Approximate Conditional Inference in Generalized Linear Models

SUMMARY Easily calculated and accurate approximations are developed to the conditional densities and distributions of sufficient statistics in generalized linear models with canonical link functions. They enable conditional inferences based on modified profile log-likelihoods and tail probabilities to be made using only the deviance and the variance matrix estimate based on fitted models. Examples are given in binary logistic regression and a log-linear model, and the results are applied to added variable tests of model adequacy.