The Use of the Incomplete Tetrad Method for Measuring the Similarities in Nonmetric Multidimensional Scaling

Research background: So far, many methods of direct measurement of similarity in multidimensional scaling have been developed (e.g. ranking, sorting, pairwise comparison and others). The method selection affects the subjective feelings of the respondents, i.e. fatigue, weariness resulting from making numerous assessments, or difficulties in expressing similarity assessments.

Purpose: In the proposed method, for all four-element sets (tetrads) of objects a respondent is asked to pick out the most similar and the least similar pair. Because the number of tetrads increases very rapidly with the number of objects, the aim of the study is to indicate the possibility of measuring similarities based on the reduced number of tetrads.

Research methodology: In order to make scaling results independent from respondents’ subjective effects the analysis was made on the basis of the given distance matrix. To construct perceptual maps based on tetrads, multidimensional scaling with the use of the MINISSA program was performed. The quality of matching the resulting points configuration to the configuration determined based on the distance matrix was tested by a Procrustes statistic.

Results: It was demonstrated that the choice of the incomplete set of tetrads has no significant effect on the results of multidimensional scaling, even when all pairs of objects in tetrads cannot be presented equally frequently.

Novelty: An original method for calculating similarities in nonmetric multidimensional scaling.