Synergy of factor analysis based on multiplicative index models and graph theory

Abstract

This article addresses the issues of solving the problems of factor analysis using the concepts of graph theory.Factor analysis, a section of multivariate statistical analysis combining mathematical and statistical methods to reduce the dimension of the studied multivariate trait, was important in statistical research.The index method of factor analysis was used in the study of the development of socio-economic systems and the adoption of appropriate policy decisions. This method provides for the use of indices - in terms of indicators, represented in the form of ratios, i.e. in dimensionless values. Thus, indices are peculiar mathematical models of the investigated processes and phenomena. Indexes and index models are the new categories used in the index method of factor analysis.Factor analysis is used to identify internal non-measurable patterns in various fields of science. The technique for conducting factor analysis is determined by the initial task.The central problem of the index method of factor analysis is that the end result of estimating factor increments in the mode depends on the order of the multiplier indices.In turn, graph theory is one of the most extensive sections of discrete mathematics, widely used in solving economic and managerial problems and other fields of knowledge.To visually display the order of the factors in the model, you can use the graphoanalytic method, which allows you to present a mathematical factor multiplicative model in the form of gras, which, in turn, allows you to identify the influence of individual factors on the effective indicator.This article explores the problem of using graph theory in solving the problems of factor analysis, which allows for corresponding generalizations, considering all the many possible solutions, including the influence of the order of the partial indices on the factors under consideration.