Generalized linear models of binary data including a logistic regression model and a probit model are considered.For testing the null hypothesis that the considered model is correct, the -divergence family of goodness-offit test statistics C * that is based on a minimum * -divergence estimator is considered.The family of statistics C * includes a power divergence family of statistics R a,b that is based on a minimum power divergence estimator.The derivation of an expression of a continuous term of asymptotic expansion for the distribution of C * under the null hypothesis is shown.Using the expression, a transformed C * statistic that improves the speed of convergence to the chi-square limiting distribution of C * is obtained.In the case of R a,b , it is numerically shown that the transformed statistics usually perform better than the original statistics with respect to speed of convergence to the chi-square limiting distribution and it is also numerically shown that the power of the transformed statistics is almost the same as that of the original statistics.
Taneichi et al. (Fri,) studied this question.