The Quality-of-Life Measurement with a Stochastic Choice of Parameters of the Weighted Principal Component

Alexey A. Mironenkov, Alexey N. Kurbatskii, Marina V. Mironenkova

Lomonosov Moscow State University Moscow, Russia

Abstract

The quality of life of the population is a latent category, and due to the impossibility of direct measurement it has to be assessed as an integral indicator of many variables. According to the established methodology, one of the main tools in this case is the first principal component, that is, a linear convolution of variables, which has the property of minimizing the variation of the original characteristics. The fact that parameters’ variation is taken into account with equal weight may cause criticism from economists. The use of a weighted principal component which is free of this drawback can be considered as a development of the initial method. In this case to minimize the total variation, the weighting coefficients of features are set expertly. However, in this case, a logical question arises: won’t expert subjectivity have a significant impact on the final integral indicator, as it happens in the case of simple linear convolution with expert weights? Thus, the purpose of this work is to test the applicability of the weighted first principal component as the main tool in constructing an integral indicator of the population quality of life. In particular, it is necessary to test the hypothesis that the influence of heterogeneity in the weights of expert assessments on the final integral indicator is insignificant. In this case, it would be useful not only to illustrate the presence or absence of this influence, but also to estimate its extent. To do this, the simulation modeling is carried out to assess the latent variable “quality of life of the population”, based on empirical expert weights and macro statistics data. Moreover, in contrast to most works related to the topic, the values of the integral indicator (and, accordingly, the ranking of observations) are presented as an interval estimate. In other words, the result is presented as a random variable where the element of randomness is the subjectivity of the expert choice of weights for the weighted principal component. It turns out that even in this case it is possible to obtain robust and meaningful results that are in good agreement with the conclusions of well-known research in this area.

Keywords

integral indicator; the quality of life; weighted first principal component; stochastic selection; simulation modeling; expert weights.

JEL classification

References

1. Ayvazyan, S.A. (2012). Quality of Life and Living Standarts Analysis (Econometric Approach). Moscow, Nauka, 432 p. (In Russ.). Available at: https://www.elibrary.ru/item.asp?id=26766525

         2. Ayvazyan, S.A., Isakin, M.A. (2006). Integral indicators of the quality of life of the population of the region as criteria for the effectiveness of socio-economic policy pursued by regional authorities. Applied Econometrics, Vol. 1, No. 1, 25–31. (In Russ.). Available at: https://www.elibrary.ru/item.asp?id=9510321

         3. Ayvazyan, S.A., Stepanov, V.S., Kozlova, M.I. (2006). Measuring synthetic categories of the quality of life of the population of the region and identifying key areas for improving socio-economic policy (using the example of the Samara region and its municipalities). Applied Econometrics, Vol. 2, No. 2, 18–84. (In Russ.). Available at: https://www.elibrary.ru/item.asp?id=9482361

         4. Makarov, V.L., Ayvazyan, S.A., Afanasyev, M.Yu., Bakhtizin, A.R., Nanavyan, A.M. (2014). Assessing the effectiveness of Russian regions taking into account intellectual capital, characteristics of readiness for innovation, level of well-being and quality of life of the population. Economy of Regions, No. 4, 9–30. (In Russ.). https://doi.org/10.17059/2014-4-1

         5. Ayvazyan S.A., Afanasyev, M.Yu., Kudrov, A.V. (2019). Indicators of the main directions of socio-economic development and their aggregates in the space of characteristics of regional differentiation. Applied Econometrics, Vol. 54, 51–69. (In Russ.). https://doi.org/10.24411/1993-7601-2019-10003

         6. Kurbatskii, A., Mironenkov, A. (2023), Estimating the Quality of Life Using Weighted Principal Components Method. Montenegrin Journal of Economics, Vol. 19, No. 1, 7–17. https://doi.org/10.14254/1800-5845/2023.19-1.1

         7. Volkova, M.I. (2010). Comparison of objectivist and subjectivist approaches to measuring synthetic latent categories of quality of life of the population: results of an empirical analysis of Russian data. Applied Econometrics, Vol. 19, No. 3, 62–90. (In Russ.). Available at: https://www.elibrary.ru/item.asp?id=15139171

