@techreport{publications32640,
          volume = {19-1028},
           month = {July},
          author = {T.H.A Nguyen and Christine Thomas-Agnan and Thibault Laurent and Anne Ruiz-Gazen},
          series = {TSE Working Paper},
       booktitle = {TSE Working Paper},
            type = {Working Paper},
         address = {Toulouse},
           title = {A simultaneous spatial autoregressive model for compositional data},
       publisher = {TSE Working Paper},
            year = {2019},
     institution = {Universit{\'e} Toulouse 1 Capitole},
        keywords = {multivariate spatial autocorrelation, spatial weight matrix, three-stage least squares, two-stage least squares, simplex, electoral data, CoDa.},
             url = {https://publications.ut-capitole.fr/id/eprint/32640/},
        abstract = {In an election, the vote shares by party on a given subdivision of a territory form a vector with positive components adding up to 1 called a composition. Using a conventional multiple linear regression model to explain this vector by some factors is not adapted for at least two reasons. The first one is the existence of the constraint on the sum of the components and the second one is the assumption of statistical independence across territorial units which may be questionable due to potential spatial autocorrelation. We develop a simultaneous spatial autoregressive model for compositional data which
allows for both spatial correlation and correlations across equations. We propose an estimation method based on two-stage and three-stage least squares. We illustrate the method with simulations and with a data set from the 2015 French departmental election.}
}