A Matrix Lie Group Formulation of Measurement Theory: Symmetries of Classical Measurement Theory

Abstract

ABSTRACT Symmetry considerations are important in science, and Group Theory is a theory of symmetry. Classical Measurement Theory is the most used measurement theory in the social and behavioral sciences. In this article, the author uses Matrix Lie (Lee) group theory to formulate a measurement model. Symmetry is defined and illustrated using symmetries of the square. Then it is shown how a matrix group can represent the symmetries of the square. A brief introduction to Group Theory follows. Then four assumptions on which the Lie matrix group model of measurement is based are articulated. Formulation of the model follows. The notion of approximate symmetry is introduced, and a measure of approximate symmetry is proposed. It is shown CMT is a special case of the Lie matrix group model. A simulation is used to test invariances predicted from the Lie matrix group model. Finally, implications of this model are considered.