ABSTRACT

In an election, the vote shares by party for a given subdivision of a territory form a compositional vector (positive components adding up to 1). Conventional multiple linear regression models are not adapted to explain this composition due to the constraint on the sum of the components and the potential spatial autocorrelation across territorial units. We develop a simultaneous spatial autoregressive model for compositional data that allows for both spatial correlation and correlations across equations. Using simulations and a data set from the 2015 French departmental election, we illustrate its estimation by two-stage and three-stage least squares methods.

摘要

在选举中，给定细分区域的当事方所占的选票构成组成矢量（正分量总计为1）。常规的多元线性回归模型由于成分之和的约束以及整个区域单位之间潜在的空间自相关性而无法适应这种解释。我们为成分数据开发了一种同时空间自回归模型，该模型可以实现空间相关性和方程之间的相关性。使用模拟和来自2015年法国部门选举的数据集，我们说明了通过两阶段和三阶段最小二乘法进行的估算。