A comprehensive review of spatially varying coefficient models: methods, challenges, and guidance for model selection

Spatially varying coefficient (SVC) models have emerged as an important class of methods in spatial analysis because they enable the explicit modelling of spatial heterogeneity in the relationships between a response variable and a set of predictors. A wide range of SVC modelling frameworks has been developed, each with distinct assumptions, strengths, and limitations. However, a comprehensive synthesis that systematically reviews and contrasts these model families remains limited. In this study, we review major categories of SVC models, frequentist local regression approaches, Bayesian SVC frameworks, eigenvector spatial filtering (ESF), and the integration of deep learning techniques in frequentist frameworks. Additionally, the study discusses key challenges in spatial analysis, presents a comparative synthesis of SVC models, and provides practical guidance for their adoption. Based on a structured literature search using predefined keywords across three major online databases, a total of 98 articles were ultimately identified as suitable for inclusion in the review. Synthesis of these studies indicates that no single SVC model consistently outperforms others across all empirical contexts, and that model choice should be guided by the research question, data characteristics, and analytical objectives rather than by the pursuit of a universally optimal approach. Furthermore, we identify five important avenues for future research: improving the computational scalability and memory efficiency of these models; advancing methodological development in Bayesian and ESF frameworks relative to frequentist approaches; rethinking the conceptualization of proximity and the optimization of spatial scale; addressing the sensitivity of frequentist local models to sample size by establishing clearer guidance on adequate sample sizes for stable and reliable inference; and providing clearer recommendations on when each category of SVC model is most appropriate for application. Addressing these challenges would significantly advance the theoretical foundations, methodological rigour, and practical accessibility of SVC models in spatial analysis.