Two-level analysis of covariance structures for unbalanced designs with small level-one samples

The main purpose of this paper is to develop basic statistical theory for two-level analysis of covariance structures. Major asymptotic results for statistical inference, such as the asymptotic distributions of the estimator and the goodness-of-fit test statistic are derived, based on an unbalanced design with only small numbers of level-one units. Computationally, it is shown that the solution can be obtained via standard programs, such as LISREL, EQS and COSAN. The behaviour of the estimates is illustrated by an artificial example and a real-life example. Some possibilities of extending the results to a more general two-level model, and to situations with arbitrary distributions and elliptical distributions are also investigated.