A spatial mixed-effects regression model for electoral data

On 4th March 2018, elections took place in Italy for the two Chambers of the Parliament. Many newspapers emphasized the victory of the 5 Star Movement (5SM) and its unprecedented dominance in most of the southern regions of Italy. Aim of this contribution is to analyze the electoral results through an ad hoc statistical model to evaluate the presence and possible impact of spatial structures. The response variable is the percentage of votes got by the 5SM in each electoral district. To handle a bounded continuous outcome with values in the open interval (0, 1), a mixture regression model is used. This model is based on a special mixture of two betas (referred to as flexible beta) sharing the same precision parameter, but displaying two distinct component means subject to an inequality constraint. Advantages of this model are its many theoretical properties which are reflected in its computational tractability. Furthermore, the special mixture structure is designed to represent a wide range of phenomena (bimodality, heavy tails, and outliers). The model is further extended through random effects to account for spatial correlation. Intensive simulation studies are performed to evaluate the fit of the proposed regression model. Inferential issues are dealt with by a (Bayesian) Hamiltonian Monte Carlo algorithm.