Social Indicators Research

, Volume 142, Issue 2, pp 451–476 | Cite as

Use and Misuse of PCA for Measuring Well-Being

  • Matteo Mazziotta
  • Adriano ParetoEmail author


The measurement of well-being of people is very difficult because it is characterized by a multiplicity of aspects or dimensions. Principal Components Analysis (PCA) is probably the most popular multivariate statistical technique for reducing data with many dimensions and, often, well-being indicators are reduced to a single index of well-being by using PCA. However, PCA is implicitly based on a reflective measurement model that is not suitable for all types of indicators. In this paper, we discuss the use and misuse of PCA for measuring well-being, and we show some applications to real data.


Data reduction Composite indicator Measurement model Well-being 



The paper is the result of the common work of the authors: in particular M. Mazziotta has written Sects. 2.1, 3.2, 4 and A. Pareto has written Sects. 1, 2.2, 2.3, 2.4, 3.1.


  1. Biswas, B., & Caliendo, F. (2002). A multivariate analysis of the human development index. Indian Economic Journal, 49, 96–100.Google Scholar
  2. Bleys, B. (2012). Beyond GDP: Classifying alternative measures for progress. Social Indicators Research, 109, 355–376.CrossRefGoogle Scholar
  3. Boarini, R., Kolev, A., & McGregor, A. (2014). Measuring well-being and progress in countries at different stages of development: Towards a more universal conceptual framework. Working Paper No. 325. OECD Development Centre.Google Scholar
  4. Bohrnstedt, G. W. (1970). Reliability and validity assessment in attitude measurement. In G. F. Summers (Ed.), Attitude measurement (pp. 80–99). London: Rand McNally.Google Scholar
  5. Booysen, F. (2002). An overview and evaluation of composite indices of development. Social Indicators Research, 59, 115–151.CrossRefGoogle Scholar
  6. Borsboom, D., Mellenbergh, G. J., & Heerden, J. V. (2003). The theoretical status of latent variables. Psychological Review, 110, 203–219.CrossRefGoogle Scholar
  7. Cadogan, J. W., & Lee, N. (2013). Improper use of endogenous formative variables. Journal of Business Research, 66, 233–241.CrossRefGoogle Scholar
  8. Chelli, F., Ciommi, M., Emili, A., Gigliarano, C., & Taralli, S. (2017). A new class of composite indicators for measuring well-being at the local level: An application to the Equitable and Sustainable Well-being (BES) of the Italian Provinces. Ecological Indicators, 76, 281–296.CrossRefGoogle Scholar
  9. Coltman, T., Devinney, T. M., Midgley, D. F., & Venaik, S. (2008). Formative versus reflective measurement models: Two applications of formative measurement. Journal of Business Research, 61, 1250–1262.CrossRefGoogle Scholar
  10. Diamantopoulos, A. (2006). The error term in formative measurement models: Interpretation and modeling implications. Journal of Modeling in Management, 1, 7–17.CrossRefGoogle Scholar
  11. Diamantopoulos, A., Riefler, P., & Roth, K. P. (2008). Advancing formative measurement models. Journal of Business Research, 61, 1203–1218.CrossRefGoogle Scholar
  12. Diamantopoulos, A., & Winklhofer, H. M. (2001). Index construction with formative indicators: An alternative to scale development. Journal of Marketing Research, 38, 269–277.CrossRefGoogle Scholar
  13. Dunteman, G. H. (1989). Principal components analysis. Newbury Park: Sage.CrossRefGoogle Scholar
  14. Edwards, J. R., & Bagozzi, R. P. (2000). On the nature and direction of relationships between constructs and measures. Psychological Methods, 5, 155–174.CrossRefGoogle Scholar
  15. Fabrigar, L. F., & Wegener, D. T. (2011). Exploratory factor analysis. New York: Oxford University Press.CrossRefGoogle Scholar
  16. Fayers, P. M., & Hand, D. J. (2002). Causal variables, indicator variables and measurement scales: An example from quality of life. Journal of the Royal Statistical Society, Series A, 165, 233–261.CrossRefGoogle Scholar
  17. Ferrara, A. R., & Nisticò, R. (2014). Measuring well-being in a multidimensional perspective: A multivariate statistical application to Italian regions. Working Paper, 6. Dipartimento di Economia, Statistica e Finanza, Università della Calabria.Google Scholar
  18. Filzmoser, P. (1999). Robust principal components and factor analysis in the geostatistical treatment of environmental data. Environmetrics, 10, 363–375.CrossRefGoogle Scholar
