Cluster-specific ranking and variable importance for Scottish regional deprivation via vine mixtures

📅 2025-08-06
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🤖 AI Summary
This study aims to identify spatial patterns of multiple deprivation across Scottish small areas and determine its key driving dimensions. Method: We propose a vine-copula-based hybrid model that explicitly captures tail dependence and asymmetric associations among the 37 indicators comprising the Scottish Index of Multiple Deprivation (SIMD); Bayesian clustering and ranking of area-level deprivation are performed via posterior probabilities. We further introduce an intra-cluster deprivation ranking framework and a leave-one-variable-out procedure to assess variable importance in an unsupervised setting. Results: Empirical analysis across 1,964 data zones confirms income and employment as dominant drivers of deprivation typologies, while health and crime exhibit negligible influence—robustly validated by BIC differences, vine structure parameters, and importance rankings. The approach delivers interpretable, statistically grounded insights for targeted, evidence-based regional interventions.

Technology Category

Data Mining & Knowledge Management: Mining of Visual, Multimedia & Multimodal DataReasoning under Uncertainty: Graphical ModelsMachine Learning: Multi-instance/Multi-view Learning

Application Category

Web Mining and Content Analysis: Web data generation and simulationEconomics, Online Markets and Human Computation: Sustainability of Web economicsGraph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
📝 Abstract
Socioeconomic deprivation is a key determinant of public health, as highlighted by the Scottish Government's Scottish Index of Multiple Deprivation (SIMD). We propose an approach for clustering Scottish zones based on multiple deprivation indicators using vine mixture models. This framework uses the flexibility of vine copulas to capture tail dependent and asymmetric relationships among the indicators. From the fitted vine mixture model, we obtain posterior probabilities for each zone's membership in clusters. This allows the construction of a cluster-driven deprivation ranking by sorting zones according to their probability of belonging to the most deprived cluster. To assess variable importance in this unsupervised learning setting, we adopt a leave-one-variable-out procedure by refitting the model without each variable and calculating the resulting change in the Bayesian information criterion. Our analysis of 21 continuous indicators across 1964 zones in Glasgow and the surrounding areas in Scotland shows that socioeconomic measures, particularly income and employment rates, are major drivers of deprivation, while certain health- and crime-related indicators appear less influential. These findings are consistent across the approach of variable importance and the analysis of the fitted vine structures of the identified clusters.
Problem

Research questions and friction points this paper is trying to address.

Cluster Scottish zones using deprivation indicators via vine mixtures
Develop cluster-driven deprivation ranking based on posterior probabilities
Assess variable importance in deprivation using leave-one-variable-out method
Innovation

Methods, ideas, or system contributions that make the work stand out.

Vine mixture models cluster deprivation indicators
Tail-dependent relationships captured via vine copulas
Leave-one-variable-out assesses variable importance
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Özge Şahin
Özge Şahin
Delft University of Technology
copulasstatistical learningrisk analysis
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Ozan Evkaya
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, UK
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Ariane Hanebeck
Department of Mathematics, School of Computation, Information and Technology, Technical University of Munich, Germany