         8. Shakleina, M.V., Volkova, M.I., Shaklein, K.I., Yakiro, S.R. (2020). Theoretical and methodological problems of measuring social comfort: results of empirical analysis based on Russian data. Economic and Social Changes: Facts, Trends, Forecast, Vol. 13, No. 5, 135–152. (In Russ.). https://doi.org/10.15838/esc.2020.5.71.8

         9. Leshchaikina, M.V. (2014). Cross-country econometric analysis of the social comfort of living of the population. Applied Econometrics, Vol. 36, No. 4, 102–117. (In Russ.). Available at: https://www.elibrary.ru/item.asp?id=22782724

         10. Volkova, M. (2018). On the methodological foundations of quality of life analysis. The historical aspect. Society and Economics, No. 10, 89–100. (In Russ.). https://doi.org/10.31857/S020736760002281-8

         11. Mironenkov, A.A. (2020). Hierarchical Pareto classification of Russian regions according to indicators of the quality of life of the population. Economic and Social Changes: Facts, Trends, Forecast, Vol. 13, No. 2, 171–185. (In Russ.). https://doi.org/10.15838/esc.2020.2.68.11

         12. Ayvazyan S.A., Afanasyev, M.Yu., Kudrov, A.V. (2019). Integral indicator of the quality of living conditions. Digital Economy, No. 1, 43–56. (In Russ.). https://doi.org/10.34706/DE-2019-01-05

         13. Ayvazyan S.A., Afanasyev, M.Yu., Kudrov, A.V. (2016). A method for clustering regions of the Russian Federation taking into account the sectoral structure of GRP. Applied Econometrics, Vol. 41, No. 1, 24–46. (In Russ.). Available at: https://www.hse.ru/mirror/pubs/share/421012695.pdf

         14. Blomquist, G.C., Berger, M.C., Hoehn, J.P. (1988). New estimates of quality of life in urban areas. The American Economic Review, Vol. 78, No. 1, 89–107. Available at: https://www.jstor.org/stable/pdf/1814700

         15. Belyaeva, L.A. (2018). Quality of life in subjective assessments of the population: Russia in the European context. RUDN Journal of Sociology, Vol. 18, No. 4, 680–694. (In Russ.). https://doi.org/10.22363/2313-2272-2018-18-4-680-694

         16. Zhgun, T.V. (2017). Construction of an integral characteristic of the quality of life of the constituent entities of the Russian Federation using the principal component method. Economic and Social Changes: Facts, Trends, Forecast, Vol. 10, No. 2, 214–235. (In Russ.). https://doi.org/10.15838/esc/2017.2.50.12

         17. Fantazzini D., Shakleina M., Yuras N. (2018). Big Data for computing social well-being indicators of the Russian population. Applied Econometrics, Vol. 50, 43–66. Available at: https://ssrn.com/abstract=3215502

         18. Greco, S., Ishizaka, A., Tasiou, M., Torrisi, G. (2019). On the Methodological Framework of Composite Indices: A Review of the Issues of Weighting, Aggregation, and Robustness. Social Indicators Research, Vol. 141, 61–94. https://doi.org/10.1007/s11205-017-1832-9

         19. Volkova, M.I. (2019). Analysis of factors in the quality of life of the population of Russia and Europe within the framework of the generalized principal components method. Economics and Mathematical Methods, Vol. 55, No. 3, 34–46. (In Russ.). https://doi.org/10.31857/S042473880004678-4

         20. Slottje, D.J. (1991). Measuring the quality of life across countries. The Review of Economics and Statistics, Vol. 74, No. 3, 684–693. https://doi.org/10.2307/2109407

         21. Mazziotta, M., Pareto, A. (2019). Use and Misuse of PCA for Measuring Well-Being. Social Indicators Research, Vol. 142, 451–476. https://doi.org/10.1007/s11205-018-1933-0

         22. Rodchenkov, M.V. (2023). Assessing the satisfaction of the Russian investment community with the quality of financial reporting according to international standards. Journal of Applied Economic Research, Vol. 22, No. 1. 165–189. (In Russ.). https://doi.org/10.15826/vestnik.2023.22.1.008

