Incorporating varying degrees of spatial cohesion in models of voter behaviour in the UK General Election 2024

Abstract Fitting models to data where multiple spatial processes are assumed to be operating simultaneously at different levels is often done by combining a hierarchical effects structure at the higher levels (region, county) with autoregressive structures at the lowest (individual data points). When dealing with areal data, an intrinsic conditional autoregressive (ICAR) component is often used to capture these lowest level spillover effects. One of the standard assumptions of ICAR models is a global spatial variance parameter, meaning all areas undergo the same degree of smoothing. We propose allowing this variance parameter to change, reflecting different degrees of spatial cohesion in different regions. We demonstrate an application using voter behaviour in the 2024 UK General Election. This technique has not enjoyed widespread exposure, particularly as regards election data. By fitting a series of models representing different hypothesized spatial processes for the vote count of each of the four largest parties and comparing the resultant marginal likelihoods, we find that this novel approach is the most plausible model, and reveals different patterns of spatial cohesion among the parties.