# Measuring Intra-Urban Inequality with Structural Equation Modeling: A Theory-Grounded Indicator

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Department of Administration, Pontifical Catholic University of Minas Gerais, Belo Horizonte, MG 30535-012, Brazil

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Department of Geography, Maringá State University, Maringá, PR 87000-000, Brazil

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Department of Geography, Pontifical Catholic University of Minas Gerais, Belo Horizonte, MG 30535-012, Brazil

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School of Information Science, Federal University of Minas Gerais, Belo Horizonte, MG 31270-901, Brazil

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Department of Computer Science, Pontifical Catholic University of Minas Gerais, Belo Horizonte, MG 30535-901, Brazil

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Department of Anatomy and Imaging, Federal University of Minas Gerais, Belo Horizonte, MG 30130-100, Brazil

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Department of Electrical Engineering, Pontifical Catholic University of Minas Gerais, Belo Horizonte, MG 30535-012, Brazil

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Department of Electrical Engineering, Federal University of Minas Gerais, Belo Horizonte, MG 31270-901, Brazil

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Author to whom correspondence should be addressed.

Received: 8 September 2020 / Revised: 12 October 2020 / Accepted: 13 October 2020 / Published: 17 October 2020

(This article belongs to the Section Human Geography and Social Sustainability)

Composite indicators are almost always determined by methods that aggregate a reasonable number of manifest variables that can be weighted—or not—as new synthesis variables. A problem arises when these aggregations and weightings do not capture the possible effects that the various underlying dimensions of the phenomenon have on each other, and consequently distort the assessment of intra-urban inequality. In this paper, we explore the direct and indirect effects that the different underlying dimensions of intra-urban inequality have on indicators that represent this phenomenon. Structural equation modeling was used to build a composite indicator that captures the direct and indirect effects of the underlying dimensions of intra-urban inequality. From this modeling that combines confirmatory factor analysis with a system of simultaneous equations, the intra-urban inequality of the urban conurbation of Maringá–Sarandi–Paiçandu, Brazil was measured. The model comprises first- and second-order structures. The first-order structure is composed of non-observed variables that represent three underlying dimensions of intra-urban inequality. The second-order structure is the intra-urban inequality composite indicator that synthesizes the non-observed variables of the first-order structure. The model aims at demonstrating how to perform a theorized measurement of urban inequality so that it makes it possible to identify which dimensions most influence the others, as well as which dimensions are more relevant to this purpose.