A grouped directional correction to the Hosmer-Lemeshow statistic yields a logistic-regression goodness-of-fit test that detects asymmetric-link misfit better than HL, at no cost in size.
Increasing the power: A practical approach to goodness-of-fit test for logistic regression models with continuous predictors
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A directional Hosmer-Lemeshow goodness-of-fit test for sparse logistic regression
A grouped directional correction to the Hosmer-Lemeshow statistic yields a logistic-regression goodness-of-fit test that detects asymmetric-link misfit better than HL, at no cost in size.