  Ordered item response models that are in common use can be divided into three
groups, cumulative, sequential and adjacent categories model. The derivation
and motivation of the models is typically based on the assumed presence of
latent traits or underlying process models. In the construction frequently
binary models play an important role. The objective of this paper is to give
motivations for the models and to clarify the role of the binary models for the
various types of ordinal models. It is investigated which binary models are
included in an ordinal model but also how the models can be constructed from a
sequence of binary models. In all the models one finds a Guttman space
structure, which has previously been investigated in particular for the partial
credit model. The consideration of the binary models adds to the interpretation
of model parameters, which is helpful, in particular, in the case of the
partial credit model, for which interpretation is less straightforward than for
the other models. A specific topic that is addressed is the ordering of
thresholds in the partial credit model because for some researchers reversed
ordering is an anomaly, others disagree. It is argued that the ordering of
thresholds is not a constitutive element of the partial credit model.
