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 H 0 that the considered model is correct, we consider a family of ϕ -divergence goodness-of-fit test statistics C ϕ that includes a power divergence family of statistics R a . We propose a transformed C ϕ statistics that improves the speed of convergence to a chi-square limiting distribution and show numerically that the transformed R a statistic performs well. We also give a real data example of the transformed R a statistic being more reliable than the original R a statistic for testing H 0 .