Spatial autocorrelation of political opinions: a kernel approach

Abstract The kernel approach to spatial analysis, well adapted to weighted, multivariate configurations involving n regions, is based on the comparison of two symmetric $$n\times n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>×</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:math> matrices, a feature kernel and a spatial kernel. The formalism handles in a natural way regional variables of numerical or categorical nature, spatial weights, and other matrix-like quantities such as geographical distances and adjacencies. It also permits to revisit and broaden classical themes, in particular factorial visualization, discriminant analysis and regional aggregation. In particular, spatial autocorrelation can be measured and tested in a nonparametric way by invariant orthogonal integration. The versatility of this kernel formalism is illustrated by considering four feature kernels and ten spatial kernels reflecting the spatial configuration of the 369 Swiss federal votes from 1971 to 2023 on the $$n=2132$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2132</mml:mn> </mml:mrow> </mml:math> municipalities. Among other findings, the pervasive association of political opinion with population size and regional language is highlighted at the municipal, district and cantonal level. Also, linguistic contributions can be converted into spatial contributions, permitting to measure the width of the so-called Röstigraben.