Testing goodness-of-fit of a logistic regression model with case-control data

A new test is proposed for testing the validity of the logistic regression model based on case-control data. The proposed test does not need a partition of the space of explanatory variables to handle the case of nonreplication. The new test is consistent against very general alternatives. The asymptotic distribution of the test statistic under a sequence of local alternatives is derived so that the behavior of the asymptotic power function of the new test can be studied. This result also gives the approximated null distribution of the test statistic. For practical sample sizes, the adequacy of the large-sample approximation to the null distribution of the test statistic are carefully examined. Power comparisons with other goodness-of-fit tests are performed to show the advantages of the new method. The test statistic is very simple to compute and the new test will be illustrated with examples.