Mémoire de Maîtrise
DOI
https://doi.org/10.11606/D.104.2024.tde-05032024-103928
Document
Auteur
Nom complet
Victor Eduardo Lachos Olivares
Unité de l'USP
Domain de Connaissance
Date de Soutenance
Editeur
São Carlos, 2024
Directeur
Jury
Guzmán, Jorge Luis Bazán (Président)
Prates, Marcos Oliveira
Serrano, Luis Hilmar Valdivieso
Titre en portugais
Uma Abordagem Estatística para a Análise dos Resultados das Eleições Presidenciais
Mots-clés en portugais
Análise de componentes principais
Modelo de regressão Beta
Transformação de razão logarítmica
Resumé en portugais
Titre en anglais
An statistical approach for analysis of presidential elections results
Mots-clés en anglais
Beta regression model
Compositional data
Log-ratio transformation
Principal component analysis
Resumé en anglais
Multiparty data has characteristics that make it compositional data such as a constant sum of components and a limited space known as simplex. Thus, the purpose of the work is to develop a methodology to analyze multi-party data from electoral elections considering their restricted nature. In this context, the proposed methodology consists of 8 steps: initially, we collect multi-party data and transform it into compositional data. Then, we apply the log-ratio transformation , removing the inherent constraints of compositional data. Next, we employ principal component analysis (PCA) to reduce dimensionality and identify the principal components that retain most of the variation in the data. These components are analyzed based on two important metrics: loadings and scores. Given that the scores have different variability in the components, they are transformed between values of zero and one. Subsequently, we propose the Beta regression model considering the scores as the response variable, and the human development indicators as the explanatory variables. The methodology is applied to multiparty data from the first round elections in Peru in 2021 and Brazil in 2022, allowing us to identify the main components and which covariates (health, education and income) are directly related to votes in different regions and states. Finally, considering that data from presidential elections of Peru 2021 with two response variables, we propose a bivariate regression model via copulas and analyze the dependence structure between these variables.

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Date de Publication
2024-03-05

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