Sequential item response models with an ordered response

A stepwise approach to the construction of latent trait models is outlined. As a special case of the derived general sequential model, a sequential Rasch model is considered. The derivation of the models is based on mechanisms of latent random variables. The unconditional maximum likelihood estimation is embedded in the framework of generalized linear models. An alternative estimation procedure which allows for ‘parameter separability’ is considered and its applicability is shown.