Hierarchical and Geographically Weighted Regression

: Estimation, Inference, and Applications

Abstract

Spatial hierarchical data, characterised by the coexistence of spatial effects and hierarchical structures, pose significant challenges for conventional modelling techniques such as Hierarchical Linear Models (HLM) and Geographically Weighted Regression (GWR). These methods often struggle to simultaneously address spatial heterogeneity in different levels, intra-group homogeneity, and inter-group heterogeneity, despite being designed to handle some of the features. To address these limitations, this thesis proposes a novel methodology: Hierarchical Geographically Weighted Regression (HGWR). The HGWR model offers a unified framework to estimate group- or sample-level fixed effects, sample-level random (SLR) effects, and group-level spatially weighted (GLSW) effects. The GLSW effects capture the spatial heterogeneity in group-level variables, fixed effects account for the intra-group homogeneity, and SLR effects model the inter-group heterogeneity, which works like spatial heterogeneity. Simulation experiments demonstrate that HGWR accurately estimates GLSW, fixed, and SLR effects, outperforming models like GWR, Multiscale GWR (MGWR), and HLM in both precision and computational efficiency. Real-world applications to data sets on housing prices in Beijing and Wuhan, China validate its practical utility, showcasing improvements in goodness of fit, model interpretability, and computational performance. Hypothesis testing for spatial heterogeneity in GLSW effects, developed using bootstrap resampling and traditional 𝐹-statistics, further enhance the model’s analytical capabilities. Significance of effects are tested via 𝑡-test methods to check the importance of a specific variable.

Additionally, the HGWR model is applied to a study exploring the inequality in quality-oriented education (QOE) in China. This case study analyses the macroeconomic factors and family-level characteristics to discover spatial heterogeneity in their impact on extracurricular course participation at both levels. The results reveal this heterogeneity is significant for the effects of provincial economic development, education funding, and income inequality. At the micro level, parental education and household assets emerge as key contributors to QOE disparities, with urban-rural differences highlighting persistent geographical inequities. Policy recommendations are proposed accordingly, focusing on reducing income inequality, and improving rural education resources to mitigate these disparities.

The thesis concludes with a discussion on the present limitations of the HGWR model, how it may be developed going forward, and how it is a powerful tool for the increasingly common availability of spatial hierarchical data.

Date of Award	22 Aug 2025
Original language	English
Awarding Institution	University of Bristol
Supervisor	Richard M Timmerman (Supervisor) & Richard J Harris (Supervisor)