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.

2018年3月4日，在意大利举行了议会两院的选举。许多报纸都强调了五星级运动（5SM）的胜利及其在意大利南部大部分地区前所未有的统治地位。该贡献的目的是通过临时统计模型分析选举结果，以评估空间结构的存在和可能的影响。响应变量是5SM在每个选举区中获得的选票百分比。要使用开放区间（0，1）中的值处理有限的连续结果，将使用混合回归模型。该模型基于共享相同精度参数的两个beta（称为灵活beta）的特殊混合，但显示两个受不等式约束的截然不同的分量。该模型的优点是其许多理论特性，这些特性反映在其计算可处理性上。此外，特殊的混合结构旨在代表各种现象（双峰，粗尾和离群值）。该模型通过随机效应进一步扩展以说明空间相关性。进行了密集的仿真研究，以评估提出的回归模型的拟合度。推论性问题由（贝叶斯）哈密顿式蒙特卡洛算法处理。进行了密集的仿真研究，以评估提出的回归模型的拟合度。推论性问题由（贝叶斯）哈密顿式蒙特卡洛算法处理。进行了密集的仿真研究，以评估提出的回归模型的拟合度。推论性问题由（贝叶斯）哈密顿式蒙特卡洛算法处理。