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.
Multivariate Spatial Autocorrelation; Spatial Weight Matrix; Three-stage Least Squares; Two-stage; Least; Squares; simplex; electorel data; CoDa;
T.H.A Nguyen, Christine Thomas-Agnan, Thibault Laurent et Anne Ruiz-Gazen, « A simultaneous spatial autoregressive model for compositional data », TSE Working Paper, n° 19-1028, juillet 2019, révision avril 2020.
Thi-Huong-An Nguyen, Christine Thomas-Agnan, Thibault Laurent et Anne Ruiz-Gazen, « A simultaneous spatial autoregressive model for compositional data », Spatial Economic Analysis, vol. 16, n° 2, 2021, p. 161–175.