Improved transformed deviance statistic for testing a logistic regression model

In logistic regression models, we consider the deviance statistic (the log likelihood ratio statistic) D as a goodness-of-fit test statistic. In this paper, we show the derivation of an expression of asymptotic expansion for the distribution of D under a null hypothesis. Using the continuous term of the expression, we obtain a Bartlett-type transformed statistic that improves the speed of convergence to the chi-square limiting distribution of D. By numerical comparison, we find that the transformed statistic performs much better than D. We also give a real data example of being more reliable than D for testing a hypothesis.