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Principal component analysis applied to multidimensional social indicators longitudinal studies: limitations and possibilities

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Matheus Pereira Libório at Pontifical Catholic University of Minas Gerais
Matheus Pereira Libório
Oséias da Silva Martinuci at State University of Maringá
Oséias da Silva Martinuci
Alexei M. C. Machado at Pontifical Catholic University of Minas Gerais
Alexei M. C. Machado
Thiago Melo Machado-Coelho at Federal University of Minas Gerais
Thiago Melo Machado-Coelho
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Abstract and Figures

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.
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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
Accepted: 11 October 2020 / Published online: 21 October 2020
ÓSpringer 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 limita-
tions 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 longitudi-
nal 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.
Keywords Longitudinal analyses
Multidimensional phenomena Synthesis indicators
Intra-urban Inequality Principal component analysis
Introduction
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 phe-
nomena (Saisana and Tarantola 2002). In short,
Composite Indicators involve the aggregation of
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: m4th32s@gmail.com
A. M. C. Machado
e-mail: alexeimcmachado@gmail.com
S. Laudares
e-mail: sandrolaudares@gmail.com
P. Bernardes
e-mail: patriciabernardes@pucminas.br
O. da Silva Martinuci
Maringa
´State University, Maringa
´, Parana
´87020-900,
Brazil
e-mail: osmartinuci@uem.br
A. M. C. Machado T. M. Machado-Coelho
Federal University of Minas Gerais,
Belo Horizonte 31270-901, Brazil
e-mail: thmmcoelho@gmail.com
123
GeoJournal (2022) 87:1453–1468
https://doi.org/10.1007/s10708-020-10322-0(0123456789().,-volV)(0123456789().,-volV)
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
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