A goodness‐of‐fit test for regression models with discrete outcomes

Regression models are often used to analyze discrete outcomes, but classical goodness‐of‐fit tests such as those based on the deviance or Pearson's statistic can be misleading or have little power in this context. To address this issue, we propose a new test, inspired by the work of Czado et al. ( Biometrics , 65(4):1254–1261, 2009), which involves no randomization, tuning parameter, or binning of covariates. The statistic's large‐sample distribution under the null hypothesis is determined; as it involves unknown parameter values, one must resort to a bootstrap procedure to compute ‐values. Simulations are conducted to investigate the ability of the test to detect a broad range of model misspecifications commonly seen in practice. The proposed procedure is seen to perform well in all the scenarios considered as well as on real data.