The Rasch model and additive conjoint measurement.

In this paper we clarify the relationship between the Rasch model, additive conjoint measurement, and Luce and Tukey's (1964) axiomatization of additive conjoint measurement. We prove a theorem which links the Rasch model with additive conjoint measurement.

The relationships among design experiments, invariant measurement scales, and domain theories.

In this paper we discuss principled design experiments, a rigorous, experimentally-oriented form of design-based research. We show the dependence of design experiments on invariant measurement scales. We discuss four kinds of invariance culminating in interpretive invariance, and how this in turn depends on increasingly adequate theories of a domain.