TRICAP edition:7 location:Brugge date:2-7 June 2012
Many studies yield multivariate multiblock data, that is, multiple data blocks that all involve the same set of variables (e.g., the scores of different groups of subjects on the same set of variables). The question then rises whether or not the same processes underlie the different data blocks. To explore the structure of such multivariate multiblock data, component analysis can be very useful. Specifically, two approaches are often applied: principal component analysis (PCA) on each data block separately and different variants of simultaneous component analysis (SCA) on all data blocks simultaneously. The PCA approach yields a different loading matrix for each data block and is thus not useful for discovering structural similarities. The SCA approach may fail to yield insight into structural differences, since the obtained loading matrix is identical for all data blocks. Recently, we introduced a new generic modeling strategy, called Clusterwise SCA (De Roover et al., 2012) that comprises the separate PCA approach and SCA as special cases. Clusterwise SCA classifies the data blocks into a number of mutually exclusive clusters on the basis of their underlying structure. Data blocks that belong to the same cluster are modeled using the same loadings, and the loadings may differ across the clusters. In this presentation, we discuss different members of the Clusterwise SCA family: the original Clusterwise SCA-ECP method (De Roover et al., 2012) which imposes Equal Cross-Product constraints on the component scores of the data blocks within a cluster, the more general Clusterwise SCA-P method (De Roover, Ceulemans, Timmerman, & Onghena, 2012) which allows for within-cluster differences in variances and correlations of component scores, as well as model adaptations for letting the number of components vary across clusters and for requiring some of the components to be common to all (clusters of) data blocks.