In this rejoinder, Maydeu-Olivares states that, in item response theory (IRT) measurement applications, the application of goodness-of-fit (GOF) methods informs researchers of the discrepancy between the model and the data being fitted (the room for improvement). By routinely reporting the GOF of IRT models, together with the substantive results of the application of the fitted model, one will be able to learn "how bad is this fit for this purpose" and establish reasonable fit criteria, which are likely to depend on the intended use of the model. In psychological research, greater attention should be paid to modeling the process used by individuals to respond to test items. GOF methods provide an invaluable tool for this purpose as they often show that the models do not capture well the underlying response process. Maydeu-Olivares contends that by using a common GOF metric in IRT studies, together with the substantive results obtained, researchers will be able to establish cut-off criteria for different purposes. In his view, this method can overcome the danger of being over-zealous about the GOF of IRT models.