         23. Litvintseva, G.P., Shmakov, A.V., Stukalenko, E.A., Petrov, S.P. (2019). Assessment of the digital component of the quality of life of the population in the regions of the Russian Federation. Terra Economicus, 17, No. 3, 107–127. (In Russ.). https://doi.org/10.23683/2073-6606-2019-17-3-107-127

         24. Tax policy of the Russian Federation in the context of sustainable development goals. Edited by I.A. Mayburov (2023). Moscow, UNITY-DANA, 359 p. (In Russ.). Available at: https://taxsymposium.ru/index.php?option=com_content&view=article&id=496:nalogovaya-politika-rossijskoj-federatsii-v-kontekste-tselej-ustojchivogo-razvitiya&catid=91&Itemid=939&lang=ru

         25. Lloyd, C.D., (2010). Analyzing population characteristics using geographically weighted principal components analysis: A case study of Northern Ireland in 2001. Computers, Environment and Urban Systems, Vol. 34, Issue 5, 389–399. https://doi.org/10.1016/j.compenvurbsys.2010.02.005

         26. Harris, P., Brunsdon, C., Charlton, M. (2011) Geographically weighted principal components analysis. International Journal of Geographical Information Science, Vol. 25, Issue 10, 1717–1736, https://doi.org/10.1080/13658816.2011.554838

         27. Wu, Ch., Peng, N., Ma, X., Li, Sh., Rao, J. (2020). Assessing multiscale visual appearance characteristics of neighborhoods using geographically weighted principal component analysis in Shenzhen, China. Computers, Environment and Urban Systems, Vol. 84, 101547. https://doi.org/10.1016/j.compenvurbsys.2020.101547

         28. Tomao, A, Mattioli, W, Fanfani, D, Ferrara, C, Quaranta, G, Salvia, R, Salvati, L. (2021). Economic Downturns and Land-Use Change: A Spatial Analysis of Urban Transformations in Rome (Italy) Using a Geographically Weighted Principal Component Analysis. Sustainability, Vol. 13, Issue 20, 11293. https://doi.org/10.3390/su132011293

         29. Fan, Z., Liu, E., Xu, B. (2011). Weighted Principal Component Analysis. In: Artificial Intelligence and Computational Intelligence. Second International Conference, AICIS 2011, Taiyuan, China, September 24-25, 2011, Proceedings, Part I. Edited by H. Deng, D. Miao, J. Lei, F.L. Wang. Springer, Berlin, Heidelberg, 569–574. https://doi.org/10.1007/978-3-642-23896-3_70

         30. Delchambre, L. (2015). Weighted principal component analysis: a weighted covariance eigendecomposition approach. Monthly Notices of the Royal Astronomical Society, Vol. 446, Issue 4, 3545–3555. https://doi.org/10.1093/mnras/stu2219

         31. Tsalmantza, P., Hogg, D. W. (2012). A data-driven model for spectra: Finding double redshifts in the sloan digital sky survey. The Astrophysics Journal, Vol. 753, No. 2, 122. https://doi.org/10.1088/0004-637X/753/2/122

         32. Swallow, B, Xiang, W, Panovska-Griffiths, J. (2022). Tracking the national and regional COVID-19 epidemic status in the UK using weighted principal component analysis. Philosophical Transactions A., Vol. 380, Issue 2233, 20210302. https://doi.org/10.1098/rsta.2021.0302

         33. Sood, A.K., Chaturvedi, V., Datta, S., Mahapatra, S.S. (2011). Optimization of process parameters in fused deposition modeling using weighted principal component analysis. Journal of Advanced Manufacturing Systems, Vol. 10, No. 2, 241–259. https://doi.org/10.1142/S0219686711002181

         34. Qi, L., Dou, W., Chen, J. (2016). Weighted principal component analysis-based service selection method for multimedia services in cloud. Computing, Vol. 98, 195–214. https://doi.org/10.1007/s00607-014-0413-x

