In a large simulation study, five existing goodness-of-fit tests (McCullagh, Osius-Rojek, le Cessie-van Houwelingen, Stute-Zhu, GiViTI) control Type I error and beat Hosmer-Lemeshow in power, but a real-data example shows no single test reliably catches omitted interactions.
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Benchmarking Goodness-of-Fit and Calibration Algorithms for Logistic Regression Classifiers: A Large-Scale Simulation Study under Sparse Data
In a large simulation study, five existing goodness-of-fit tests (McCullagh, Osius-Rojek, le Cessie-van Houwelingen, Stute-Zhu, GiViTI) control Type I error and beat Hosmer-Lemeshow in power, but a real-data example shows no single test reliably catches omitted interactions.