  The Rasch model is the most prominent member of the class of latent trait
models that are in common use. The main reason is that it can be considered as
a measurement model that allows to separate person and item parameters, a
feature that is referred to as invariance of comparisons or specific
objectivity. It is shown that the property is not an exclusive trait of Rasch
type models but is also found in alternative latent trait models. It is
distinguished between separability in the theoretical measurement model and
empirical separability with empirical separability meaning that parameters can
be estimated without reference to the other group of parameters. A new type of
pairwise estimator with this property is proposed that can be used also in
alternative models. Separability is considered in binary models as well as in
polytomous models.

Methodology