Milligan presented the conditions that are required for a hierarchical clustering strategy to be monotonic, based on a formula by Lance and Williams. The statement of the conditions is improved and shown to provide necessary and sufficient conditions. (Author/GK)

Hierarchical and non-hierarchical tree structures as models of similarity data are proposed and procedures for fitting both types of trees to data are discussed. Trees are viewed as intermediate between multidimensional scaling and simple clustering. Multiple tree structures and hybrid models are discussed and examples are presented. (Author/JKS)

Nonmetric multidimensional scaling and hierarchical clustering procedures are applied to a confusion matrix of numerals. Two dimensions were interpreted: straight versus curved, and locus of curvature. Four major clusters of numerals were developed. (Author/JKS)

A strategy for reordering the hierarchical tree structure is presented. While the order of terminal nodes of Johnson's procedure is arbitrary, this procedure will rearrange every triad of nodes under a common least upper node so that the middle node is nonarbitrarily closest to the anchored node. (Author/CTM)

Three dissimilarity measures for the unconstrained sorting task are investigated. All three are metrics, but differ in the kind of compensation which they make for differences in the sizes of cells within sortings. Empirical tests of the measures are done with sorting data for occupations names and the names of behaviors, using multidimensional…

Tree representations of similarity data are investigated. Hierarchical clustering is critically examined, and a more general procedure, called the additive tree, is presented. The additive tree representation is then compared to multidimensional scaling. (Author/JKS)

A method based on homogeneity analysis (multiple correspondence analysis or multiple scaling) is proposed to reduce many categorical variables to one variable with "k" categories. The method is a generalization of the sum of squared distances cluster analysis problem to the case of mixed measurement level variables. (SLD)

Two-dimensional euclidean planes and additive trees are two of the most common representations of proximity data for multidimensional scaling. Guidelines for comparing these representations and discovering properties that could help identify which representation is more appropriate for a given data set are presented. (Author/JKS)

A flexible data analysis approach is proposed that combines the psychometric procedures seriation and multidimensional scaling. The method, which is particularly appropriate for analysis of proximities containing temporal information, is illustrated using a matrix of cocitations in publications by 18 presidents of the Psychometric Society.…

Introduces a new approach for partitioning test items into dimensionally distinct item clusters. The core of this approach is a new item-pair conditional-covariance-based proximity measure that can be used with hierarchical cluster analysis. The procedure can correctly classify, on average, over 90% of the items for correlations as high as 0.9.…

Measuring object similarity using the method of free clustering is gaining in popularity. Instructions are usually simple and since no structure is imposed on the subject's selection, response bias is reduced. More importantly, measures of object similarity derived from the judges' clustering can be adequately analyzed by the methods of…

A new computing algorithm, MAPCLUS (Mathematical Programming Clustering), for fitting the Shephard-Arabie ADCLUS (Additive Clustering) model is presented. Details and benefits of the algorithm are discussed. (Author/JKS)