Structured correlation in models for clustered data.

Correlation is always a concern in the analysis of clustered data. One area of interest is to develop a general correlation modelling approach for high dimensional data with unbalanced hierarchical and heterogeneous data structures, e.g. multilevel data. Commonly used correlation structures might have limitation for such situations. In this paper, we propose two extensions, multiblock and multilayer correlations. These methods are very flexible in modelling correlation and can be incorporated in many multivariate approaches, while the major discussion focuses on the applications under the generalized estimating equations (GEE) methods. The approaches are especially useful in GEE when each cluster is large and complex but the number of clusters is small. If an incorrect correlation is applied to such data, the results are less efficient. Multiblock and multilayer correlations extend GEE methods to model complicated multilevel data with arbitrary number of levels and cluster size. The extended estimating equation for correlation parameters has an orthogonal property, and the computation is very efficient. A simulation study compares the conventional methods versus the proposed methods, and it shows the gain in relative efficiency and the flexibility in modelling various structures.