Hierarchical Linkage Analysis for the Isolation of Types

ELEMENTARY linkage analysis (McQuitty, 1957b) is a rapid method for the isolation of types, but it results in a first-level classification only. Agreement analysis (McQuitty, 1956), on the other hand, classifies into successive levels such as species, genera, families, etc., but it has the disadvantage of being prohibitively laborious if performed by pencil and paper on other than a small matrix; large matrices require an electronic computer and even then the analyses are relatively laborious. Typological studies, which have classified subjects objectively into types on the basis of major patterns of responses, indicate that there are many psychological types and that large sets of data are essential to isolate them (McQuitty, 1957a). A method of analysis which would enable investigators to analyze large matrices into hierarchical types, as illustrated in Chart 1, is needed. This paper develops and illustrates such a method. It can be performed by pencil and paper on even relatively large matrices. Definitions Hierarchical linkage analysis is an elaboration of elementary linkage analysis. Both methods start with tables of interassociation between individuals, such as a matrix of intercorrelations or agree-ment scores (McQuitty, 1956). Elementary linkage analysis utilizes the concepts of reciprocal pairs, where a pair ij is reciprocal if and only if the index of associa-tion, aij, is the highest a for all pairs in which either i or j occurs. Analogously, hierarchical linkage analysis uses the concept of re-ciprocal combinations, where the latter term means a combination