Principal component analysis applied to multidimensional social indicators longitudinal studies: limitations and possibi
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Principal component analysis applied to multidimensional social indicators longitudinal studies: limitations and possibilities Matheus Pereira Libo´rio . Oseias da Silva Martinuci . Alexei Manso Correa Machado Thiago Melo Machado-Coelho . Sandro Laudares . Patrı´cia Bernardes
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Accepted: 11 October 2020 Ó Springer Nature B.V. 2020
Abstract Principal component analysis (PCA) is a popular technique for building social indicators in the field of spatial analysis. However, literature shows that there is no consensus on how to apply PCA to longitudinal studies, and researchers have done the analysis using different approaches, varying the way data are combined and the frequency in which the data are sampled. This research explores such approaches with two objectives: to draw attention to the limitations of using PCA in longitudinal analyses, and to show how to overcome these limitations. For this
purpose, indicators of urban inequality of eight cities are compared in each approach. The results show that the use of PCA presents limitations for the longitudinal study of urban inequality either because the evolution of the phenomenon is not always captured, or a large part of the indicators does not explain the phenomenon properly, or yet when a change in the calculation of the indicator distorts and enhances the differences in urban inequality through the years. An analytical chart is proposed to guide researchers with explanations and justifications that should accompany the use of PCA in longitudinal analyses.
M. P. Libo´rio (&) A. M. C. Machado S. Laudares P. Bernardes Pontifical Catholic University of Minas Gerais, Belo Horizonte 30535-012, Brazil e-mail: [email protected]
Keywords Longitudinal analyses Multidimensional phenomena Synthesis indicators Intra-urban Inequality Principal component analysis
A. M. C. Machado e-mail: [email protected] S. Laudares e-mail: [email protected]
Introduction
P. Bernardes e-mail: [email protected]
Phenomena such as development, progress, poverty and inequality are characterized by a combination of variables and assessed from a large amount of data of multiple dimensions (Mazziotta and Pareto 2017). By using a combination of appropriated variables, it is possible to obtain Composite Indicators that facilitate the interpretation of these originally complex phenomena (Saisana and Tarantola 2002). In short, Composite Indicators involve the aggregation of
O. da Silva Martinuci Maringa´ State University, Maringa´, Parana´ 87020-900, Brazil e-mail: [email protected] A. M. C. Machado T. M. Machado-Coelho Federal University of Minas Gerais, Belo Horizonte 31270-901, Brazil e-mail: [email protected]
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individual indicators weighted according to their relative importance (Nardo et al. 2005; JRC-EC 2008). Although not exempted from criticism, Composite Indicators have aroused the interest of researchers from the most varied areas of knowledge (KucCzarnecka et al. 2020), and
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