The generalized approach to multidimensional scaling

Abstract

Often in the practice of solving economic problems, there is a need to analyze objects with properties that are measured in different non-metric scales. The most popular mathematical approach to processing properties is the multidimensional scaling method. There are metric and non-metric scaling. The most reasonable of them is the Torgerson metric method, but it is supposed to have metric scale input variables. The paper proposes a modified method of factor analysis, which allows non-metric data as input. The paper presents arguments that the proposed modification is an improvement of the method of multidimensional scaling. The proposed method is less time-consuming than the Torgerson method but is mathematically justified as well. So the mathematical explanation of the generalized multidimensional scaling method has been described. This approach broadens the range of possible ways to describe objects in economics by means of factors measured on different scales.