  19. Götz, O., Liehr-Gobbers, K., & Krafft, M. (2010). Evaluation of structural equation models using the partial least squares (PLS) approach. In V. Esposito Vinzi, W. W. Chin, J. Henseler, & H. Wang (Eds.), Handbook of partial least squares: Concepts, methods, and applications (pp. 691–711). Berlin: Springer.CrossRefGoogle Scholar
  20. Guttman, L. (1954). Some necessary conditions for common factor analysis. Psychometrika, 19, 149–161.CrossRefGoogle Scholar
  21. Haq, R., & Zia, U. (2013). Multidimensional wellbeing: An index of quality of life in a developing economy. Social Indicators Research, 114, 997–1012.CrossRefGoogle Scholar
  22. Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology, 24, 417–441.CrossRefGoogle Scholar
  23. Howell, R. D., Breivik, E., & Wilcox, J. B. (2007). Reconsidering formative measurement. Psychological Methods, 12, 205–218.CrossRefGoogle Scholar
  24. Hubert, M., Rousseeuw, P. J., & Vanden Branden, K. (2005). Robpca: A new approach to robust principal component analysis. Technometrics, 47, 64–79.CrossRefGoogle Scholar
  25. Istat (2015a). BES 2015. Il benessere equo e sostenibile in Italia. Accessed 21 May 2018.
  26. Istat (2015b). Il benessere equo e sostenibile delle province. Accessed 21 May 2018.
  27. Jarvis, C. B., Mackenzie, S. B., & Podsakoff, P. M. (2003). A critical review of construct indicators and measurement model misspecification in marketing and consumer research. Journal of Consumer Research, 30, 199–218.CrossRefGoogle Scholar
  28. Jolliffe, I. T., & Cadima, J. (2016). Principal component analysis: A review and recent developments. Philosophical Transactions of the Royal Society, A, 374, 20150202. Scholar
  29. Kaiser, H. F. (1961). A note on Guttman’s lower bound for the number of common factors. British Journal of Mathematical ans Statistical Psychology, 14, 1–2.CrossRefGoogle Scholar
  30. Kendall, M. G., & Stuart, A. (1968). The advanced theory of statistics (Vol. 3). London: Charles Griffin & Co.Google Scholar
  31. Krishnakumar, J., & Nagar, A. L. (2008). On exact statistical properties of multidimensional indices based on principal components, factor analysis, MIMIC and structural equation models. Social Indicators Research, 86, 481–496.CrossRefGoogle Scholar
  32. Lai, D. (2003). Principal component analysis on human development indicators of China. Social Indicators Research, 61, 319–330.CrossRefGoogle Scholar
  33. Lavit, C., Escoufier, Y., Sabatier, R., & Traissac, P. (1994). The ACT (STATIS method). Computational Statistics & Data Analysis, 18, 97–119.CrossRefGoogle Scholar
  34. Linting, M., Meulman, J. J., Groenen, P. J. F., & Van der Kooij, A. J. (2007). Nonlinear principal components analysis: Introduction and application. Psychological Methods, 12, 336–358.CrossRefGoogle Scholar
  35. Maggino, F. (2017). Developing indicators and managing the complexity. In F. Maggino (Ed.), Complexity in society: From indicators construction to their synthesis (Vol. 70, pp. 87–114)., Social indicators research series Cham: Springer.CrossRefGoogle Scholar
  36. Maggino, F., & Zumbo, B. D. (2012). Measuring the quality of life and the construction of social indicators. In K. C. Land, A. C. Michalos, & M. J. Sirgy (Eds.), Handbook of social indicators and quality-of-life research (pp. 201–238). Dordrecht: Springer.CrossRefGoogle Scholar
  37. Markus, K. A., & Borsboom, D. (2013). Frontiers of test validity theory. Measurement, causation, and meaning. New York: Routledge.Google Scholar
  38. Mazziotta, M., & Pareto, A. (2013). Methods for constructing composite indices: One for all or all for one. Rivista Italiana di Economia Demografia e Statistica, LXVII(2), 67–80.Google Scholar
  39. Mazziotta, M., & Pareto, A. (2016a). On a generalized non-compensatory composite index for measuring socio-economic phenomena. Social Indicators Research, 127, 983–1003.CrossRefGoogle Scholar
  40. Mazziotta, M., & Pareto, A. (2016b). On the construction of composite indices by principal components analysis. Rivista Italiana di Economia Demografia e Statistica, LXX(1), 103–109.Google Scholar
  41. Mazziotta, M., & Pareto, A. (2017). Synthesis of indicators: The composite indicators approach. In F. Maggino (Ed.), Complexity in society: From indicators construction to their synthesis (Vol. 70, pp. 159–191)., Social indicators research series Cham: Springer.CrossRefGoogle Scholar
