  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 1
error rate (and hence power) of the HL test decreases as model complexity
grows, provided that the sample size remains fixed and binary replicates are
present in the data. We demonstrate that the generalized version of the HL test
by Surjanovic et al. (2020) can offer some protection against this power loss.
We conclude with a brief discussion explaining the behaviour of the HL test,
along with some guidance on how to choose between the two tests.
