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

A unified toolbox of goodness-of-fit and calibration tests for binary logistic regression, callable in a single line via run.all.gof. The package is aimed particularly at sparse data, where the classical Hosmer–Lemeshow test loses power, and at penalized fits, where it is not merely weak but invalid.

Choosing a test

The battery is the place to start; the table below is for when you already know something about what you are looking for.

No prior idea of what is wrong: run.all.gof — runs the whole battery and groups the results by the departure each test detects.
Sparse data, no direction in mind: ef.gof — the omnibus Ebrahim–Farrington test, which groups automatically and needs no model object.
Misfit expected in the shape of the calibration curve: edge.gof — spends its few degrees of freedom on the smooth directions where structured misfit concentrates.
Misfit expected in the covariates themselves: cdef.gof — the covariate-space directed test.
Unwilling to choose one direction: edges.gof — a Cauchy combination over the directed bases, which pays little for the directions that turn out to be empty.
Wanting one number, reproducible between analysts: legoft — weights fixed offline and shipped frozen, so nothing is retrained when you call it; legoft.localize then says which domain of evidence carries the misfit, with familywise error control.
Willing to spend a bootstrap for more power: deepgof1 — a pretrained convolutional statistic whose level comes from your own parametric bootstrap rather than from the network.
A penalized (ridge) fit: calm.gof for a closed-form reference from a single fit, or shrink.gof for the same correction referred to a prepivoting bootstrap. Under a penalty the usual chi-squared references are wrong, not just conservative.
A scorer of your own: gof.features turns a fit into a feature vector and deploy.gof applies a scorer to it.

Aggregated tests (for comparison)

run.all.gof also runs, in one call, a wide range of classical and modern tests — Hosmer–Lemeshow, McCullagh, Osius–Rojek, le Cessie–van Houwelingen, Stute–Zhu, the binary-adaptive BAGofT test, and the givitiR calibration test. Each aggregated test is obtained from its own package (where installed) and is attributed to its authors; these are provided for head-to-head comparison, not claimed as original to this package. gof_install_suggests installs the optional packages they need.

Data

gof_demo is a bundled example dataset with a documented, reproducible misfit for illustrating the battery.

Citing the methods

Each of the author's tests has a paper behind it. Run citation("ebrahim.gof") for the current references; they are kept there rather than duplicated here, because several are moving from preprint to journal.

Author

Maintainer: Ebrahim Khaled Ebrahim ebrahimkhaled@alexu.edu.eg (ORCID)

Examples

set.seed(1)
n <- 200
x <- rnorm(n)
y <- rbinom(n, 1, plogis(0.3 + 0.9 * x))
fit <- glm(y ~ x, family = binomial())

# the omnibus test on the fitted probabilities
ef.gof(y, fitted(fit))
#>                 Test Test_Statistic   p_value
#> 1 Ebrahim-Farrington     -0.7714014 0.7666854

# the directed test, when misfit is expected in the calibration shape
edge.gof(fit)
#>   Test Basis Test_Statistic       df        Method   p_value
#> 1 EDGE poly3       2.642516 2.057006 satterthwaite 0.2717296