Large sample convergence diagnostics for likelihood based inference: Logistic regression

A general diagnostic approach to the evaluation of asymptotic approximation in likelihood based models is developed and applied to logistic regression. The expected asymptotic and observed log-likelihood functions are compared using a chi distribution in a directional Bayesian setting. This provides a general approach to assessing and visualizing non-convergence in higher dimensional models. Several well-known examples from the logistic regression literature are discussed.