A perfect match between a model and a mode

Abstract

When the partial least squares estimation methods, the “modes,” are applied to the standard latent factor model against which methods are designed and calibrated in PLS, they will not yield consistent estimators without adjustments.We specify a different model in terms of observables only, that satisfies the same rank constraints as the latent variable model, and show that now mode B is perfectly suitable without the need for corrections. The model explicitly uses composites, linear combinations of observables, instead of latent factors. The composites may satisfy identifiable linear structural equations, which need not be regression equations, estimable via 2SLS or 3SLS. Each time practitioners contemplate the use of PLS’ basic designmodel the compositesmodel is a viable alternative. The chapter is conceptual mainly, but a small Monte Carlo study exemplifies the feasibility of the new approach.