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EDGE: Directed Goodness-of-Fit Test for Binary Logistic Regression

Source: R/edge_gof.R
edge.gof.Rd

edge.gof() is the primary interface to the EDGE test (Ebrahim Directed Goodness-of-fit Evaluation): a grouped, directed goodness-of-fit test for binary logistic regression under sparse data. EDGE projects the grouped standardized residuals onto a small pre-specified basis of calibration shapes (cubic "poly3" by default) and refers the resulting quadratic form to its closed-form weighted chi-squared null distribution – no refit, no resampling, no tuning.

edge.gof() computes exactly the same statistic as the legacy name def.gof (retained for backward compatibility); the returned Test label is "EDGE".

Usage

edge.gof(
  object,
  predicted_probs = NULL,
  X = NULL,
  G = 10,
  basis = "poly3",
  method = "satterthwaite"
)

Arguments

object

A fitted binary logistic glm, or a binary (0/1) response vector y (then supply predicted_probs).

predicted_probs

Numeric predicted probabilities; required when object is a y vector, ignored when it is a glm.

X

Optional design matrix, used only with the y/predicted_probs form: it enables the exact estimation-adjusted (\(\Omega\)) calibration (logit working weights assumed). Without it the conservative \(\chi^2_k\) reference is used and a warning is issued. Ignored when object is a glm.

G

Integer number of equal-frequency groups (default 10; must be >= 3).

basis

One of "poly3" (default), "poly2", "stukel", or "ensemble".

method

One of "satterthwaite" (default) or "imhof".

Value

A one-row data.frame with columns Test ("EDGE"), Basis, Test_Statistic, df, Method, and p_value, as documented in def.gof.

References

Ebrahim EK, El-Kotory A (2026). "EDGE: A Closed-Form Directed Goodness-of-Fit Test for Sparse Logistic Regression." arXiv:2608.20511 [stat.ME]. doi:10.48550/arXiv.2608.20511

Ebrahim EK, El-Kotory A (2026). "A Directional Hosmer-Lemeshow Goodness-of-Fit Test for Sparse Logistic Regression." arXiv:2607.15454 [stat.ME]. doi:10.48550/arXiv.2607.15454

See also

def.gof (legacy name), ef.gof, def.ensemble.gof, run.all.gof.

Author

Ebrahim Khaled Ebrahim ebrahimkhaled@alexu.edu.eg

Examples

set.seed(1)
x <- runif(500, -3, 3)
y <- rbinom(500, 1, plogis(0.6 * x))
fit <- glm(y ~ x, family = binomial())
edge.gof(fit)                      # default cubic basis, G = 10
#>   Test Basis Test_Statistic       df        Method   p_value
#> 1 EDGE poly3       1.291194 2.024052 satterthwaite 0.5264813
edge.gof(fit, basis = "stukel")    # Stukel-shape basis
#>   Test  Basis Test_Statistic       df        Method  p_value
#> 1 EDGE stukel       1.222571 1.858582 satterthwaite 0.444966