Asymptotic theory of two-level structuralequation model with constrained conditions

Abstract

In the context of a general two-level structural equation model with an unbalanced design and small samples at the individual levels, maximum likelihood theory is developed for estimation of the unknown parameters subject to functional constraints. It is shown that the constrained maximum likelihood estimates are consistent and asymptotically normal. A goodness-of-fit statistic is established to test the validity of the constraints. The asymptotic results are illustrated with an exampl