, is the prediction interval (https://en.wikipedia.org/wiki/Prediction_interval).

The same for level.

Example image (from the documentation), dark grey area:

Or have I made a mistake?

If not, this should be changed.

[teunbrand]

I'm not a statistician by training, but I think there might be a misunderstanding here.

You'd only get a constant width around the line if you exclusively have errors in the intercept. If you have errors in the intercept and slope, you get the shape that the confidence band around the line indicates.

To illustrate:

library(ggplot2)

plot_lines <- function(i, s) {
  data.frame(i = i, s = s) |>
    ggplot() +
    geom_abline(aes(slope = s, intercept = i), alpha = 0.01) +
    scale_x_continuous(limits = c(-5, 5)) +
    scale_y_continuous(limits = c(-5, 5))
}

plot_lines(i = 1 + rnorm(1e4, sd = 0.2), s = 1) +
  ggtitle("Variable intercept, fixed slope")

plot_lines(i = 1, s = 1 + rnorm(1e4, sd = 0.2)) +
  ggtitle("Fixed intercept, variable slope")

plot_lines(i = 1 + rnorm(1e4, sd = 0.2), s = 1 + rnorm(1e4, sd = 0.2)) +
  ggtitle("Variable intercept and slope")

^{Created on 2024-08-04 with reprex v2.1.1}

[clauswilke]

It is neither a prediction interval nor a confidence interval. It is a confidence band.
https://en.m.wikipedia.org/wiki/Confidence_and_prediction_bands

You can see some code to manually calculate it here, in case that is of interest. https://wilkelab.org/dataviz_shortcourse/materials/2024-06-27.html

[teunbrand]

Conceptual distinction from the wikipedia article:

Confidence bands are closely related to confidence intervals, which represent the uncertainty in an estimate of a single numerical value

Should we adjust the wording in ggplot2 to read 'confidence bands' instead of 'confidence intervals'? stats::predict.lm() also calls it the relevant argument interval and its documentation makes no mention of 'bands'.

[clauswilke]

I'm away from my desktop and can't easily check what exactly the documentation says but yes, I'd be in favor of confidence band over confidence interval.