A chi-squared goodness-of-fit test for logistic regression models based on case-control data

We propose a chi-squared-type statistic to test the validity of the logistic regression model based on case-control data by adapting the goodness-of-fit test of Nikulin-Rao-Robson-Moore. The proposed test statistic requires a high-dimensional matrix inversion, but is otherwise easy to compute and has an asymptotic chi-squared distribution. This test statistic is an alternative to the Kolmogorov-Smirnov-type statistic of Qin & Zhang (1997) and does not need to employ a bootstrap method to evaluate its critical values. We present some results on simulation and on analysis of two real datasets.