The Appropriateness of Sum Scores as Estimates of Factor Scores in the Multiple Factor Analysis of Ordered-Categorical Responses

Abstract

Unit-weight sum scores (UWSSs) are routinely used as estimates of factor scores on the basis of solutions obtained with the nonlinear exploratory factor analysis (EFA) model for ordered-categorical responses. Theoretically, this practice results in a loss of information and accuracy, and is expected to lead to biased estimates. However, the practical relevance of these limitations is far from clear. In this article, we adopt an empirical view and propose indices and procedures (some of them new) for assessing the appropriateness of UWSSs in nonlinear EFA applications. A new automated approach for obtaining UWSSs that maximize fidelity and correlational accuracy is proposed. The appropriateness of UWSSs under different conditions and the behavior of the present proposal in comparison with other more common approaches are assessed with a simulation study. A tutorial for interested practitioners is presented using an illustrative example based on a well-known personality questionnaire. All the procedures proposed in the article have been implemented in a well-known noncommercial EFA program.