A generalized Hosmer-Lemeshow goodness-of-fit test for a family of generalized linear models.
Test (Madr)
; 33(2): 589-608, 2024.
Article
em En
| MEDLINE
| ID: mdl-38868722
ABSTRACT
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. Supplementary Information The online version contains supplementary material available at 10.1007/s11749-023-00912-8.
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2024
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Article