A generalized Hosmer–Lemeshow goodness-of-fit test for a family of generalized linear models
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Nikola Surjanovic [1] ; Richard A. Lockhart [2] ; Thomas M. Loughin [2]
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[1] University of British Columbia
University of British Columbia
Canadá
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[2] Simon Fraser University
Simon Fraser University
Canadá
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- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 33, Nº. 2, 2024, págs. 589-608
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
Generalized linear models (GLMs) are very widely used, but formal goodness-of-fit (GOF) tests for the overall fit of the model seem to be in wide use only for certain classes of GLMs. We develop and apply a new goodness-of-fit test, similar to the well-known and commonly used Hosmer–Lemeshow (HL) test, that can be used with a wide variety of GLMs. The test statistic is a variant of the HL statistic, but we rigorously derive an asymptotically correct sampling distribution using methods of Stute and Zhu (Scand J Stat 29(3):535–545, 2002) and demonstrate its consistency. We compare the performance of our new test with other GOF tests for GLMs, including a naive direct application of the HL test to the Poisson problem. Our test provides competitive or comparable power in various simulation settings and we identify a situation where a naive version of the test fails to hold its size. Our generalized HL test is straightforward to implement and interpret and an R package is publicly available.
