Representing Multidimensional Phenomena of Geographic Interest: Benefit of the Doubt or Principal Component Analysis?

Abstract

Composite indicators are one-dimensional measures of multidimensional phenomena. Through the composite indicators, it is possible to have a single map of the different subindicators of poverty, inequality, sustainability, and economic development. This research employs two well-known methods of building composite indicators to represent the social exclusion of eight cities. This research shows that the benefit of the doubt and principal component analysis have limitations to representing multidimensional phenomena of geographic interest, but adaptations in these methods reduce these limitations. The benefit of the doubt constrained (BoD-c) restricts subindicator weight variations, increasing the composite indicator’s capacity to represent the most important subindicator in the concept of the multidimensional phenomenon. The principal component analysis adjusted (PCA-a) discards poorly correlated subindicators, ensuring a variance extracted in the first component above the acceptance threshold of 0.50. Contrasting BoD-c and PCA-a, geographically weighted principal component analysis has a limited capacity to capture the most important subindicator in the concept of the multidimensional phenomenon. Among twenty-three experts from nine countries, eighteen preferred PCA-a to BoD-c, indicating that information loss is not as critical a property as full comparability across geographic areas. Local experts agree that both maps represent local social reality, but PCA-a is more faithful to that reality.

复合指标是多维现象的一维度量。通过复合指标, 可以用一张地图展示贫困、不平等、可持续性和经济发展的各项子指标。本研究采用两种常用方法构建复合指标, 以表达八个城市的社会排斥。本研究表明, 假定和主成分分析在表达地理多维现象时有局限性, 但对这些方法进行修订则能减少这些局限性。假定约束（BoD-c）能约束子指标权重的变化, 提高复合指标表达多维现象的最主要子指标的能力。主成分分析调整（PCA-a）舍弃相关性较差的子指标, 确保第一主成分方差高于接受阈值（0.50）。与BoD-c和PCA-a相比, 地理加权主成分分析在获取多维现象的最主要子指标时有局限性。在来自9个国家的23位专家中, 18位更倾向于PCA-a而非BoD-c, 这表明信息损失的重要性低于跨区域的完全可比性。本地专家认为, 两张地图都表达了本地社会现实, 但PCA-a更忠实于这一现实。

Los indicadores compuestos son medidas unidimensionales de fenómenos multidimensionales. Por medio de los indicadores compuestos es posible tener un mapa único de los diferentes subindicadores de la pobreza, la desigualdad, la sustentabilidad y el desarrollo económico. Esta investigación utiliza dos métodos bien conocidos de construcción de indicadores compuestos para representar la exclusión social en ocho ciudades. La investigación muestra que el beneficio de la duda y el análisis de componentes principales tienen limitaciones para representar fenómenos multidimensionales de interés geográfico, pero que las adaptaciones en estos métodos reducen esas limitaciones. El beneficio de la duda constreñido (BoD-c) restringe las variaciones del peso de los subindicadores, aumentando la capacidad del indicador compuesto para representar al subindicador más importante en el concepto del fenómeno multidimensional. El análisis de componentes principales ajustado (PCA-a) descarta los subindicadores pobremente correlacionados, asegurando así una varianza extraída en el primer componente por encima del umbral de aceptación de 0,50. Al contrastar BoD-c y PCA-a, el análisis de componentes principales geográficamente ponderado tiene una capacidad limitada para capturar el subindicador más importante en el concepto del fenómeno multidimensional. Entre veintitrés expertos de nueve países, dieciocho prefirieron el PCA-a al BoD-c, indicando con eso que la pérdida de información no es una propiedad tan crítica como la comparabilidad plena entre áreas geográficas. Los expertos locales están de acuerdo en que ambos mapas representan la realidad social local, pero el PCA-a es más fiel a esa realidad.

Key Words:

• benefit of the doubt
• component analysis
• composite indicators
• multidimensional phenomenon
• principal component analysis
• social exclusion

关键词:

• 假定
• 成分分析
• 复合指标
• 多维现象
• 主成分分析
• 社会排斥。

Palabras clave:

• análisis de componentes
• análisis de componentes principales
• beneficio de la duda
• exclusión social
• fenómeno multidimensional
• indicadores compuestos

Acknowledgments

We thank the anonymous reviewers for their support and advice in preparing this article and the experts interviewed for their valuable information. The data that support the findings of this study are openly available in Mendeley Data at http://dx.doi.org/10.17632/8j836n4bys.4 and in figshare at https://doi.org/10.6084/m9.figshare.16944166.v1

Additional information

Funding

This research was supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) Finance Code 0001 and the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Grant Numbers 423443/2016-0 and 311032/2016-8.

Notes on contributors

Matheus Pereira Libório

MATHEUS PEREIRA LIBÓRIO is a PhD Student in business administration at Pontifical Catholic University of Minas Gerais, Belo Horizonte, MG 30535-012, Brazil. E-mail: [email protected]. His research interests include decision-making models and methods in economics, business, geography, and operational research.

Oseias da Silva Martinuci

OSEIAS DA SILVA MARTINUCI is an Adjunct Professor in the Department of Geography at State University of Maringá, Maringá, PR 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 at Pontifical Catholic University of Minas Gerais, Belo Horizonte, MG 30535-012, Brazil, and at the School of Medicine of the Federal University of Minas Gerais, Belo Horizonte, MG 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.

Petr Iakovlevitch Ekel

PETR IAKOVLEVITCH EKEL is Full Professor in the Department of Electrical engineering at Pontifical Catholic University of Minas Gerais, Belo Horizonte, MG 30535-012, and at Federal University of Minas Gerais, Belo Horizonte, MG 31270-901. E-mail: [email protected]. His research interests include modeling, optimization, and control of systems and processes and decision making in complex scenarios.

João Francisco de Abreu

JOÃO FRANCISCO DE ABREU is Full Professor in the Department of Geography at Pontifical Catholic University of Minas Gerais, Belo Horizonte, MG 30535-012, Brazil. E-mail: [email protected]. His research interests include spatial analysis, geographic information systems, analytical cartography, multivariate statistics, and neural networks.

Sandro Laudares

SANDRO LAUDARES is Assistant Professor in the Department of Geography at Pontifical Catholic University of Minas Gerais, Belo Horizonte, MG 30535-012, Brazil. E-mail: [email protected]. His research interests include spatial analysis, geocollaboration, geographic databases, and geovisualization systems for the Web.