Working paper

A simultaneous spatial autoregressive model for compositional data

T.H.A Nguyen, Christine Thomas-Agnan, Thibault Laurent, and Anne Ruiz-Gazen

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 existence of the constraint on the sum of the components and the assumption of statistical independence across territorial units 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.

Keywords

multivariate spatial autocorrelation; spatial weight matrix; three-stage least squares; two-stage least squares; simplex; electoral data; CoDa.;

Replaced by

Thi-Huong-An Nguyen, Christine Thomas-Agnan, Thibault Laurent, and Anne Ruiz-Gazen, A simultaneous spatial autoregressive model for compositional data, Spatial Economic Analysis, vol. 16, n. 2, 2021, pp. 161–175.

Reference

T.H.A Nguyen, Christine Thomas-Agnan, Thibault Laurent, and Anne Ruiz-Gazen, A simultaneous spatial autoregressive model for compositional data, TSE Working Paper, n. 19-1028, July 2019, revised April 2020.

See also

Published in

TSE Working Paper, n. 19-1028, July 2019, revised April 2020