The concept of a behavior domain is a reasonable and essential foundation for psychometric work based on true score theory, the linear model of common factor analysis, and the nonlinear models of item response theory. Investigators applying these models to test data generally treat the true scores or factors or traits as abstractive psychological attributes: common properties of the items, possibly with some inconsistency between their practice and their theoretical statements. A countably infinite item domain defines an attribute uniquely, and a function of the domain item scores gives an identified measure of it, to be estimated from a finite set of item scores, with a defined error of measurement. In test development the investigator must consider and justify the assumption that an item domain exists for the specific measurement application and is large enough to be treated as infinite for that application.