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 replications design. The computations employ a two-stage least squares solution that is based on a sequential application of the Eckart and Young (1936) decomposition. Second, relatively homogeneous 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" interpretation of multidimensional scaling. Depending upon the model chosen, the independent contribution of elevation, scatter, and shape parameters may be differentiated in defining profile similarity