  42. McGillivray, M. (2005). Measuring non-economic well-being achievement. Review of Income and Wealth, 51, 337–364.CrossRefGoogle Scholar
  43. Michalos, A. C. (2014). Encyclopedia of quality of life and well-being research. Dordrecht: Springer.CrossRefGoogle Scholar
  44. Michalos, A. C., Smale, B., Labonté, R., Muharjarine, N., Scott, K., Moore, K., et al. (2011). The Canadian Index of wellbeing. Technical report 1.0. Waterloo, ON: Canadian Index of Wellbeing and University of Waterloo.Google Scholar
  45. Mishra, S. K. (2007). A comparative study of various inclusive indices and the index constructed by the principal components analysis. MPRA Paper, No. 3377. MPRA. Accessed 21 May 2018.
  46. Mishra, S. K. (2008). On Construction of Robust Composite Indices by Linear Aggregation. SSRN. Accessed 21 May 2018.
  47. Nahman, A., Mahumani, B. K., & De Lange, W. J. (2016). Beyond GDP: Towards a green economy index. Development Southern Africa. Scholar
  48. OECD. (2004). The OECD-JRC handbook on practices for developing composite indicators. Paper presented at the OECD Committee on Statistics, 7–8 June 2004, OECD, Paris.Google Scholar
  49. OECD. (2008). Handbook on constructing composite indicators. Methodology and user guide. Paris: OECD Publications.CrossRefGoogle Scholar
  50. OECD. (2015). How’s life? 2015: Measuring well-being. Paris: OECD Publishing.CrossRefGoogle Scholar
  51. Osborne, J. W. (2014). Best practices in exploratory factor analysis. Newbury Park: Jason W. Osborne.Google Scholar
  52. Ram, R. (1982). Composite indices of physical quality of life, basic needs fulfilment, and income: A principal component representation. Journal of Development Economics, 11, 227–247.CrossRefGoogle Scholar
  53. Salzman, J. (2003). Methodological choices encountered in the construction of composite indices of economic and social well-Being. Technical Report. Center for the Study of Living Standards, Ottawa.Google Scholar
  54. Sen, A. K. (1985). Commodities and capabilities. Amsterdam: North Holland Publishing Company.Google Scholar
  55. Shalizi C. R. (2009). The truth about principal components and factor analysis.
  56. Shwartz, M., Restuccia, J. D., & Rosen, A. K. (2015). Composite measures of health care provider performance: A description of approaches. The Milbank Quarterly, 93, 788–825.CrossRefGoogle Scholar
  57. Simonetto, A. (2012). Formative and reflective models: State of the art. Electronic Journal of Applied Statistical Analysis, 5, 452–457.Google Scholar
  58. Slottje, D. J. (1991). Measuring the quality of life across countries. The Review of Economics and Statistics, 73, 684–693.CrossRefGoogle Scholar
  59. Somarriba, N., & Pena, B. (2009). Synthetic indicators of quality of life in Europe. Social Indicators Research, 94, 115–133.CrossRefGoogle Scholar
  60. Stiglitz, J., Sen, A. K., & Fitoussi, J. P. (2009). Report of the commission on the measurement of economic performance and social progress. Paris. Available online from the Commission on the Measurement of Economic Performance and Social Progress: Accessed 21 May 2018.
  61. UNDP. (1990). Human development report 1990. New York: Oxford University Press.Google Scholar
  62. UNDP. (2010). Human development report 2010. New York: Palgrave Macmillan.Google Scholar
  63. Van Beuningen, J., Van der Houwen, K., & Moonen, L. (2014). Measuring well-being. An analysis of different response scales. Discussion Paper, 3. Statistics Netherlands.Google Scholar
  64. Vinzi, V. E., Lauro, C., & Tenenhaus, M. (2003). PLS path modeling. Working paper. DMS – University of Naples, HEC – School of Management, Jouy-en-Josas.Google Scholar
  65. Wong, K. M. (2012). Well-being and economic development: A principal components analysis. International Journal of Happiness and Development, 1, 131–141.CrossRefGoogle Scholar
  66. Zumbo, B. D. (2007). Validity: Foundational issues and statistical methodology. In C. R. Rao & S. Sinharay (Eds.), Handbook of statistics (Vol. 26, pp. 45–79)., Psychometrics Boston: Elsevier.Google Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Italian National Institute of StatisticsRomeItaly
  2. 2.Italian National Institute of StatisticsRomeItaly

Personalised recommendations