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On the Problem of Correctness and Stability of Composite Indices of Complex Systems

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Modern Information Technology and IT Education (SITITO 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1201))

Abstract

The construction of the integral characteristic of the system 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. Composite index weights 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 for social systems description. 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 calculated using the author’s method have a good stability.

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References

  1. Klyatskin, V.I.: Integral characteristics: a key to understanding structure formation in stochastic dynamic systems. Phys. Usp. 54(5), 441–464 (2011). https://doi.org/10.3367/UFNe.0181.201105a.0457

    Article  Google Scholar 

  2. Bandura, R., del Campo, C.: Indices of National Performance: A Survey. Office of Development Studies, United Nations Development Programme, New York (2016)

    Google Scholar 

  3. Bandura, R.: A survey of composite indices. Measuring country performance: 2008 update. Technical report, Office of Development Studies, United Nations Development Programme (UNDP), New York (2008)

    Google Scholar 

  4. Bandura, R.: Composite indicators and rankings: inventory 2011. Technical report, Office of Development Studies, United Nations Development Programme (UNDP), New York (2011)

    Google Scholar 

  5. Nardo, M., Saisana, M., Saltelli, A., Tarantola, S. (eds.): Tools for composite indicators building. Ispra, Italy: Joint Research Centre – European Commission (2005)

    Google Scholar 

  6. Foa, R., Tanner, J.C.: Methodology of the Indices of Social Development. ISD Working Paper Series, vol. 4, pp. 1–66 (2012). http://hdl.handle.net/1765/50510

  7. Saltelli, A., Munda, G., Nardo, M.: From complexity to multidimensionality: the role of composite indicators for advocacy of EU reform. Tijdschrift vor Economie en Management L1(3), 221–235 (2006)

    Google Scholar 

  8. Sharpe, A.: Literature Review of Frameworks for Macro-indicators. CSLS Research Reports 2004-03. Centre for the Study of Living Standards, Ottawa, Canada (2004). http://www.csls.ca/reports/LitRevMacro-indicators.pdf

  9. Nicoletti, G., Scarpetta, S., Boylaud, O.: Summary indicators of product market regulation with an extension to employment protection legislation. Economics department working papers No. 226, ECO/WKP(99)18 (2000). https://www.oecd.org/eco/outlook/1880867.pdf

  10. Saltelli, A.: Composite Indicators between analysis and advocacy. Soc. Indic. Res. 81(1), 65–77 (2007). https://doi.org/10.1007/s11205-006-0024-9

    Article  Google Scholar 

  11. Nardo, M., Saisana, M., Saltelli, A., Tarantola, S., Hoffman, A., Giovannini, E.: Handbook on Constructing Composite Indicators: Methodology and User Guide. OECD Publication, Paris (2008)

    Google Scholar 

  12. Tarantola, S., Saisana, M., Saltelli, A.: Internal Market Index 2002: Technical details of the methodology. JRC European Commission. Institute for the Protection and Security of the Citizen Technological and Economic Risk Management Unit I-21020 Ispra (VA), Italy (2002). https://www.ec.europa.eu/internal_market/score/docs/score11/im-index-2002_en.pdf

  13. Hightower, W.L.: Development of an index of health utilizing factor analysis. Med. Care 16(3), 245–255 (1978). https://doi.org/10.1097/00005650-197803000-00006

    Article  Google Scholar 

  14. McKenzie, D.J.: Measuring inequality with asset indicators. J. Popul. Econ. 18(2), 229–260 (2005). https://doi.org/10.1007/s00148-005-0224-7

    Article  Google Scholar 

  15. Vyas, S., Kumaranayake, L.: Constructing socio-economic status indices: how to use principal components analysis. Health Policy Plann. 21(6), 459–468 (2006). https://doi.org/10.1093/heapol/czl029

    Article  Google Scholar 

  16. Lindman, C., Sellin, J.: Measuring Human Development. The Use of Principal Component Analysis in Creating an Environmental Index. University essay from Uppsala universitet, Uppsala (2011). http://www.diva-portal.org/smash/get/diva2:464378/FULLTEXT03

  17. Somarriba, N., Pena, B.: Synthetic indicators of quality of life in Europe. Soc. Indic. Res. 94(1), 115–133 (2009). https://doi.org/10.1007/s11205-008-9356-y

