Statistica Sinica

Sik-Yum Lee and Wai-Yin Poon

Abstract:In this paper, the maximum likelihood estimation of a general two-level structural equation model with an unbalanced design is formulated as a missing data problem by treating the latent random vectors at the group level as hypothetical missing data. The commonly usedEMalgorithm is utilized to obtain the solution. Expressions for theE-step are derived and it is shown that the complex optimization of theM-step can be completed conveniently with existing software. Some accelerated procedures such as theEMgradient algorithm and the Quasi-NewtonEMalgorithm are modified to improve the convergence rate of the basicEMalgorithm. Results from simulation studies and analysis of examples illustrate the features and potential of theEMapproach.

Key words and phrases:EMgradient algorithm, EQS, information matrix, latent random vectors, LISREL,