An investigation of assignment rules for fitting new subjects into clusters established by hierarchical pattern analysis

Abstract

Cluster analysis has been used fairly extensively as a means of grouping objects or subjects on the basis of their similarity over a number of variables. Almost all of the work to this point has been for the purpose of classifying an extant collection of similar objects into clusters or types. However, there often arises a need for methods of identifying additional objects as members of clusters that have already been established. Discriminant function analysis has been used for this purpose even though its underlying assumptions often cannot be met.

This study explored a different approach to the problem, namely, the use of distance functions as a means of identifying subjects as members of types which had been established by hierarchical pattern analysis. A sample of subjects was drawn randomly from a population; these subjects were assigned to the types that appeared in other samples that were drawn from the same population. Each type was defined by the vector of mean scores on selected variables for the subjects in that cluster. A new subject was identified as a member of a type if the distance function described by the assignment rule was a minimum for that type. Various criteria were established for judging the adequacy of the assignments.

Five distance functions were identified as being potential ways of assigning new subjects to types. Recommendations were not made for immediate practical application. However, the results were generally positive, and successful applications should be possible with the suggested methodological refinement.