When continuous predictors are present, classical Pearson and deviance goodness-of-fit tests to assess logistic model fit break down. We propose a new method for goodness-of-fit testing which uses a very general partitioning strategy (clustering) in the covariate space and is based on either a Pearson statistic or a score statistic. Properties of the proposed statistics are discussed. Simulation studies on many commonly encountered model scenarios are presented to compare the proposed tests to the existing tests. Applications of these different methods on a real clinical trial study are also performed to demonstrate the usefulness of the new method in practice and certain advantages over the widely used Hosmer-Lemeshow test. Discussions on extending this new method to other data situations, such as ordinal response regression models and marginal models for correlated binary data are also included. This method can also be extended to models for multinomial outcomes where generalized logit models are often used.

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