ebrahim.gof - Ebrahim-Farrington Goodness-of-Fit Test for Logistic Regression

Implements the Ebrahim-Farrington goodness-of-fit test for logistic regression models, particularly effective for sparse data and binary outcomes. This test provides an improved alternative to the traditional Hosmer-Lemeshow test by using a modified Pearson chi-square statistic with data-dependent grouping. The test is based on Farrington (1996) theoretical framework but simplified for practical implementation with binary data. Includes functions for both the original Farrington test (for grouped data) and the new Ebrahim-Farrington test (for binary data with automatic grouping), the Directed Ebrahim-Farrington (DEF) test that targets calibration-shape departures, and an ensemble that combines the DEF bases via the Cauchy combination test. For more details see Hosmer (1980) <doi:10.1080/03610928008827941> and Farrington (1996) <doi:10.1111/j.2517-6161.1996.tb02086.x>.