localize.gof: Localize the misfit of a fitted logistic model, with error...
In ebrahim.gof: Goodness-of-Fit and Calibration Tests for Logistic Regression

localize.gof

R Documentation

Localize the misfit of a fitted logistic model, with error control

Description

The in-sample counterpart of localize.external: checks a logistic glm on the data it was fitted to and names which part of the misfit is present, with the familywise error rate held at alpha. After a fit with an intercept the INTERCEPT and SLOPE parts are identically zero, so two groups remain:

LINK: bends of the map from the linear predictor to risk.
COV: misfit among observations that share a fitted risk: a missed interaction or curved covariate.

The bases are those of localize.external, also made orthogonal to the model matrix. The reference is the parametric bootstrap: B outcome vectors are drawn from the fitted model, the model is refitted to each on the same design matrix, and every member p-value is recomputed. A refit that fails is dropped; the number used is returned.

Usage

localize.gof(
  fit,
  X = NULL,
  B = 199L,
  alpha = 0.05,
  dealias = FALSE,
  cov_df = 5,
  naming = c("closure", "holm", "bonferroni"),
  robust = FALSE,
  seed = NULL,
  plot = interactive()
)

Arguments

`fit`	a fitted `glm` with `family = binomial(link = "logit")`, a 0/1 outcome, one row per observation, no prior weights and no offset.
`X`	a numeric matrix or data frame of covariates, one row per observation. By default the numeric columns of the model frame other than the response; a term such as `log(x)` enters as its column `log(x)`, while matrix terms (`ns()`, `poly()`) and factors are left out. `COV` needs two columns.
`B`	number of parametric-bootstrap replicates; each p-value lies on a grid of `1 / (B_used + 1)`.
`alpha`	familywise level.
`dealias`	if `TRUE`, de-alias the `LINK` group from model columns that are curved in the score; see Details.
`cov_df`, `naming`	as in `localize.external`.
`robust`	if `TRUE`, build the bases on normal scores; see Details.
`seed`	optional integer, passed to `set.seed()` before the bootstrap. The random number stream of the session is restored on exit.
`plot`	if `TRUE`, draw the verdict with `plot.gof_localize` (a misfit compass beside the lattice of closed tests). The default draws it in an interactive session and not in scripts, simulations or examples.

Details

In-sample, a model column whose mean given the score is curved can make LINK read covariate misfit. dealias = TRUE selects such columns once, on the observed fit (a weighted F test of a 3-df spline in the score against a line, level .05), and makes the LINK bases orthogonal to their spline fits on the observed score, frozen for every bootstrap draw, so that LINK reads link shape only. The price is power of LINK against departures that resemble those columns.

naming is as in localize.external. robust = TRUE builds the bases on normal scores, so that a few extreme covariate values cannot drive a verdict: the covariates and the model columns are transformed once, from the data, and the score of every fit, observed or refitted, is transformed too (de-aliasing then uses the transformed score and columns). The level is unaffected, since the bootstrap still refits the model on the original model matrix.

Only a logistic fit is served, since the bases and the refits assume the logit link. A model with another link, or any model that is not a glm, can be checked on validation data with localize.external, which needs only its predictions.

Value

An object of class "gof_localize", as described in localize.external; draws is the number of bootstrap replicates used and dealiased names the model columns removed from LINK (if any).

Reading a verdict

Act on the highest group named. COV: revise the model; the remaining parts are assessed again after the revision. LINK without COV: adding a function of the score to the model, or changing the link, is consistent with the data; it is not proof that no revision is needed. Nothing named: no misfit was detected, a verdict limited by the sample size.

References

Ebrahim, E. K., El-Kotory, A. and Hussein, O. A. E.-A. (2026). One goodness-of-fit test is not enough: error-controlled localization of misfit in logistic risk models. Preprint. Reproduction materials: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.5281/zenodo.23192535")}

Marcus, R., Peritz, E. and Gabriel, K. R. (1976). On closed testing procedures with special reference to ordered analysis of variance. Biometrika, 63(3), 655–660. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/biomet/63.3.655")}

Liu, Y. and Xie, J. (2020). Cauchy combination test: a powerful test with analytic p-value calculation under arbitrary dependency structures. Journal of the American Statistical Association, 115(529), 393–402. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/01621459.2018.1554485")}

Van Calster, B., Nieboer, D., Vergouwe, Y., De Cock, B., Pencina, M. J. and Steyerberg, E. W. (2016). A calibration hierarchy for risk models was defined: from utopia to empirical data. Journal of Clinical Epidemiology, 74, 167–176. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jclinepi.2015.12.005")}

Steyerberg, E. W., Borsboom, G. J. J. M., van Houwelingen, H. C., Eijkemans, M. J. C. and Habbema, J. D. F. (2004). Validation and updating of predictive logistic regression models: a study on sample size and shrinkage. Statistics in Medicine, 23(16), 2567–2586. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/sim.1844")}

Examples

set.seed(2)
n  <- 500
x1 <- rnorm(n); x2 <- rnorm(n)
y  <- rbinom(n, 1, plogis(-0.3 + 0.8 * x1 + 0.6 * x2 + 0.8 * x1 * x2))
fit <- glm(y ~ x1 + x2, family = binomial())   # the interaction is missed
localize.gof(fit, B = 49, seed = 1)   # B = 49 to keep the example fast; use 199 or more

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