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 used EM algorithm is utilized to obtain the solution. Expressions for the E-step are derived and it is shown that the complex optimization of the M-step can be completed conveniently with existing software. Some accelerated procedures such as the EM gradient algorithm and the Quasi-Newton EM algorithm are modified to improve the convergence rate of the basic EM algorithm. Results from simulation studies and analysis of examples illustrate the features and potential of the EM approach.
Key words and phrases: EM gradient algorithm, EQS, information matrix, latent random vectors, LISREL.