Estimating Latent Variable Systems When Specification is Uncertain: Generalized Component Analysis and the Eliminant Method

Abstract

This article argues that, to relieve the specification difficulties that frequently accompany latent variable models, a first application should in most cases employ an estimator that makes no assumption about the nature of the unobservables. The two possibilities are generalized component analysis, with the unobservables treated as incidental parameters; and the eliminant method, where they are removed by transformation of the model before estimation. It is shown that these are equivalent, whichever transformation is used, but that the latter has substantial practical advantages.