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 level latent random vectors as hypothetical missing-data. Then, the popular EM algorithm is extended to obtain the constrained maximum likelihood estimates. For general nonlinear constraints, the multiplier method is used at the M -step to find the constrained minimum of the conditional expectation. An accelerated EM gradient procedure is derived to handle linear constraints. The empirical performance of the proposed EM type algorithms is illustrated by some artifical and real examples.