British Journal of Mathematical and Statistical Psychology vol:66 issue:1 pages:81-102
This paper presents a clusterwise simultaneous component analysis for tracing structural differences and similarities between data of different groups of subjects. This model partitions the groups into a number of clusters according to the covariance structure of the data of each group and performs a Simultaneous Component Analysis with invariant Pattern restrictions (SCA-P) for each cluster. These restrictions imply that the model allows for between-group differences in the variances and the correlations of the cluster-specific components. As such, Clusterwise SCA-P is more flexible than the earlier proposed Clusterwise SCA-ECP model, which imposed Equal average Cross-Products constraints on the component scores of the groups that belong to the same cluster. Using Clusterwise SCA-P, a more fine-grained, yet parsimonious picture of the group differences and similarities can be obtained. An algorithm for fitting Clusterwise SCA-P solutions is presented and its performance is evaluated by means of a simulation study. The value of the model for empirical research is illustrated with data from psychiatric diagnosis research.