Multilevel component analysis.

A general framework for the exploratory component analysis of multilevel data (MLCA) is proposed. In this framework, a separate component model is specified for each group of objects at a certain level. The similarities between the groups of objects at a given level can be expressed by imposing constraints on component models of the groups using the approach adopted in simultaneous component analysis. The constraints used are based on the loading matrices and on the covariances of the component scores of each group. MLCA is related to three-way component analysis and to currently available multilevel structural equation models. It is shown that the latter are less flexible than MLCA. The use of MLCA is illustrated by means of an empirical example.