Latent Variable Estimation in Factor Analysis and Item Response Theory

Abstract

This essay sketches the historical development of latent variable scoring procedures in the item response theory (IRT) and factor analysis literatures, observing that the most commonly used score estimates in both traditions are fundamentally the same; only methods of calculation differ. Different procedures have been used to derive factor score estimates and latent variable estimates in IRT, and different computational procedures have been the result. Due to differences in the context of score usage, challenges have led to different solutions in the IRT and factor analytic traditions. The needs for bias corrections differ, as do the corrections that have been proposed. While the standard factor analysis model has naturally Gaussian likelihoods, IRT does not, but in IRT normal approximations have been used in various contexts to make the IRT computations more like those of factor analysis. Finally, factor analysis alone has been the home of decades of controversy over factor score indeterminacy, while IRT has not, even though the scores in question are the same. That is an artifact of history and the ways the models have been written in the IRT and factor analytic literatures. IRT has never been plagued with questions of indeterminacy, which helps to clarify the position that what is referred to as indeterminacy is not a problem.