The Rasch model assumes that the item characteristic functions are logistic functions, which is a very specific choice. In particular, in the early days of item response modeling the normal-ogive model proposed by Lord (1952) has been considered an important alternative. In the following, a wider class of models is considered. Alternative binary models are also useful when considering models with more than two answer categories since they are contained in most of the current polytomous item response models. An important extension of the Rasch model is the model with varying slopes or discrimination parameters. The model allows that the discriminatory power varies over items and typically shows better fit to the data than the simpler versions. In the following, the functional forms of extended models are specified. It is implicitly assumed that conditional independence of responses given the latent trait holds.