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Goodness-of-fit statistics for log-link regression models

journal contribution
posted on 2023-05-18, 07:07 authored by Quinn, SJ, Hosmer, DW, Christopher BlizzardChristopher Blizzard
The use of log binomial regression, regression on binary outcomes using a log link, is becoming increasingly popular because it provides estimates of relative risk. However, little work has been done on model evaluation. We used simulations to compare the performance of five goodness-of-fit statistics applied to different models in a log binomial setting, namely the Hosmer–Lemeshow, the normalized Pearson chi-square, the normalized unweighted sum of squares, Le Cessie and van Howelingen's statistic based on smoothed residuals and the Hjort–Hosmer test. The normalized Pearson chi-square was unsuitable as the rejection rate depended also on the range of predicted probabilities. The Le Cessie and van Howelingen's test statistic had poor sampling properties when evaluating a correct model and was also considered to be unsuitable in this context. The performance of the remaining three statistics was comparable in most simulations. However, using real data the Hjort–Hosmer outperformed the other two statistics.

Funding

National Health & Medical Research Council

History

Publication title

Journal of Statistical Computation and Simulation

Volume

85

Issue

12

Pagination

2533-2545

ISSN

0094-9655

Department/School

Menzies Institute for Medical Research

Publisher

Taylor & Francis Ltd

Place of publication

4 Park Square, Milton Park, Abingdon, England, Oxon, Ox14 4Rn

Rights statement

Copyright 2014 Taylor & Francis

Repository Status

  • Restricted

Socio-economic Objectives

Other health not elsewhere classified

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