Maximizing the information and validity of a linear composite in the factor analysis model for continuous item responses

Abstract

This paper develops results and procedures for obtaining linear composites of factor scores that maximize: (a) test information, and (b) validity with respect to external variables in the multiple factor analysis (FA) model. I treat FA as a multidimensional item response theory model, and use Ackerman’s multidimensional information approach based on maximum likelihood (ML) estimation of trait levels. This approach, when applied to the FA model, leads to particularly simple results as far as maximizing test information is concerned. Developments concerned with validity appear to be new, and I use ML results in the context of error-in-variables regression. Graphical procedures for representing both type of results are proposed. The developments are illustrated with two empirical examples in personality measurement