Essays on unit models for analysing vote proportions

Abstract

Defined as the district vote shares by the total number of valid votes cast in the district, the vote proportion is auseful measure for analyzing election data. Since it is a variable bounded in the standard unit interval, we consider unit distributions for analyzing the probabilistic behavior of vote proportions in Brazilian presidential elections runoff in 2018. The objective of this master thesis is twofold. Firstly, we introduce the two-component unit Weibull mixture model for describing the characteristics of these data, such as the asymmetric behavior, bimodality, and unit interval support. We provide some useful statistical properties of the new model, such as quantile function, moments, and incomplete moments. The Expectation-Maximization (EM) algorithm is derived for maximum-likelihood estimation, and a Monte Carlo study is carried out to evaluate the performance of these estimators on finite samples. The proposed model’s superiority is verified when comparing the fit with some usual unit mixing models related in the literature: the two-component beta mixture and the two-component Kumaraswamy mixture models. The second objective is to identify the covariates associated with the elected candidate’s vote proportion in the Brazilian municipalities with a population greater than 300.000 inhabitants. Thus, a study on unit regression models is performed using the Generalized Additive Models for Location, Scale, and Shape (GAMLSS) framework. We fitted the beta and simplex regressions considering mean and dispersion sub-models. The Akaike information criterion (AIC), Schwarz’s Bayesian criteria (SBC), and pseudo-R2 statistics are considered as goodness-of-fit measures, and residual analysis is performed for diagnostics. The simplex regression is superior to the beta and is suitable for modeling the variable of interest. The covariates with significant effects are monthly household income per capita, the proportion of evangelicals and the political spectrum of the governors’ party elected in 2014 and 2018. We also verify that some Brazilian regions impact the vote proportions’ mean and dispersion.