Procrustes analysis, multivariate regression, variable selection and outlier detection in compositional data for social vulnerability
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Abstract
Vulnerability means delicate and weak in the behavior of people, objects, situations and ideas. People considered “socially vulnerable” are those who lose their representation in society and generally depend on help from third parties to ensure survival. The main characteristics that mark this vulnerability are precarious housing conditions, sanitation, non-existent means of subsistence and the absence of a family environment. Among the different types, they highlight youth in the area of health, marginalization, exclusion and territorial. Social Vulnerability Index (SVI) is composed of indicators of income and social impairment in dimensions such as identification, housing, education, income, poverty, family, work and other assets. Variable selection is finding a subset of variables that best explains a response vector, without losing relevant information. Procrustes Analysis is a method that aims to determine how much a subset of variables best represents the structure of the original data. Compositional data are quantitative descriptions of the parts of a whole, which convey information in a relative way. Principal components are linear combinations of all original variables, independent of each other and estimated with the purpose of retaining, in order of estimation, the maximum amount of information to explain the total variance. Univariate outliers are observations that differ greatly from the others. Multivariate outlier corresponds to cases involving two or more variables. In this work we use the Procrustes method and other regression methods to select variables formed from compositional data after detecting multivariate outliers using Mahalanobis Distance and comedian approach.
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