plot.edge_gof: Plot an EDGE result: the grouped residuals, the shape tested...

In ebrahim.gof: Goodness-of-Fit and Calibration Tests for Logistic Regression

Plot an EDGE result: the grouped residuals, the shape tested and the bands

Description

Draws one row of an edge.gof result: the standardized residual of each risk group against its mean predicted risk, the part of the residuals that the test squared (P_Z r, the EDGE direction) as a curve, a pointwise band and a simultaneous band. Groups beyond the band are drawn as filled triangles.

Usage

## S3 method for class 'edge_gof'
plot(
  x,
  row = c("verdict", "check"),
  scale = c("residual", "rate"),
  band = c("simultaneous", "pointwise", "none"),
  colour = TRUE,
  level = 0.95,
  ...
)

Arguments

x	An "edge_gof" object from edge.gof.
row	Which row to draw: "verdict" (default), "check", or a row number.
scale	"residual" (default), "rate", or c("residual", "rate") for both panels side by side.
band	"simultaneous" (default; the pointwise band is then drawn dashed), "pointwise" or "none". Groups beyond the chosen band are marked.
colour	FALSE draws in greys only.
level	Coverage of the bands. Default 0.95.
...	Not used.

Details

For group g with O_g events, E_g = \sum \hat p_i and V_g = \sum \hat p_i(1 - \hat p_i), the residual is r_g = (O_g - E_g)/\sqrt{V_g}.

Frozen predictions (external = TRUE). Nothing was estimated from these outcomes, so the residuals are independent with unit variance under a calibrated model and the bands are the ones of the EDGE paper: pointwise at \pm z_{1-(1-\mathrm{level})/2} and simultaneous at \pm z_{1-(1-\mathrm{level}^{1/G})/2}, the Sidak form of the Bonferroni band, which has exact coverage level for G independent normal residuals.

In-sample (a fitted glm, or X given). The fit removes part of every residual, so r has covariance \Omega = I - U(X'WX)^{-1}U', not I. Each residual and the curve are divided by \sqrt{\Omega_{gg}} before the same constants are applied. The pointwise band is then right to first order, and the simultaneous band is conservative for correlated normal residuals (Sidak's inequality). Both rest on the normal approximation and on an estimated \Omega, so the legend calls them approximate. When only y and predicted_probs were given, without X, \Omega = I is used and the bands are conservative.

The rate scale. scale = "rate" shows the observed event rate O_g/n_g against the predicted rate E_g/n_g with the same band around the diagonal, half-width times \sqrt{V_g \Omega_{gg}}/n_g, cut at 0 and 1. The bars join each group to the diagonal: vermilion when more events were seen than predicted, blue when fewer.

The band is a description of where the misfit lies. The verdict is the p-value of the row, which does not depend on the band.

Value

x, invisibly.

See Also

edge.gof; edge.belt returns the same quantities as a table, with a simulated simultaneous band.

Examples

set.seed(1)
n <- 1000
x <- runif(n, -3, 3)
y <- rbinom(n, 1, 1 - exp(-exp(0.8 * x)))   # log-log truth, fitted as logit
fit <- glm(y ~ x, family = binomial())
e <- edge.gof(fit)
plot(e)
plot(e, row = "check", scale = c("residual", "rate"))

## frozen predictions: the bands are exact
xv <- runif(n, -3, 3)
yv <- rbinom(n, 1, plogis(0.3 + 0.6 * xv))
pv <- plogis(0.6 * xv)                       # the model misses the intercept shift
plot(edge.gof(yv, predicted_probs = pv, external = TRUE), scale = "rate", colour = FALSE)

ebrahim.gof documentation built on Oct. 11, 2026, 5:07 p.m.