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District-Level Food Environment Indicators and Social Vulnerability in São Paulo
Pedro Lemes Sixel Lobo, Eric Tokuda, Kuruvilla Joseph Abraham, Roberto Fray, Dirce Maria Marchioni, Alexandre Cláudio Botazzo Delbem, Rogerio Salvini
TL;DR
Evidence on how urban food environments relate to social vulnerability is limited at the district level in Brazilian cities. This exploratory ecological study integrated São Paulo administrative data and machine-learning classifiers, finding that food-environment indicators contained information associated with district-level IPVS distribution, while design and sample limitations constrain interpretation.
Problem
District-level evidence on whether urban food-environment indicators discriminate social-vulnerability levels remains limited in Brazilian cities.
Method
The study integrated IPVS, RAIS, and CAISAN data aggregated at district level and evaluated eight classifiers using leave-one-out cross-validation.
Results
Mean F-scores ranged from 0.62 to 0.75, with XGBoost highest; healthy- and unhealthy-establishment densities jointly contributed approximately 60% of Random Forest impurity-based feature importance.
Takeaways & Limitations
Publicly available food-environment indicators may help characterize territorial differences represented by the IPVS.
Takeaways & Limitations
The ecological design, 76-district imbalanced sample, IPVS binarization, and exclusion of 20 unclassified districts limit stability and household-level or causal interpretation.
Abstract
from arXiv · showhide
Urban food environments may reflect broader socioeconomic inequalities, but district-level evidence remains limited in Brazilian cities. This study examined whether indicators of food retail and street-market availability discriminate between levels of social vulnerability across the 96 districts of São Paulo. We conducted an exploratory cross-sectional ecological analysis integrating the São Paulo Social Vulnerability Index (IPVS), establishment records from the Relação Anual de Informações Sociais (RAIS), and street-market data from CAISAN. Census-sector information was aggregated at the district level. Twenty districts without an IPVS classification were excluded, resulting in 76 observations. The outcome distinguished districts classified as IPVS level 1 from those classified as levels 2--7. Predictors described the densities of healthy and unhealthy food establishments, the number of street markets, and the availability of establishments selling fresh or in natura food. Eight conventional machine-learning classifiers were evaluated using leave-one-out cross-validation. Reported mean F-scores ranged from 0.62 to 0.75, with XGBoost obtaining the highest value. In the Random Forest model, the densities of healthy and unhealthy food establishments jointly accounted for approximately 60% of the total impurity-based feature importance. These findings indicate that publicly available food-environment indicators contain information associated with the district-level distribution of social vulnerability. However, the small ecological sample, class imbalance, outcome binarization, and cross-sectional design limit predictive generalization and preclude causal or household-level interpretations.
I. INTRODUCTION
The study frames district-level food environments as contextual indicators potentially associated with social vulnerability in São Paulo. It integrates administrative food-retail, street-market, and vulnerability data to test whether these indicators discriminate between IPVS groups.
- Motivation: Socioeconomic and spatial inequalities can shape local food environments and opportunities to obtain fresh, minimally processed foods.District-level analysis is relevant because citywide indicators may conceal inequalities among districts.
- Interpretive scope: District-level food availability is contextual and does not directly measure household consumption, food insecurity, or individual food access.The study therefore treats ecological associations as distinct from household-level or causal effects.
- Research gap: Brazilian household studies do not fully characterize the urban contexts surrounding households, motivating complementary district-level analysis of territorial food resources.Street markets and food-retail establishments are presented as indicators that may inform hypotheses about urban inequalities.
- Study design: The analysis integrates IPVS, RAIS, and CAISAN data at the district level to describe food-establishment densities, street markets, and fresh or in natura food availability.These sources align social vulnerability with administrative food-environment indicators.
- Objective: The objective is to assess whether publicly available food-environment variables contain information that discriminates between district-level IPVS groups.Machine-learning classifiers are used exploratorily, not as evidence that food availability determines vulnerability.
II. METHODS
This exploratory ecological study combines São Paulo vulnerability, food-retail, and street-market records at the district level. The resulting indicators characterize food establishments and markets without directly measuring household consumption, affordability, or food insecurity.
