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.