A Goodness-of-Fit Test for Binary Regression Models, Based on Smoothing Methods

A new global test statistic for models with continuous covariates and binary response is introduced. The test statistic is based on nonparametric kernel methods. Explicit expressions are given for the mean and variance of the test statistic. Asymptotic properties are considered and approximate corrections due to parameter estimation are presented. Properties of the test statistic are studied by simulation. The goodness-of-fit method is illustrated on data from a Dutch follow-up study on preterm infants. Recommendations for practitioners are given.