Modeling differences in the dimensionality of multiblock data by means of clusterwise simultaneous component analysis

Given multivariate multiblock data (e.g., subjects nested in groups are measured on multiple variables), one may be interested in the nature and number of dimensions that underlie the variables, and in differences in dimensional structure across data blocks. To this end, clusterwise simultaneous component analysis (SCA) was proposed which simultaneously clusters blocks with a similar structure and performs an SCA per cluster. However, the number of components was restricted to be the same across clusters, which is often unrealistic. In this paper, this restriction is removed. The resulting challenges with respect to model estimation and selection are resolved.