Beta Regressions and Geographically Weighted Beta Regressions for Analyzing Municipal Voting in Russia

Networks and Spatial Economics. 2026.

Olga Demidova, Diana Turchak

This study investigates the determinants of vote shares for different political parties using municipal election data from Russia for 2021–2022. For many countries, it has been shown that geographically weighted regressions (GWR) and multiscale geographically weighted regressions (MGWR) yield superior results compared to linear models. The significance of the global Moran’s I, Geary’s C, and Getis-Ord G indices suggest that similar results would be obtained for Russia.

Since the dependent variables (vote shares) are fractional, this study employs beta regression and geographically weighted beta regressions (GWBR), estimating the models using data for 2,272 Russian municipalities. The bandwidths chosen through the Golden Section Search method were relatively large, consequently, the GWBR estimates were very similar to those of the global beta models. A comparison of goodness-of-fit metrics (AICc, Pseudo R2 , Pseudo R2  adjusted) also failed to reveal any substantial advantages of the GWBR models, although some differences in the magnitude and significance of local versus global coefficient estimates were observed. The three primary hypotheses tested received only partial empirical confirmation (the presence of spatial autocorrelation in municipal-level voting outcomes, the impact of economic and social factors on electoral results, and the spatial heterogeneity of these effects). It was shown that the higher the municipal budget and the better the quality of life in municipalities (reflected by the higher proportion of illuminated streets, the share of local public roads meeting regulatory requirements, and the share of the population that received housing and improved living conditions), the higher the share of voters supporting the ruling party. Conversely, the better the development of SMEs in a region, the higher the share of voters supporting candidates from opposition parties. However, it was demonstrated that the spatial dependence is not particularly strong.

Keywords: Россия, Russia, муниципальные выборы, municipal elections, предпочтения избирателей, Voting preferences, geographically weighted beta regression, бета регрессия, географически взвешенная бета регрессия, beta regression

Publication based on the results of: Усовершенствование пространственно-эконометрических моделей с учетом иерархической структуры данных и неоднородной динамики процессов (2026)