This paper describes an approach to the issue of selecting a measurement model that
is based on a comprehensive framework for measurement consisting of four conceptual
building blocks: The construct map, the items design, the outcome space, and the
measurement model. Starting from this framework of building blocks, the measurement
model selected must conform to the constraints imposed by the other three
components. Specifically, to preserve the interpretability of the construct map, the
models must preserve the order of items throughout the range of person locations, and
must do so in a way that is consistent with the interpretational requirements of the
map. In the case of item response modeling, this translates into selecting models that
have a constant slope—i.e., they must be from the Rasch family. In the conclusion,
some next steps in investigating these issues are discussed.