Constrained maximum likelihood estimation of two-level covariance structure model via EM type algorithms

In this paper, the constrained maximum likelihood estimation of a two-level covariance structure model with unbalanced designs is considered. The two- level model is reformulated as a single-level model by treating the group l evel latent random Vectors as hypothetical missing-data. Then, the popular EM algorithm is extended to obtain the constrained maximum likelihood estim ates. For general nonlinear constraints, the multiplier method is used at t he M-step to find the constrained minimum of the conditional expectation. A n accelerated EM gradient procedure is derived to handle linear constraints . The empirical performance of the proposed EM type algorithms is illustrat ed by some artifical and real examples.