COPS in Action: Exploring Structure in the Usage of the Youth Psychotherapy MATCH

This article is an introduction to Cluster Optimized Proximity Scaling (COPS) aimed at practitioners, as well as a tutorial on the usage of the corresponding R package cops. COPS is a variant of multidimensional scaling (MDS) that aims at providing a clustered configuration while still representing multivariate dissimilarities faithfully. It subsumes most popular MDS versions as special cases. We illustrate the ideas, use, flexibility and versatility of the method and the package with data from clinical psychology on how modules of the Modular Approach to Therapy for Children (MATCH) are used by clinicians in the wild. We supplement the COPS analyses with density-based hierarchical clustering in the original space and faceting with support vector machines. We find that scaling with COPS gives a sensible and insightful spatial arrangement of the modules, allows easy identification of clusters of modules and provides clear facets of modules corresponding to the MATCH protocols. In that respect COPS works better than both standard MDS and clustering.