Dimensions and Clusters: A Hybrid Approach to Classification

A hybrid strategy is described for integrating the dimensional and discrete clusters approaches to classification research. First, a parsimonious set of dimensions is sought through a multiple repli cations design. The computations employ a two- stage least squares solution that is based on a se quential application of the Eckart and Young (1936) decomposition. Second, relatively homo geneous subgroups are identified within this low dimensional space using a clustering or density search algorithm. To facilitate interpretation of the final solution, an ideal type concept is introduced that is similar to the "idealized individual" inter pretation of multidimensional scaling. Depending upon the model chosen, the independent contri bution of elevation, scatter, and shape parameters may be differentiated in defining profile similarity.