{
  "abstract": "The Hosmer-Lemeshow test is the routine check of fit for logistic regression, yet it is weak against a wrong link, and the directed tests that are stronger lose their level when a single covariate is recorded in error. We apply Farrington's correction to its risk groups, which removes the single-record terms of the statistic and keeps the within-group products of residuals. The result is the score test for records of similar fitted risk sharing a miscalibration: locally most powerful against a smooth misfit in either direction, and as robust to gross errors as the Hosmer-Lemeshow test. One alignment functional, mapped in advance for asymmetric links, decides when it is more powerful than the Hosmer-Lemeshow test, at second order with ten groups and at first order with many. For the many groups of large samples, normal limits for both statistics correct the chi-squared reference of the widely used grouping rule of Paul and colleagues, under which the Hosmer-Lemeshow test reached a size of 12% or lost all its power, and they explain why that rule hid a clear misfit in 8873 SUPPORT patients that groups of 25 records detected. In pre-registered simulations, one gross covariate error in a thousand records raised the false-alarm rates of Stukel's, the cubic calibration and the GiViTI tests to 25-39%, while the risk-grouped tests stayed near 5%; among these, the corrected test was the most powerful in all 34 settings with negative alignment and a visible difference. The test is in the R package ebrahim.gof.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.15454",
  "author_total": 3,
  "authors": [
    {
      "name": "Ebrahim Khaled Ebrahim"
    },
    {
      "name": "Ibrahim Galal Khattab"
    },
    {
      "name": "Ahmed El-Kotory"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2kh3wq7hd7ndn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.15454",
  "fulltext_url": null,
  "id": "2kh3wq7hd7ndn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.15454",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.AP"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7169778698",
  "pdf_url": "https://arxiv.org/pdf/2607.15454",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2kh3wq7hd7ndn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:16Z",
      "native_id": "2607.15454",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.15454"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "A modified Hosmer-Lemeshow goodness-of-fit test for asymmetric links: second-order power and robustness",
  "title_text": "A modified Hosmer-Lemeshow goodness-of-fit test for asymmetric links: second-order power and robustness",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:16Z",
  "url": "https://research.draconitic.com/paper/2kh3wq7hd7ndn",
  "venue": "arXiv",
  "versions": []
}