The Rasch model instantiates the principles of probabilistic conjoint measurement to produce invariant interval-scale measures in which the principles of concatenation apply. Duncan Luce and his colleagues have outlined the principles and properties of axiomatic conjoint measurement that would bring the same sort of rigorous measurement to the human sciences as the physical sciences have enjoyed for a considerable time. The Rasch model is used for another purpose: the construction of fundamental measures. This is distinctly different from other item response theory (IRT) models and true score theory (TST), where the observed data have primacy and the results of the analyses are descriptive of those data. Smith outlines a range of psychometric indicators of reliability and internal consistency from Rasch analysis in order to draw direct one-to-one correspondences between the eight facets of construct validity identified by Messick and inferences drawn directly from the theory and practice of Rasch measurement.