A clusterwise simultaneous component method for capturing within‐cluster differences in component variances and correlations

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 finer‐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.