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Statistica Sinica 11(2001), 135-145



ASYMPTOTIC THEORY OF TWO-LEVEL STRUCTURAL

EQUATION MODELS WITH CONSTRAINTS


Wenyang Zhang and Sik-Yum Lee


The London School of Economics and Political Science

and The Chinese University of Hong Kong


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 example.



Key words and phrases: Asymptotic distribution, goodness-of-fit statistic, maximum likelihood, two-level structural equation models.



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