On the Correctness of the Computational Problem of Composite Indices Construction

Abstract

The computation composite indices of a poorly formalized system, based on data containing errors, can be considered as a problem signal-to-noise discrimination. The signal in this case is the weight coefficients of the linear convolution of indicators. The weights to be determined should reflect the structure of the system being evaluated. The successful application of principal component analysis in different systems structure description allows us to suggest that the method will also provide adequate results to describe social systems. However, principal component analysis and factor analysis determine the structure of principal components and principal factors differently for different observations. The reason for this may be the presence of inevitable errors in the used data. As a method of avoiding this, a modification of the principal component analysis method is proposed, taking into account the presence of errors in the data used. A solution of the problem requires a detailed understanding of input data errors’ influence on the calculated model’s parameters. Therefore, the question of the problem correctness is essential. A clarification of the concept of computation a system’s quality changes composite index problem correctness is proposed. The consequence of the stability is on average a slight change (increment) of objects Rank for different measurements. This increment can be estimated a posteriori using a number of observations of the proposed variance criterion. The results of different composite index evaluation stability according to this criterion are presented. The integral indicators computed using the author's method have a good stability.

Keywords

• composite index
• data error
• principal component analysis
• correctness and stability of composite index
• rank robustness tests