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Constrained optimization for addressing spatial heterogeneity in principal component analysis: an application to composite indicators

Author

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  • Paolo Postiglione

    (“G. d’Annunzio” University of Chieti-Pescara)

  • Alfredo Cartone

    (“G. d’Annunzio” University of Chieti-Pescara)

  • M. Simona Andreano

    (Universitas Mercatorum)

  • Roberto Benedetti

    (“G. d’Annunzio” University of Chieti-Pescara)

Abstract

Principal component analysis, in its standard version, might not be appropriate for the analysis of spatial data. Particularly, the presence of spatial heterogeneity has been recognized as a possible source of misspecification for the derivation of composite indicators using principal component analysis. In recent times, geographically weighted approach to principal component analysis has been used for the treatment of continuous heterogeneity. However, this technique poses problems for the treatment of discrete heterogeneity and the interpretation of the results. The aim of this paper is to present a new approach to consider spatial heterogeneity in principal component analysis by using simulated annealing algorithm. The proposed method is applied for the definition of a composite indicator of local services for 121 municipalities in the province of Rome.

Suggested Citation

  • Paolo Postiglione & Alfredo Cartone & M. Simona Andreano & Roberto Benedetti, 2023. "Constrained optimization for addressing spatial heterogeneity in principal component analysis: an application to composite indicators," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(5), pages 1539-1561, December.
    • Handle: RePEc:spr:stmapp:v:32:y:2023:i:5:d:10.1007_s10260-023-00697-y
    DOI: 10.1007/s10260-023-00697-y
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    1. Daniele Trogu & Michele Campagna, 2018. "Towards Spatial Composite Indicators: A Case Study on Sardinian Landscape," Sustainability, MDPI, vol. 10(5), pages 1-21, April.
    2. David Wheeler & Catherine Calder, 2007. "An assessment of coefficient accuracy in linear regression models with spatially varying coefficients," Journal of Geographical Systems, Springer, vol. 9(2), pages 145-166, June.
    3. Fusco, Elisa & Vidoli, Francesco & Sahoo, Biresh K., 2018. "Spatial heterogeneity in composite indicator: A methodological proposal," Omega, Elsevier, vol. 77(C), pages 1-14.
    4. D’Inverno, Giovanna & De Witte, Kristof, 2020. "Service level provision in municipalities: A flexible directional distance composite indicator," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1129-1141.
    5. Matheus Pereira Libório & Oseias da Silva Martinuci & Alexei Manso Correa Machado & Renata de Mello Lyrio & Patrícia Bernardes, 2022. "Time–Space Analysis of Multidimensional Phenomena: A Composite Indicator of Social Exclusion Through k-Means," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 159(2), pages 569-591, January.
    6. Roberto Benedetti & Monica Pratesi & Nicola Salvati, 2013. "Local stationarity in small area estimation models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(1), pages 81-95, March.
    7. Paolo Postiglione & M. Andreano & Roberto Benedetti, 2013. "Using Constrained Optimization for the Identification of Convergence Clubs," Computational Economics, Springer;Society for Computational Economics, vol. 42(2), pages 151-174, August.
    8. Marko Kallio & Joseph H. A. Guillaume & Matti Kummu & Kirsi Virrantaus, 2018. "Spatial Variation in Seasonal Water Poverty Index for Laos: An Application of Geographically Weighted Principal Component Analysis," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 140(3), pages 1131-1157, December.
    9. Koen Decancq & María Ana Lugo, 2013. "Weights in Multidimensional Indices of Wellbeing: An Overview," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 7-34, January.
    10. Giacalone, Massimiliano & Mattera, Raffaele & Nissi, Eugenia, 2022. "Well-being analysis of Italian provinces with spatial principal components," Socio-Economic Planning Sciences, Elsevier, vol. 84(C).
    11. M. Simona Andreano & Roberto Benedetti & Paolo Postiglione, 2017. "Spatial regimes in regional European growth: an iterated spatially weighted regression approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(6), pages 2665-2684, November.
    12. Havard, Sabrina & Deguen, Séverine & Bodin, Julie & Louis, Karine & Laurent, Olivier & Bard, Denis, 2008. "A small-area index of socioeconomic deprivation to capture health inequalities in France," Social Science & Medicine, Elsevier, vol. 67(12), pages 2007-2016, December.
    13. Paolo Postiglione & Maria Simona Andreano & Roberto Benedetti, 2017. "Spatial Clusters in EU Productivity Growth," Growth and Change, Wiley Blackwell, vol. 48(1), pages 40-60, March.
    14. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
    15. Salvati, Luca & Ciommi, Maria Teresa & Serra, Pere & Chelli, Francesco M., 2019. "Exploring the spatial structure of housing prices under economic expansion and stagnation: The role of socio-demographic factors in metropolitan Rome, Italy," Land Use Policy, Elsevier, vol. 81(C), pages 143-152.
    16. Anna Gloria Billé & Roberto Benedetti & Paolo Postiglione, 2017. "A two-step approach to account for unobserved spatial heterogeneity," Spatial Economic Analysis, Taylor & Francis Journals, vol. 12(4), pages 452-471, October.
    17. Alfredo Cartone & Paolo Postiglione, 2021. "Principal component analysis for geographical data: the role of spatial effects in the definition of composite indicators," Spatial Economic Analysis, Taylor & Francis Journals, vol. 16(2), pages 126-147, April.
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