- Study design: The study analyzes São Paulo’s 96 administrative districts using a cross-sectional ecological design and district-level integration of heterogeneous data sources.Census-sector information was aggregated before integration because the sources used different geographical resolutions.
- Data sources: The IPVS, RAIS, and CAISAN sources provide social-vulnerability, food-retail, and street-market information for the analysis.RAIS establishment records support indicators related to healthy, unhealthy, fresh, and in natura food availability.
- Measurement scope: Food-environment variables measure district-level establishment and market availability rather than household food consumption, affordability, or food insecurity.They are therefore contextual measures of the urban food environment.
C. Geographical aggregation and data integration
Census-sector information was reduced to district-level representations so it could be integrated with the other administrative datasets. Mean aggregation was selected after distance-matrix comparisons indicated substantial agreement among representations.
- Geographical aggregation: 18,363 census sectors across São Paulo’s 96 districts required reduction to one district-level value before dataset integration.The number of census sectors per district ranged from 28 to 609.
- Aggregation assessment: Mean and median aggregation were compared against unaggregated features using normalized compression distance and Mantel tests with Pearson correlation.Comparisons were repeated using minimum, gzip, and bzip2 compression schemes.
- Aggregation assessment: Table I reports Mantel-test results comparing distance matrices before and after district-level aggregation.The table supports evaluation of whether aggregation preserved relationships in the original data.
- Data integration: Mean aggregation was selected because the resulting distance representations showed substantial agreement, producing 96 district-level observations.District names and geographical identifiers were harmonized before merging the databases.
D. Outcome definition
The study uses IPVS as the outcome and converts its original categories into two analytical groups because the remaining categories were highly imbalanced. Food-environment predictors combine establishment densities and district-level counts, with continuous variables standardized during model fitting.
- Outcome definition: The IPVS ranges from 0 to 7, with higher classified values generally indicating greater social vulnerability.The index distribution across São Paulo districts is presented in Table II.
- Analytical sample: 20 districts with IPVS level 0 were excluded, leaving 76 districts for analysis.No vulnerability category was available for the excluded districts.
- Outcome definition: IPVS level 1 formed the reference class with n=56, while levels 2–7 formed the positive class with n=20.The groups are not labeled non-vulnerable and vulnerable because IPVS level 2 is formally very low vulnerability.
- Food-environment predictors: Five predictors comprise healthy- and unhealthy-establishment densities, street-market counts, natural-food-establishment counts, and in natura food-establishment counts.Density indicators were retained as provided, while the remaining indicators were district-level counts.
- Preprocessing: Continuous predictors were standardized using training-data means and standard deviations within the model-fitting procedure.This prevents held-out observations from influencing preprocessing.
F. Classification models and evaluation
The study compared eight conventional classifiers for distinguishing district-level IPVS groups using food-environment indicators, with performance assessed through leave-one-out cross-validation and supplementary feature analysis.
- Eight algorithms spanning linear, probabilistic, distance-based, kernel-based, and tree-ensemble approaches were evaluated.
- Leave-one-out cross-validation tested each district once while fitting models on the other 75 districts.Hyperparameters were selected by grid search, and data-dependent preprocessing was fitted within each training partition.
- The primary performance measure was F-score because the positive IPVS 2–7 group was substantially smaller than the IPVS 1 group.Districts in the IPVS 2–7 group were treated as positive cases.
- Random Forest feature importance and permutation analysis were used after classifier comparison to examine predictor contributions.The permutation procedure focused on whether the number of natural-food establishments remained contributory after predictor disruption.
A. Analytical sample and classification performance
The analysis used 76 districts divided into IPVS level 1 versus levels 2–7, and classifier performance varied from 0.62 to 0.75 in mean F-score, with XGBoost highest.
- 76 districts remained after excluding 20 of the 96 source districts without an IPVS category.The final groups contained 56 IPVS level 1 districts and 20 IPVS levels 2–7 districts.
- The classification problem included 56 IPVS level 1 districts and 20 IPVS levels 2–7 districts, creating class imbalance.
- 0.62–0.75 was the range of mean F-scores under leave-one-out cross-validation, with XGBoost achieving 0.75.LDA, Naïve Bayes, and Random Forest obtained 0.72, 0.71, and 0.70, respectively.