    Article  Google Scholar 

  18. Ajvazjan, S.A.: Empirical analysis of the population’s life quality synthesized categories. Econ. Math. Methods 39(3), 19–53 (2003). https://elibrary.ru/item.asp?id=17299169. (in Russian)

  19. Zhgun, T.V.: Constructing the integral characteristic of the system quality changes on the basis of statistical data as a solution to the problem of signal allocation under conditions of prior uncertainty. Vestnik Yaroslav Wise Novgorod State Univ. (81), 10–16 (2014). https://elibrary.ru/item.asp?id=22777430. (in Russian)

  20. Strizhov, V.V., Shakin, V.V.: Coordination of expert assessments. In: Proceedings of 10th Russ. Simp. Mathematical Methods of Pattern Recognition, Moscow, pp. 137–138 (2001). http://strijov.com/papers/mmro10.pdf. (in Russian)

  21. Kuznetsov, M.P., Strijov, V.V.: Integral indicator construction using rank-scaled design matrix. In: Proceedings of the International conference “Intelligent Information Processing” IIP-9, Montenegro, Budva, pp. 130–132 (2012). http://strijov.com/papers/Kuznetsov2012IOI.pdf. (in Russian)

  22. Puzachenko, Yu.G., Onufrenia, I.A., Aleshcenko, G.M.: Multidimentional analyses of relief structure (principle components method). Izvestiya RAN (Akad. Nauk SSSR). Seriya Geograficheskaya (1), 26–36 (2004). https://elibrary.ru/item.asp?id=17636361. (in Russian)

  23. Oddershede, J., Nielsen, K., Stahl, K.: Using X-ray powder diffraction and principal component analysis to determine structural properties for bulk samples of multiwall carbon nanotubes. Zeitschrift für Kristallographie - Crystalline Materials 222(3–4), 186–192 (2007). https://doi.org/10.1524/zkri.2007.222.3-4.186

    Article  Google Scholar 

  24. da Silva, J.P.B., Ramos, M.N.: Principal component analysis of molecular geometries of cis- and trans-C2H2X2. J. Braz. Chem. Soc. 15(1), 43–49 (2004). https://doi.org/10.1590/s0103-50532004000100009

    Article  Google Scholar 

  25. Li, W., Zhong, Y., Yu, D., Qu, D., Sun, B., Li, M., Liu, J.: Application of principal component analysis for identification of drugs packed in anthropomorphic phantom. ARPN J. Eng. Appl. Sci. 7(7), 915–921 (2012). https://arpnjournals.com/jeas/research_papers/rp_2012/jeas_0712_740.pdf

  26. Teslyuk, A.B., Senin, R.A., Ilyin, V.A.: Applying principal component analysis for macromolecular objects diffraction images sorting. Math. Biol. Bioinform. 8(2), 708–715 (2013). https://doi.org/10.17537/2013.8.708. (in Russian)

    Article  Google Scholar 

  27. Rao, C.R.: Linear Statistical Inference and Its Applications, 2nd edn. Wiley, Hoboken (1973)

    Book  Google Scholar 

  28. Isenmann, A.J.: Modern Multivariate Statistical Techniques. Regression, Classification and Manifold Learning. Springer, New York (2008). https://doi.org/10.1007/978-0-387-78189-1

    Book  Google Scholar 

  29. Ajvazjan, S.A.: Integrated Indicators of the Quality of Life: Their Construction and Use in Social and Economic Management and Interregional Comparisons. CJeMI RAN, Moscow (2000). (in Russian)

    Google Scholar 

  30. Ajvazjan, S.A.: Towards a methodology of measuring of the population’s life quality synthesized categories. Econ. Math. Methods 39(2), 33–53 (2003). https://elibrary.ru/item.asp?id=17293598. (in Russian)

  31. Hadamard, J.: Le probleme de Cauchy et les eguations aux derives particlee lineaires hyperbolique. Hermann, Paris (1932)

    Google Scholar 

  32. Tikhonov, A.N., Arsenin, V.Ya.: Methods for Solving Ill-Posed Problems. Nauka, Moscow (1986). (in Russian)

    Google Scholar 

  33. Tikhonov, A.N., Goncharsky, A.V., Stepanov, V.V., Yagola, A.G.: Regularizing Algorithms and A Priori Information. Nauka, Moscow (1988). (in Russian)

    Google Scholar 

  34. Saltelli, A., Ratto, M., Andres, T., Campolongo, F.: Global Sensitivity Analysis: The Primer. Wiley (2008). https://doi.org/10.1002/9780470725184

