Transformed goodness-of-fit statistics for a generalized linear model of binary data

In a generalized linear model of binary data, we consider models based on a general link function including a logistic regression model and a probit model as special cases. For testing the null hypothesis H0 that the considered model is correct, we consider a family of ϕ-divergence goodness-of-fit test statistics Cϕ that includes a power divergence family of statistics Ra. We propose a transformed Cϕ statistics that improves the speed of convergence to a chi-square limiting distribution and show numerically that the transformed Ra statistic performs well. We also give a real data example of the transformed Ra statistic being more reliable than the original Ra statistic for testing H0.