         35. Burnaev, E.V., Chernova, S.S. (2015). On an iterative algorithm for calculating weighted principal components. Journal of Communications Technology and Electronics, Vol. 60, 619–624. https://doi.org/10.1134/S1064226915060042

         36. De Mol, C., Giannone, D., Reichlin, L. (2008). Forecasting using a large number of predictors: Is Bayesian shrinkage a valid alternative to principal components? Journal of Econometrics, Vol. 146, Issue 2, 318–328. https://doi.org/10.1016/j.jeconom.2008.08.011

         37. Audigier, V., Husson, F., Josse, J. (2016). Multiple imputation for continuous variables using a Bayesian principal component analysis. Journal of Statistical Computation and Simulation, Vol. 86, Issue 11, 2140–2156. https://doi.org/10.1080/00949655.2015.1104683

         38. Jolliffe, I.T. (2002). Principal Component Analysis. Second Edition. New York, Springer, 488 p. https://doi.org/10.1007/b98835

         39. Mironenkov, A.A. (2022). Interval estimates of indicators of the integral indicator of the quality of life of the population depending on the choice of weights of the weighted principal component. Application of Multidimensional Statistical Analysis in Economics and Quality Assessment. Proceedings of XII International Scientific Conference named after. S.A. Ayvazyan. Moscow, National Research University Higher School of Economics, 96–98. (In Russ.). https://doi.org/10.17323/978-5-7598-2716-0

         40. Polterovich, V.M. (2022). Competition, cooperation and life satisfaction. Part 1. Seven European leaders. Economic and Social Changes: Facts, Trends, Forecast, Vol. 15, No. 2, 31–43. (In Russ.). https://doi.org/10.15838/esc.2022.2.80.2

         41. Helliwell, J.F., Layard, R., Sachs, J., De Neve, J.-E., Aknin, L.B., Wang, S. (2021). World Happiness Report 2021. New York, Sustainable Development Solutions Network, 210 p. Available at: https://www.wellbeingintlstudiesrepository.org/hw_happiness/5/

         42. Helliwell, J.F., Huang H., Wang, S., Norton, M. (2021). Statistical Appendix 1 for Chapter 2 of World Happiness Report 2021, 51 p. Available at: https://happiness-report.s3.amazonaws.com/2021/Appendix1WHR2021C2.pdf

Acknowledgements

The Research is funding from the Russian Science Foundation, project No. 20-68-47030.

About Authors

Alexey Alekseevich Mironenkov

Senior Lecturer, Department of Econometrics and Mathematical Methods in Economy, Moscow School of Economics, Lomonosov Moscow State University, Moscow, Russia (119234, Moscow, Leninskie Gory, 1, Building, 61); ORCID https://orcid.org/0000-0001-5754-8825 e-mail: mironenkov@mse.msu.ru

Aleksei Nikolaevich Kurbatskii

Candidate of Physical and Mathematical Sciences, Associate Professor, Head of the Department of Econometrics and Mathematical Methods in Economy, Moscow School of Economics, Lomonosov Moscow State University, Moscow, Russia (119234, Moscow, Leninskie Gory, 1, Building, 61); ORCID https://orcid.org/0000-0001-6478-8034 e-mail: kurbatskiian@my.msu.ru

Marina Vladimirovna Mironenkova

Senior Lecturer, Department of Econometrics and Mathematical Methods in Economy, Moscow School of Economics, Lomonosov Moscow State University, Moscow, Russia (119234, Moscow, Leninskie Gory, 1, Building, 61); ORCID https://orcid.org/0009-0002-5297-0642 e-mail: mironenkovamv@my.msu.ru

For citation

Mironenkov, A.A., Kurbatskii, A.N., Mironenkova, M.V. (2024). The Quality-of-Life Measurement with a Stochastic Choice of Parameters of the Weighted Principal Component. Journal of Applied Economic Research, Vol. 23, No. 1, 82-109. https://doi.org/10.15826/vestnik.2024.23.1.004

Article info

Received October 5, 2023; Revised November 24, 2023; Accepted December 6, 2023.

DOI: https://doi.org/10.15826/vestnik.2024.23.1.004

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