Matrices with special reference to applications in psychometrics

Abstract

Multidimensional scaling, item response theory, and factor analysis may be considered three major contributions of psychometricians to statistics. Matrix theory played an important role in early developments of these techniques. Unfortunately, nonlinear models are currently very prevalent in these areas. Still, one can identify several areas of psychometrics where matrix algebra plays a prominent role. They include analysis of asymmetric square tables, multiway data analysis, reduced-rank regression analysis, and multiple-set ( T-set) canonical correlation analysis among others. In this article we review some of the important matrix results in these areas and suggest future studies.