def.ensemble.gof: Combine Directed GOF Tests into One Decision (Ensemble)

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

Combine Directed GOF Tests into One Decision (Ensemble)

Description

Combines the three Directed Ebrahim-Farrington (DEF) basis tests ("poly2", "poly3", "stukel") into a single goodness-of-fit decision, so the user does not have to choose a basis. By default the p-values are combined with the Cauchy Combination Test (CCT), which controls the error rate under the strong dependence between tests computed on the same fitted model. The omnibus EF test can optionally be added to the vote.

Usage

def.ensemble.gof(
  object,
  predicted_probs = NULL,
  X = NULL,
  components = c("poly2", "poly3", "stukel"),
  add_ef = FALSE,
  combine = c("cct", "minp", "fisher"),
  G = 10,
  extra_pvalues = NULL,
  weights = c("unit", "score")
)

Arguments

object	A fitted binary logistic glm, or a binary (0/1) vector y (then supply predicted_probs).
predicted_probs	Numeric predicted probabilities; required when object is a y vector.
X	Optional design matrix, threaded to def.gof for the exact calibration (only used with the y/predicted_probs form).
components	Character vector, a subset of c("poly2","poly3","stukel","sym"). Default is "poly2", "poly3" and "stukel", the three bases EDGES is defined on.
add_ef	Logical; if TRUE, the omnibus EF p-value (ef.gof) is appended to the components. Default FALSE.
combine	One of "cct" (default), "minp", "fisher".
G	Integer number of groups passed to def.gof/ef.gof (default 10), or "auto" for max(10, ceiling(n / 25)) as in def.gof.
extra_pvalues	Optional named numeric vector of additional p-values to include (e.g. a Tsiatis test computed elsewhere). Default NULL.
weights	"unit" (default) or "score", passed to def.gof for every component.

Details

Because the component tests are computed on the same fit, their p-values are strongly dependent. The CCT (combine = "cct") has an asymptotic standard-Cauchy null whose tail is robust to this dependence, so it needs no calibration. The "minp" (Sidak) and "fisher" rules assume independence and are offered for comparison only; under positive dependence "minp" is conservative and "fisher" is anti-conservative, so they should be calibrated by simulation before use (not done here).

With no event, or no non-event, the model has no maximum-likelihood fit: the p-value is NA, with one warning of class def_degenerate.

Value

A one-row data.frame with columns Test, Combiner, Components, k, and p_value.

Author(s)

Ebrahim Khaled Ebrahim [e-mail]

References

Liu, Y. and Xie, J. (2020). Cauchy combination test. JASA, 115(529), 393-402.

See Also

def.gof, ef.gof.

Examples

data("gof_demo", package = "ebrahim.gof")
wrong <- glm(outcome ~ age + bmi + sex + treatment,
             data = gof_demo, family = binomial())
def.ensemble.gof(wrong)                 # CCT of the three DEF bases
def.ensemble.gof(wrong, add_ef = TRUE)  # add the omnibus EF

## the corrected model, for contrast
right <- glm(outcome ~ poly(age, 2) + bmi + sex + treatment,
             data = gof_demo, family = binomial())
def.ensemble.gof(right)

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