ebrahim.gof 2.0.0

New features

• def.gof() - the Directed Ebrahim-Farrington (DEF) goodness-of-fit test. Projects grouped standardized residuals onto a smooth calibration-shape basis ("poly2", "poly3", "stukel") and calibrates the statistic as a weighted sum of chi-square_1 variables (Satterthwaite by default; Imhof via the suggested CompQuadForm). basis = "ensemble" is a shortcut to def.ensemble.gof().
• def.ensemble.gof() - combines the three DEF bases (optionally the omnibus EF, or extra p-values) into one decision via the Cauchy combination test (default), with minp and fisher offered for comparison.
• ef.gof(), def.gof(), and def.ensemble.gof() now accept either a fitted glm or (y, predicted_probs) as input. For def.gof, supplying the design matrix X (with the y/predicted_probs form) gives the exact calibration; without it a conservative chi-square reference is used and a warning is issued.

Breaking changes

• ef.gof() now defaults to the chi-square reference (method = "chisq"): the grouped statistic is referred to a chi-square_{G-2} distribution. Use method = "normal" to reproduce the previous (standardized-normal) p-value.

• run.all.gof() - a one-shot runner that returns a tidy data.frame, one row per test. Pass a fitted glm for the whole battery, or (y, predicted_probs) for the prediction-only tests. One failing test never aborts the run. This build bundles Pearson, Deviance, Osius-Rojek, Copas-RSS, Hosmer-Lemeshow (deciles and equal-width), Pigeon-Heyse, EF, the three DEF bases, Stukel, the covariate-space tests Tsiatis, Xie, and Pulkstenis-Robinson, and the two Cauchy-combination ensemble rows. Osius-Rojek, Copas-RSS, Pigeon-Heyse, Tsiatis, and Pulkstenis-Robinson were verified to match their original implementations to ~1e-15 (Xie’s statistic also matches).

• All run.all.gof() tests were verified to reproduce the implementations used in the original thesis simulation. In particular Osius-Rojek and Stukel now follow LogisticDx::gof.glm (Stukel via statmod::glm.scoretest; statmod added to Suggests), matching it numerically; Copas-RSS matches rms’s gof residual; HL matches ResourceSelection::hoslem.test; and HL-equalwidth, Pigeon-Heyse, Tsiatis, Xie, and Pulkstenis-Robinson match their source scripts.

• A second EF row, EF-normal, reports the omnibus EF test with the normal reference used in the thesis simulation (the EF row uses the chi-square default).

• More opt-in slow (include_slow = TRUE) tests: the GAM-based HL-GAM, PR-GAM, and Xie-GAM (Xie et al. 2021; need mgcv; HL-GAM and PR-GAM match the source gam_gof_tests exactly, Xie-GAM uses a fixed clustering seed), and Stute-Zhu (cumulative-residual parametric-bootstrap test; sequential, set reps via control = list("Stute-Zhu" = list(B = ...)); statistic matches the source exactly).

• Lai-Liu-HL (Lai & Liu 2018, standardized-power procedure for the Hosmer-Lemeshow test). It has no p-value: it resamples to a target size, fits the model, estimates the HL rejection rate (“standardized power”), and returns a randomized accept/reject decision. The standardized power is reported as the statistic and the decision in the Note (set n0/k via control). Verified to match the source lai_liu_test exactly.

• Two further opt-in slow tests: eHL (the e-value Hosmer-Lemeshow test of Henzi et al. 2024; base-R reimplementation, with attribution, of the marius-cp/eHL code, matching it to ~1e-11; reported as p = min(1, 1/e)), and BAGofT (the binary-adaptive GOF test, wrapping the BAGofT package; set nsim via control = list(BAGofT = list(nsim = ...))).

• An opt-in slow test, le-Cessie (le Cessie-van Houwelingen 1995, general multivariate smoothed-residual test), runs when include_slow = TRUE. It is O(n^2)-O(n3). Adapted with attribution from the USGS smwrStats package (public domain); verified to match it exactly.

• The Xie test uses the corrected degrees of freedom G - k/2 - 1 with k the number of predictors. (Earlier thesis runs used df = G - 0.5, an artifact of coef() returning NULL on a predicted-probability list; the statistic is the same, only the p-value differs.)

• Added the Information-Matrix test (White 1982 / Orme 1988), the closed-form IM test; verified to match the thesis IMtest_fast exactly.

Pending for the 2.0.0 release

• The remaining thesis tests are all slow / third-party and will be added as opt-in include_slow = TRUE tests in a later build: the GAM-based tests (HL-GAM, PR-GAM, Xie-GAM; need mgcv), the bootstrap tests (Hosmer bootstrap, Stute-Zhu), the e-value HL (eHL; needs isotone), and BAGofT. (McCullagh is not added: it appears only in the unused goflogit macro, not in the thesis simulation.)

ebrahim.gof 1.0.0

Initial Release

This is the first release of the ebrahim.gof package, implementing the Ebrahim-Farrington goodness-of-fit test for logistic regression models.

Features

• Main Function: ef.gof() - Performs the Ebrahim-Farrington goodness-of-fit test
• Dual Mode Support:
  • Ebrahim-Farrington test with automatic grouping for binary data
  • Original Farrington test for grouped binomial data
• Comprehensive Documentation: Detailed help files and vignette
• Robust Testing: Extensive test suite with edge case handling
• Input Validation: Thorough parameter checking and error messages

Key Capabilities

• Binary Data: Automatic grouping of binary (0/1) responses
• Grouped Data: Support for binomial data with multiple trials
• Flexible Grouping: User-specified number of groups (G)
• Statistical Rigor: Based on Farrington’s (1996) theoretical framework
• Sparse Data: Optimized for sparse and challenging datasets

Advantages over Existing Tests

• Better Power: More sensitive than Hosmer-Lemeshow test
• Simplified Implementation: Easy-to-use interface
• Theoretical Foundation: Rigorous asymptotic properties
• Computational Efficiency: Fast execution for binary data

Technical Details

• Test Statistic: Uses modified Pearson chi-square with correction term
• Distribution: Standard normal under null hypothesis
• Expected Value: G - 2 for grouped binary data
• Variance: 2(G - 2) for grouped binary data

References

• Farrington, C. P. (1996). On Assessing Goodness of Fit of Generalized Linear Models to Sparse Data. Journal of the Royal Statistical Society. Series B (Methodological), 58(2), 349-360.
• Ebrahim, Khaled Ebrahim (2025). Goodness-of-Fits Tests and Calibration Machine Learning Algorithms for Logistic Regression Model with Sparse Data. Master’s Thesis, Alexandria University.

Author

Ebrahim Khaled Ebrahim (Alexandria University) Email: ebrahimkhaled@alexu.edu.eg