Abstract
This paper introduces a statistical procedure, to be applied after a goodness-of-fit test has rejected a null model, that provides diagnostic information to help the user decide on a better model. The procedure goes through a list of departures, each being tested by a local smooth test. The list is organized into a hierarchy by seeking answers to the questions " Where is the problem ? " and " What is the problem there ?. This hierarchy allows to focus on finer departures as the data becomes more abundant. The procedure controls the family-wise Type 1 error rate. Simulations show that the procedure can succeed in providing useful diagnostic information.