Adequacy and Consistency of an Intraurban Inequality Indicator Constructed through Principal Component Analysis

Abstract

This research explores the relationship between the implicit importance of the variables of a multidimensional phenomenon within the context of urban inequalities and the weights attributed to these variables during the process of building a composite indicator (CI) by data-based weighting methods, such as principal component analysis (PCA). The objective is to test whether a CI can be statistically consistent or even adequate to represent the phenomenon but, at the same time, be composed of variables with weights that do not adhere to reality and, consequently, transmit false information, hide problems, and lead to wrong policies. This hypothesis is tested in a study of the intraurban inequality of a Brazilian urban conurbation. The results show a CI that is internally (Cronbach’s α = 0.80) and externally (Pearson’s correlation coefficient = 0.64) consistent but that captures only 20 percent of the information related to the phenomenon and is unable to completely represent its dimensions or account for important variables. The results suggest that the external validation of CI based on known indicators might not be a good strategy and that qualitative indicators can be useful to verify the extent to which a CI is suitable to represent a phenomenon.

在城市不平等的研究中, 有两个问题：多维现象的各变量的隐性重要性, 以及在建立基于数据加权方法（如主成分分析）的综合指标（CI）过程中这些变量的权重。本文探讨了这两者之间的关系。本文旨在检验CI在统计上是否一致、甚至足以表达该多维现象。同时, 检验了CI能否包括拥有不切实际权重的变量, 从而传递虚假信息、隐藏问题、导致错误的政策。通过研究巴西城市群的城市内部不平等, 本文对该假设进行了验证。结果表明, CI在内部（克朗巴哈系数为0.80）和外部（皮尔森相关系数为0.64）都是一致的, 但它只捕获了20%的有关信息, 无法完全表达现象的维度、解释现象的重要变量。本文认为, 基于已知指标的外部CI验证可能不是一个好策略, 而定性指标则有助于验证CI在多大程度上能表达现象。

Esta investigación explora la relación entre la importancia implícita de las variables de un fenómeno multidimensional, dentro del contexto de las desigualdades urbanas, y los pesos atribuidos a estas variables durante el proceso de construir un indicador compuesto (CI) mediante métodos de ponderación basados en datos, tales como el análisis de componentes principales (PCA). Se pretende establecer si un CI puede ser estadísticamente consistente o incluso adecuado para representar el fenómeno, pero, al mismo tiempo, estar compuesto de variables con pesos que no corresponden a la realidad y que, en consecuencia, trasmiten información falsa, ocultan problemas y conducen a políticas equivocadas. Esta hipótesis se pone a prueba en un estudio de desigualdad intraurbana en una conurbación brasileña. Los resultados muestran un CI que es consistente internamente (α = 0.80 de Cronbach) y externamente (el coeficiente de correlación de Pearson = 0.64), pero que solamente capta el 20 por ciento de la información relacionada con el fenómeno y es incapaz de representar completamente sus dimensiones o responder por variables importantes. Los resultados sugieren que la validación externa del CI basada en indicadores conocidos podría no ser una buena estrategia, y que indicadores cualitativos pueden ser útiles para verificar el alcance con el cual un CI es adecuado para representar un fenómeno.

Key Words:

• analytic hierarchy process
• composite indicators
• geographical perspective
• intraurban inequality
• principal component analysis

关键词:

• 层次分析法
• 综合指标
• 地理视角
• 城市内部不平等
• 主成分分析。

Palabras clave:

• análisis de componentes principales
• desigualdad intraurbana
• indicadores compuestos
• perspectiva geográfica
• proceso analítico de jerarquía

Acknowledgments

We thank the anonymous reviewers for their support and advice in preparing this article and the experts interviewed for their valuable information.

Data Availability Statement

The data that support the findings of this study are openly available in Mendeley Data at http://dx.doi.org/10.17632/8j836n4bys.4.

Notes

1 The Vegetation cover indicator was created through the Normalized Difference Vegetation Index. The Normalized Difference Vegetation Index is a procedure that highlights the spectral differences between soil and vegetation, widely used in estimating biomass and vegetation cover. The images used are from the Landsat 5 satellite for the year 2010, with a spatial resolution of 30 m and with cloud coverage below 1 percent.

2 CIs are built from variables of different natures. Quantitative-objective variables are directly measurable, such as, for example, the number of inhabitants per household (VD1). Qualitative-objective variables are not measured but are verified from the presence or absence of something, such as, for example, the presence of a sewage network (VH4) or a water network (VH5). Qualitative-subjective variables are obtained from an assessment or opinion, such as, for example, the external conditions of the dwellings (CE 2005).

3 Landscape is understood as an exteriority that can be apprehended by perception. Even though it results from complex processes not apparent, the landscape analysis can be a consistent methodological strategy for checking the presence or absence of features that indicates the conditions of the urban areas (M. Santos 2002).

Additional information

Funding

This research was supported by the National Scientific and Technological Development of Brazil (CNPq) Grant Number 423443/2016-0 and by the Coordination for the Improvement of Personnel in Higher Education–Brasil (CAPES) Finance Code 0001.

Notes on contributors

Matheus Pereira Libório

MATHEUS PEREIRA LIBÓRIO is a PhD student in the Business Administration Program at the Pontifical Catholic University of Minas Gerais, Belo Horizonte 30535-012, Brazil. E-mail: [email protected]. His research interests include decision-making models and methods in economics, business management, telecommunications, and geography.

Oseias da Silva Martinuci

OSEIAS DA SILVA MARTINUCI is an Adjunct Professor in the Department of Geography, State University of Maringá, Paraná 87020-900, Brazil. E-mail: [email protected]. His research interests include public policy (social welfare and public health), territory, inequalities, and thematic cartography.

Alexei Manso Correa Machado

ALEXEI MANSO CORREA MACHADO is Associate Professor in the Department of Computer Science, Pontifical Catholic University of Minas Gerais, Belo Horizonte 30535-012, Brazil, and the School of Medicine of the Federal University of Minas Gerais, Belo Horizonte 31270-901, Brazil. E-mail: [email protected]. His research interests include medical image analysis, computer vision, machine learning, big data analytics, statistical inference, and dimensionality reduction.

Renato Moreira Hadad

RENATO MOREIRA HADAD is a Visiting Professor Center for Development and Regional Planning at the Federal University of Minas Gerais, Belo Horizonte 31270-901, Brazil, and an Adjunct Professor at the Pontifical Catholic University of Minas Gerais, Belo Horizonte 30535-012, Brazil. E-mail: [email protected]. His research interests include computer science, working mainly on the following themes: digital image processing, geoprocessing, knowledge discovery in databases, data mining, and operational research.

Patrícia Bernardes

PATRÍCIA BERNARDES is an Adjunct Professor in the Administration Program at the Pontifical Catholic University of Minas Gerais, Belo Horizonte 30535-012, Brazil. E-mail: [email protected]. Her research interests include transaction costs economics and law and economics.

Vitor Augusto Luizari Camacho

VITOR AUGUSTO LUIZARI CAMACHO is now a Geoprocessing Specialist at the Projeto Meios, São Carlos do Pinhal, Sao Paulo, Brazil. E-mail: [email protected].  His research interests include thematic cartography, remote sensing in the environment, urban planning, and territorial environmental and public policies.