Factor Score Estimation from the Perspective of Item Response Theory

Abstract

The factor scores of confirmatory factor analysis (CFA) models and the latent variables of item response theory (IRT) models are similar statistical entities, so one would expect that their estimation or characterization would follow parallel tracks in CFA and IRT. However, historically they have not. Different procedures have been used to derive factor score estimates and latent variable estimates in IRT, and different computational procedures have been the result. In this chapter we approach factor score estimation for some simple CFA models from the perspective of IRT, with the kinds of graphics that are used to explain IRT estimates of proficiency, and the computational procedures that are used in test theory. We compare traditional “regression” and “Bartlett” factor score estimates with alternative computational approaches to likelihood-based factor score estimates, referring to the expected a posteriori and maximum likelihood estimates of IRT latent variables to clarify relations among the scores. This provides insights into the ways in which the data are combined into factor score estimates. The results provide an alternative method to compute factor scores in some simple models in the presence of observations that may be missing at random for some variables.