Click here to download

Geographically Weighted Principal Component Analysis for the Definition of Composite Indicators
Author/s: Alfredo Cartone, Paolo Postiglione 
Year:  2016 Issue: Language: Italian 
Pages:  20 Pg. 33-52 FullText PDF:  200 KB
DOI:  10.3280/REST2016-001002
(DOI is like a bar code for intellectual property: to have more infomation:  clicca qui   and here 

The paper investigates the problem of the definition and the construction of composite indicators. The indicators are increasingly a valuable tool to assist people for the definition of appropriate policy that is based on effective analysis of real-world.
Methods and Results
Principal component analysis is often used to define composite indicators. Unfortunately, when dealing with spatial units, this technique is not appropriate, since it does not consider the spatial effects, namely spatial heterogeneity and dependence that are inherent characteristics in spatial data. To overcome this problem, the authors use a modified version of principal component analysis that has recently been introduced in literature and that explicitly considers the spatial heterogeneity effect. This method is denoted as geographically weighted principal component analysis. The method is applied for the definition of well-being composite indicators at local level for 110 Italian provinces. The analysis is performed for 2011.
The empirical evidence shows that the multidimensional concept of well-being is differentiated at local level, supporting the extent of spatial heterogeneity. Therefore, the obtained results support the use of the geographically weighted principal component analysis as more suitable method for handling spatial data.
Keywords: Geographically weighted regression, composite indicators, well-being indicators, spatial econometrics, kernel function
Jel Code: C01, C21, C43, C54.

  1. Anselin L. (1988), Spatial Econometrics: Methods and Models. Dordrecht: Kluwer Academic Publishers.
  2. Bernini C., Guizzardi A., Angelini G. (2013), DEA-like Model and Common Weights Approach for the Construction of a Subjective Community Well-being Indicator, Social Indicator Research, 114, pp. 405-424.
  3. Brunsdon C., Fotheringham A.S., Charlton M. (1998), Geographically Weighted Regression – Modelling Spatial Non-stationarity, Journal of the Royal Statistical Society D, 47, pp. 431-443.
  4. Dumanski J., Pieri C. (1997), Application of the Pressure-state-response Framework for the Land Quality Indicators (LQI) programme, in Land Quality Indicators and Their Use in Sustainable Agriculture and Rural Development, in Proceedings of the Workshop organized by the Land and Water Development Division, FAO Agriculture Department and the Research, Extension and Training Division, FAO Sustainable Development Department, 25-26 January 1996.
  5. Fotheringham A.S., Brunsdon C., Charlton M. (2002), Geographically Weighted Regression – The Analysis of Spatially varying Relationships. Chichester, UK: Wiley.
  6. Gollini I., Lu B., Charlton M., Brunsdon C., Harris P. (2015), GWmodel: An R Package for Exploring Spatial Heterogeneity using Geographically Weighted Models, Journal of Statistical Software, 63, 17, pp. 1-50.
  7. Harris P., Brunsdon C., Charlton. M. (2011), Geographically Weighted Principal Components Analysis, International Journal of Geographical Information Science, 25, pp. 1717-36.
  8. Harris P., Clarke A., Juggins S., Brunsdon C., Charlton M. (2014), Geographically Weighted Methods and Their Use in Network Re-designs for Environmental Monitoring, Stochastic Environmental Research and Risk Assessment, 28, pp. 1869-1887.
  9. Harris P., Clarke A., Juggins S., Brunsdon C., Charlton M. (2015), Enhancements to a Geographically Weighted Principal Component Analysis in the Context of an Application to an Environmental Data Set, Geographical Analysis, 47, pp. 146-172.
  10. Hotelling H. (1933), Analysis of a Complex of Statistical Variables into Principal Components, Journal of Educational Psychology, 24, pp. 417-441.
  11. ISTAT (2015), Rapporto BES 2015.
  12. Jolliffe I.T. (2002), Principal Component Analysis. New York: Springer Verlag.
  13. Jombart T., Devillard S., Dufour A-B., Pontier D. (2008), Revealing Cryptic Patterns in Genetic Variability by a New Multivariate Method, Heredity, 101, pp. 92-103.

  14. 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, pp. 67-80.
  15. OECD (1993), OECD Core Set of Indicators for Environmental Performance Reviews, Environment Monographs, 83.
  16. Pampalon R., Raymond G. (2000), A Deprivation Index for Health and Welfare Planning in Quebec, Chronic Diseases in Canada, 21, pp. 104-13.
  17. Panzera D., Postiglione P. (2014), Economic Growth in Italian NUTS 3 Provinces, The Annals of Regional Science, 53, pp. 273-293.
  18. Pearson K. (1901), On Lines and Planes of Closest Fit to a System of Points in a Space, Philosophical Magazine (Series 6), 2, pp. 559-572.
  19. Postiglione P., Andreano M.S., Benedetti R. (2013), Using Constrained Optimization for the Identification of Convergence Clubs, Computational Economics, 42, pp. 151-174.
  20. Stiglitz J., Sen A., Fitoussi J. (2009), Report by the Commission on the Measurement of Economic Performance and Social Progress,

Alfredo Cartone, Paolo Postiglione, Geographically Weighted Principal Component Analysis for the Definition of Composite Indicators in "RIVISTA DI ECONOMIA E STATISTICA DEL TERRITORIO" 1/2016, pp. 33-52, DOI:10.3280/REST2016-001002


FrancoAngeli is a member of Publishers International Linking Association a not for profit orgasnization wich runs the CrossRef service, enabing links to and from online scholarly content