Improving the Hosmer-Lemeshow goodness-of-fit test in large models with replicated Bernoulli trials

The Hosmer-Lemeshow (HL) test is a commonly used global goodness-of-fit (GOF) test that assesses the quality of the overall fit of a logistic regression model. In this paper, we give results from simulations showing that the type I error rate (and hence power) of the HL test decreases as model complexity grows, provided that the sample size remains fixed and binary replicates (multiple Bernoulli trials) are present in the data. We demonstrate that a generalized version of the HL test (GHL) presented in previous work can offer some protection against this power loss. These results are also supported by application of both the HL and GHL test to a real-life data set. We conclude with a brief discussion explaining the behavior of the HL test, along with some guidance on how to choose between the two tests. In particular, we suggest the GHL test to be used when there are binary replicates or clusters in the covariate space, provided that the sample size is sufficiently large.

Automated summary

This paper discusses the application of the Hosmer-Lemeshow (HL) test in logistic regression models and explores the performance of the HL and generalized HL (GHL) tests through simulations and analysis of real-life data. The results show that the power of the HL test decreases with increasing model complexity, while the GHL test offers some protection in the presence of binary replicates or clusters.