gof_certificate: Can DeepGOF-1 detect this departure? A certificate from the...

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

Can DeepGOF-1 detect this departure? A certificate from the frozen weights

Description

Decides, without running the test, whether deepgof1 is consistent against a departure you name: its power tends to one precisely when the certificate below is positive. The answer costs one forward pass on the shipped weights – no bootstrap, no simulation, no data beyond the fitted model.

Usage

gof_certificate(
  fit,
  pi_star = NULL,
  eta_shift = NULL,
  direction = NULL,
  K = 6L
)

Arguments

fit	a fitted glm with family = binomial(): the null model whose adequacy is in question. Not needed if direction is given.
pi_star	true success probabilities under the alternative, one per observation.
eta_shift	the omitted term on the linear-predictor scale, one per observation; used only when pi_star is not given.
direction	a K by K matrix, or a vector of length K * K in row-major order, giving the map direction directly.
K	grid resolution. Leave at 6: the shipped weights are valid at no other resolution.

Details

Give the departure in whichever form you have it. pi_star is the vector of true success probabilities under the alternative, one per observation of fit. eta_shift is the term the fitted linear predictor is missing, so that the truth is plogis(eta_hat + eta_shift) – an omitted quadratic is eta_shift = c * x^2. direction skips the data entirely and takes a K by K map direction, which is what a theoretical question ("a checkerboard at the cell scale") usually looks like.

A non-positive certificate does not mean the test never rejects; it means the guarantee of power tending to one is unavailable for that direction, which for this network happens on a thin cone of sub-resolution oscillation – the failure mode every binned statistic shares. Because the grid reads two covariates, a departure that integrates to zero within every cell has direction zero and is certified blind, which is the representation limit of the method stated as a computation rather than a caveat.

With a fitted model the direction is built on the map of the default reading of deepgof1 (reading = "axes"): the two covariates of its axis rule, or the 36 cells along the only covariate. For the all-pairs reading, name the pair's map yourself through direction.

Value

An object of class "gof_certificate": certificate (the recession slope at unit map norm; positive certifies consistency), verdict, mirror (the slope of the same departure with its sign flipped, since a test may see a departure one way and not the other), direction (normalized), axes and method.

References

Ebrahim EK, Hussein OAE-A, El-Kotory A (2026). "Where Does a Logistic Risk Model Fail? An Audited Neural Goodness-of-Fit Test for Model Development and External Validation." arXiv:2609.29575 [stat.ME]. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.48550/arXiv.2609.29575")}

See Also

deepgof1

Examples

set.seed(1)
n  <- 200
x1 <- runif(n, -3, 3); x2 <- rnorm(n)
y  <- rbinom(n, 1, plogis(0.3 + 0.8 * x1 - 0.5 * x2))
fit <- glm(y ~ x1 + x2, family = binomial())

# an omitted quadratic in x1: is this test consistent against it?
gof_certificate(fit, eta_shift = 0.9 * (x1^2 - mean(x1^2)))

# a map direction named directly: a threshold departure along the first axis
gof_certificate(direction = matrix(rep(c(-1, -1, -1, 1, 1, 1), each = 6), 6, 6, byrow = TRUE))

# the blind cone is thin but not empty: multi-start minimization over the sphere reaches
# -0.281 for these weights, at a direction that oscillates cell by cell. Directions like
# that are the ones this function is for.

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