- Several classifiers had modestly different mean values, while large standard deviations indicated substantial variation across held-out observations.The model ranking was therefore interpreted as exploratory rather than as evidence of clear algorithmic superiority.
B. Relative importance of food-environment indicators
Random Forest impurity-based importance placed healthy- and unhealthy-establishment densities first, while permutation analysis supported the relevance of natural-food establishments within the fitted classifier.
- Random Forest was selected for predictor interpretation because its tree structure provides a direct measure of variable importance.This analysis was separate from predictive-performance comparison, where XGBoost had the highest mean F-score.
- Approximately 60% of total impurity-based feature importance came jointly from healthy- and unhealthy-food-establishment densities.The remaining importance was distributed among natural-food establishments, in natura establishments, and street markets.
- Impurity-based importance measures split contribution frequency and effectiveness, not the proportion of vulnerability explained or the direction or causality of associations.
- Natural-food establishments received non-zero permutation importance, and their contribution persisted after additional predictors were included.The authors identified this variable as potentially relevant based on prior domain knowledge.
C. Selected model configurations
The study’s selected classifier configurations were documented in Table V and used to produce the performance estimates reported in Table IV.
- These configurations generated the performance estimates presented in Table IV.
- Table V reports the hyperparameters used to generate the classification models.
IV. DISCUSSION
The study finds that district-level food-environment indicators contain information associated with São Paulo’s spatial distribution of social vulnerability, while emphasizing substantial limits on interpretation and generalization.
- Findings: The densities of healthy and unhealthy food establishments jointly accounted for approximately 60% of Random Forest impurity-based feature importance.These importance values indicate contribution to tree splits, not the proportion of social vulnerability explained or a causal effect.
- Interpretation: The predictors may capture interconnected aspects of urban inequality rather than an isolated effect of food-retail availability.Commercial location, purchasing power, transportation infrastructure, land use, and public services may jointly shape food environments and social vulnerability.
- Interpretation: District-level food-environment indicators are contextual measures and do not directly represent household food access, consumption, or food insecurity.They do not measure prices, travel time, transportation barriers, product quality, household income constraints, or individual dietary experiences.
- Findings: Several classifiers showed similar discrimination, but XGBoost’s higher mean F-score does not establish clear algorithmic superiority.Differences among the best-performing models were modest, and large standard deviations indicated instability across held-out districts.
- Implications: Administrative and geospatial data enabled a reproducible district-level analysis without primary data collection, but should not replace household surveys, field assessments, or community consultation.Future work should address city heterogeneity and differences in administrative data coverage when extending the analysis.
- Limitations: The ecological analysis used only 76 districts, excluded 20 unclassified districts, and combined substantively different IPVS levels through outcome binarization.These choices limit model stability, precision, and the ability to assess possible selection bias from exclusions.
- Limitations: Administrative sources covered different collection periods and omitted some changes in business activity, informal establishments, geographic errors, and within-district heterogeneity.District aggregation can mask local variation, while periodic database updates make external temporal validation difficult.
- Implications: The findings support further investigation of food-environment indicators but not claims that changing them would directly reduce vulnerability.Policy assessments should combine administrative evidence with direct measures of affordability, mobility, household food insecurity, and local demand.
V. CONCLUSION
The study found that publicly available district food-environment indicators contained information associated with social vulnerability across São Paulo. These exploratory findings support contextual use of such indicators while limiting causal, household-level, and definitive predictive interpretations.
- Conclusion: Food-environment indicators contained information associated with the distribution of social vulnerability across São Paulo.The result concerns district-level spatial patterns rather than individual households.
- Conclusion: Healthy and unhealthy food-establishment densities contributed most strongly to Random Forest classification, while XGBoost had the highest reported mean F-score.The conclusion identifies these as model results, not causal effects or definitive evidence of algorithmic superiority.
- Scope: The findings do not show that food-establishment availability causes social vulnerability or directly measures household food insecurity.Small and imbalanced data, district aggregation, temporal differences, and IPVS binarization restrict generalizability.
- Implications: Integrating IPVS, RAIS, and CAISAN records demonstrates the value of Brazilian administrative data for examining urban food environments at a submunicipal scale.Future studies should add affordability, mobility, household food insecurity, population exposure, and spatial-dependence measures.