  35. Huergo, L., Münnich, R., Saisana, M.: Robustness Assessment for Composite Indicators with R. The second international conference useR! Vienna, Austria (2006). https://www.r-project.org/conferences/useR-2006/Abstracts/Huergo+Munnich+Saisana.pdf

  36. Saltelli, A., Annoni, P., Azzini, I., Campolongo, F., Ratto, M., Tarantola, S.: Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Comput. Phys. Commun. 181(2), 259–270 (2010). https://doi.org/10.1016/j.cpc.2009.09.018

    Article  MathSciNet  MATH  Google Scholar 

  37. Woodward, P.M.: Probability and Information Theory with Applications to Radar. Pergamon Press, London (1955)

    Google Scholar 

  38. Zhgun, T.V.: Building an integral measure of the quality of life of constituent entities of the Russian Federation using the principal component analysis. Econ. Soc. Changes Facts Trends Forecast 10(2), 214–235 (2017). https://doi.org/10.15838/esc/2017.2.50.12. (in Russian)

    Article  Google Scholar 

  39. Zhgun, T.V.: An algorithm for constructing integral quality indicator of complex systems for a sequence of observations. Bull. South Ural State Univ. Ser. Comput. Math. Softw. Eng. 6(1), 5–25 (2019). https://doi.org/10.14529/cmse170101. (in Russian)

    Article  Google Scholar 

  40. Golyandina, N.E., Usevich, K.D., Florinsky, I.V.: Singular spectrum analysis for filtering of digital terrain models Geodesy Cartography (5), 21–28 (2008). https://elibrary.ru/item.asp?id=11516739. (in Russian)

  41. Gaydamak, I.V., Khokhlov, A.G.: Modelling of integral indexes of life quality for the south of Tyumen region. Tyumen State Univ. Herald. Phys. Math. Model. Oil Gas Energy (6), 176–186 (2009). https://elibrary.ru/item.asp?id=13287475. (in Russian)

  42. Ajvazjan, S.A., Stepanov, V.S., Kozlova, M.I.: Measurement of synthetic categories of quality of life of the population of the region and identify key areas of improvement in socio-economic policy (in the Samara region and its municipalities an example. Appl. Econ. 2(2), 18–84 (2006). https://elibrary.ru/item.asp?id=9482361

  43. Foster, J.E., McGillivray, M., Seth, S.: Rank Robustness of Composite Indices: Dominance and Ambiguity. OPHI Working Papers 26b. University of Oxford (2012)

    Google Scholar 

  44. Seth, S., McGillivray, M.: Composite Indices, Alternative Weights, and Comparison Robustness. OPHI Working Paper 106. University of Oxford (2016)

    Google Scholar 

  45. Human Development Reports 1990–2014. United Nations Development Programme (1990–2014). http://hdr.undp.org/en/reports/. Accessed 7 Sept 2018

  46. Sustainable Society Index. http://www.ssfindex.com/data-all-countries. Accessed 20 May 2019

  47. Environmental Performance Index. http://epi.yale.edu/reports/2016-report. Accessed 6 June 2019

  48. Environmental Performance Index. https://epi.envirocenter.yale.edu/downloads/epi2018policymakerssummaryv01.pdf. Accessed 6 June 2019

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Authors and Affiliations

  1. Yaroslav-the-Wise Novgorod State University, Bolshaya St. Petersburg Str. 41, 173003, Velikiy Novgorod, Russia

    Tatyana Zhgun, Aleksandr Lipatov & German Chalov

Authors
  1. Tatyana Zhgun
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  2. Aleksandr Lipatov
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  3. German Chalov
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Correspondence to Tatyana Zhgun .

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Editors and Affiliations

  1. Moscow State University, Moscow, Russia

    Vladimir Sukhomlin

  2. Moscow State University, Moscow, Russia

    Elena Zubareva

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Zhgun, T., Lipatov, A., Chalov, G. (2020). On the Problem of Correctness and Stability of Composite Indices of Complex Systems. In: Sukhomlin, V., Zubareva, E. (eds) Modern Information Technology and IT Education. SITITO 2018. Communications in Computer and Information Science, vol 1201. Springer, Cham. https://doi.org/10.1007/978-3-030-46895-8_21

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  • DOI: https://doi.org/10.1007/978-3-030-46895-8_21

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