Subject-centered scalability: the sine qua non of summated ratings.
A unifying theory of subject-centered scalability is offered that is grounded in structural true score modeling, is conceptually distinct from internal consistency and homogeneity as determined by item correlations, and is empirically confirmable. Scalability holds when item true scores are perfectly correlated but differ in their individual scale metric. The condition of scalability imposes constraints that allow individual item reliability to be estimated independently of scalability. Scalability is shown to imply unit rank and to be testable by a single-factor confirmatory factor analysis reinterpreted as a test of unit rank. High item correlations are shown, contrary to intuition, to be an insufficient condition for scalability. Conversely, low item correlations do not necessarily imply lack of scalability. A stepped decision-oriented procedure is offered as a guideline in summated rating scale construction.
Drewes
Donald W
DW
Department of Psychology, College of Humanities and Social Sciences, North Carolina State University, Raleigh, NC 27695-7650, USA. donald_drewes@ncsu.edu
D005163:Factor Analysis, Statistical; D006801:Humans; D015233:Models, Statistical; D016011:Normal Distribution; D011581:Psychological Tests / Q000706:statistics & numerical data*; D011584:Psychology / Q000706:statistics & numerical data*; D011594:Psychometrics / Q000706:statistics & numerical data*; D015203:Reproducibility of Results