Complex index of a system’s quality for a set of observations

Abstract

This paper discusses the solution to the problem of constructing latent complex indexes of a change in a system’s quality for several observations in the absence of training. The algorithm for constructing complex indexes is implemented with the definition of non-random variables of the principal component characterizing the structure of the system under discussion. The algorithm uses a new approach to choose the principal component number, determine the weights of the considered variables and subsystems, and to determine the information content of the complex index based on the selected signal-to-noise ratio parameter. The algorithm was used to obtain complex indexes of quality of life for Russia’s constituent entities for 2007-2016.

The Use of Composite Quality of Life Indices for the Assessment of the Territorial Differentiation of Regions of the Russian Federation

“…Another major point of criticism with the use of multivariate analysis methods to obtain the weights of composite indices is the lack of socio-economic interpretation of the resulting weights [12][13][14] and the instability of computed composite indices [15,16]. The author of this study proposed a modification of the PCA, which determines the weight coefficients (1) as characteristics of the structure of the evaluated system based on a number of observations [17,18]. The interpretation of weight coefficients as characteristics of the structure of a system solves one of the main problems in the construction of composite indices, when the expert assessment of the importance of a variable differs significantly from the calculated weights [15,16].…”